Mesosphere-stratosphere-troposphere radar observations of characteristics of lower atmospheric high-frequency gravity waves passing through the tropical easterly jet



[1] In this study, we have examined the characteristics of high-frequency gravity waves (5–50 min periodicity) over a tropical region using the mesosphere-stratosphere-troposphere (MST) radar installed at Gadanki (13.5°N, 79.2°E), India. The MST radar (53 MHz) was operated continuously for ∼15.5 h during 1700–0840 LT on 2–3 June 2005. During this period, a strong unstable wind shear region existed above the tropical easterly jet at the height of tropopause. This has provided an excellent opportunity to study the characteristics of internal atmospheric high-frequency (∼15–40 min periodicity) gravity waves, generated in the boundary layer and passing through the shear layer. The study reveals the generation of higher-frequency (5–15 min periodicity) gravity waves from this strong shear region and their vertical propagation both below up to a few kilometers and above the shear layer (∼0.5 km thick). These waves showed upward propagation even above 20 km in the lower stratosphere, indicating that unstable shear layers are the important source of momentum and energy fluxes that contribute significantly to the middle atmospheric dynamics in terms of gravity waves. Further, a close association was also observed between the dissipating gravity waves and the distinctly enhanced signal-to-noise ratio and Doppler spectral width of the MST radar echoes. The present observation of radiation of high-frequency gravity waves that propagate vertically upward from a strong wind shear region located immediately below a highly stratified layer is in accordance with the “direct mechanism” explained by nonlinear numerical simulation studies. For the first time, the present study illustrates the existence of layers of polarized refractive index structures in the heights of 10–15 km.

1. Introduction

[2] Several different characteristics of unstable layers of vertical shear in horizontal winds and the associated internal atmospheric gravity waves have been studied by many researchers [e.g., McIntyre and Weissman, 1978; Fritts, 1982, 1984, 1985; Chimonas and Grant, 1984; Buhler and McIntyre, 1999; Buhler et al., 1999; Sutherland et al., 1994; Holton et al., 1995; Jin et al., 1996; Singh et al., 1999; Hecht et al., 2001; Didebulidze et al., 2002; Fritts et al., 2003; Kelley et al., 2005; Sutherland, 2006]. In the lower atmosphere, these unstable shear layers can dissipate or overreflect an upward propagating gravity wave and generate new gravity waves. These waves can propagate even up to the lower thermosphere region carrying momentum and energy. Strong unstable shear layers located near the tropopause region have attracted particular attention as any kind of disturbances in these layers can cause vertical transport of air mass including water vapor from the upper troposphere to lower stratosphere (UTLS) through dynamical coupling mechanisms [Holton et al., 1995]. Numerical simulations on this UTLS region indicate that it is possible for internal waves, on the scale of Kelvin-Helmholtz (KH) billows, to be generated by KH instability occurring in layers of strong vertical shear of horizontal winds in a nonuniformly stratified fluid [Sutherland et al., 1994; Sutherland and Peltier, 1995; Sutherland, 1996, 2006]. The generated waves can transport momentum far from the source and cross even the critical layer of a nearby stably stratified shear layer [Smyth and Moum, 2002].

[3] Unstable mean or wave-induced vertical wind shear can lead to shear or Kelvin-Helmholtz (KH) instabilities [Chandrasekhar, 1961; Fritts and Yuan, 1989; Yuan and Fritts, 1989; Dunkerton, 1997]. The Richardson number should be less than 1 (Ri < 1), a necessary condition, for the maintenance of turbulence occurring in an unstable shear region dominated by KH instabilities [Richardson, 1920; Taylor, 1931]. Studying the detailed breaking process of two-dimensional finite amplitude Kelvin-Helmholtz waves, Klaassen and Peltier [1985a] found that there is an energy exchange between the wave and mean flow [Sutherland, 2006]. Moreover, Klaassen and Peltier [1985b] showed that two-dimensional Kelvin-Helmholtz waves are unstable with respect to three-dimensional perturbations leading to longitudinally symmetric secondary instabilities. Earlier, theoretical calculations by McIntyre and Weissman [1978] showed that shear instabilities can radiate waves far from the seat of instability. Further, using a linear theory, they showed that the trapping of instabilities can be described and distinguished from wave radiation for slowly growing instabilities. Using a numerical simulation model, Scinocca and Ford [2000] studied unstable KH layers and the large-scale gravity wave radiation induced by them in the mid latitude upper troposphere. The radiated gravity waves are associated with nonlinear interaction of eddies developing during the evolution of clear air turbulence (CAT) from an unstable patch of flow with Ri < 0.25. The vertical flux of horizontal momentum of propagating gravity waves forced by this mechanism was also estimated. Further, Scinocca and Ford [2000] argued that the nonlinear interaction of individual pairs of wave numbers, existing within a group of wave numbers (in a shear layer) as unstable disturbances with finite amplitudes, leads to the forcing of large scale gravity waves through introduction of larger-scale disturbances into the shear layer. Fritts et al. [2003] used high-resolution simulations of turbulence arising from KH shear instability and gravity wave breaking to point out that the turbulence generated by gravity wave breaking moves with the phase of the wave. However, the turbulence and the associated mixing caused by shear instability is confined by stratification to a narrow layer and persists for much longer than those of the turbulence generated by gravity-wave breaking.

[4] Using the equations of dispersion relation including Doppler shift and the conservation of wave action and mean momentum, Grimshaw [1975] investigated the interaction of a wave packet of internal gravity waves with mean wind in a region containing wind shear and also a critical level. Grimshaw [1975] demonstrated that there is an exchange of energy from the waves to the mean wind in the vicinity of the critical level. Further, Grimshaw [1975] found that if the initial amplitude is small, then the wave packet narrows and grows in magnitude with height, while propagating toward the critical level, until reaching maximum after which it gets dissipated. If the initial amplitude is larger, however, the wave packet remains broader, achieves maximum amplitude at lower heights further away from the critical level, and decays less rapidly after the maximum has been reached. Booker and Bretherton [1967] showed that when the internal gravity waves propagate through a region of wind shear, the vertical flux of wave horizontal momentum remains constant except at critical levels, where the waves are attenuated by a factor exp[−2π(Rc − 0.25)1/2], where Rc is the Richardson number at the critical level [Eliassen and Palm, 1961]. On the basis of linear theory and the condition that the ratio |equation image| > 1 (equation image = penetration depth to the vertical wavelength of the excited internal gravity waves [IGW]), Sutherland et al. [1994] showed that only the waves generated by incident disturbances with absolute value of Doppler shifted frequency less than the Brunt-Vaisala frequency, N, and the growth rate less than N/81/2 may successfully propagate from unstable shear region to far field region. Using a nonlinear, viscous, and time-dependent numerical model, Fritts [1978] showed that nonlinear interactions among the forcing gravity waves can cause changes in the heights of gravity wave critical levels (GW-CL), stability of the mean state and can have pronounced effects on the evolution of unstable velocity shears associated with GW-CL interaction. For example, destabilization of a mean flow below a critical level can lead to more extensive unstable shear than predicted by the linear model. When the KH instabilities grow larger in amplitude in an unstable shear layer, the zone of maximum momentum flux (associated with unstable waves) convergence occurs farther below the critical level, tending to cancel the upward momentum flux associated with upward propagating gravity waves. This causes a vertical spreading of the wave momentum absorbed by the mean flow, leading to downward motion of the critical levels of gravity waves.

[5] Gravity waves generated in an unstable shear layer can sometimes be trapped there itself and get dissipated owing to turbulence induced by nonlinear or resonant interactions among the trapped waves. This would lead to strong echoes of the incident electromagnetic waves transmitted by the radars [Fritts, 1985; Dunkerton, 1987; Dewan and Good, 1986; Smith et al., 1987; Crook, 1988; Jin et al., 1996; Liu et al., 1999; Kelley et al., 2005]. The mesosphere-stratosphere-troposphere (MST) radars have made particularly significant contributions to the study of fine structures of the unstable shear layers and the mechanisms that give rise to turbulence, giving strong echoes of the incident electromagnetic waves [Rottger, 1980; Sato and Woodman, 1982a, 1982b; Woodman and Rastogi, 1984; Gage, 1990; Chilson et al., 1997; Singh et al., 1999; Yamamoto et al., 2003; Kelley et al., 2005]. As a case study, using an MST radar at the Indian tropical station of Gadanki (13.5°N, 79.2°E), the present work brings out with illustrative examples the essential characteristics of internal atmospheric gravity waves that pass through a strong wind shear (vertical) region associated with tropical easterly jet near the tropopause level.

2. MST Radar and Experimental Setup

[6] The Indian mesosphere-stratosphere-troposphere (MST) radar located at Gadanki (13.5°N, 79.2°E) is a large-power, highly sensitive, and phased-array Doppler radar operating at a carrier frequency of 53 MHz with an average power aperture product of 7 × 108 Wm2. With 3° beam width, a gain of 36 dB and a side lobe level of −20 dB, the radar consists of 1024 pairs of crossed Yagi-Uda antenna elements (1024 pairs of crossed-half-wave dipoles) arranged in a 32 × 32 matrix over an area of 130 m × 130 m. The radar beam can be tilted up to 20° in steps of 1° from the zenith in the north-south and east-west planes. Rao et al. [1995] give full details of this radar system. For the present work, the radar was operated from 1700 LT of 2 June 2005 to 0837 LT of 3 June 2005, spanning ∼15.5 h of continuous operation. The radar was operated in a six-beam mode; for one scan cycle, the narrow-transmitting-radar beam was tilted 10° from the zenith in the east, west, north, and south directions, and two zero zeniths with antennae aligned along two orthogonal polarizations (east-west and north-south). The coded pulse length of the transmitting beam was 16 microseconds with a baud length of one microsecond, which corresponds to a height resolution of 150 m, and the length of the interpulse period was one millisecond. Successive 64 pulses were coherently added to get one data point and 256 successive such data points were utilized to perform Fast Fourier Transform (FFT) analysis separately for each of the six beams and all the range bins. As a result, one height profile of wind velocities (zonal, meridional and vertical) and the other atmospheric scattering parameters were obtained in total 112 s, corresponding to a time resolution of 112 s. This period of 112 s is less than 2 min so that a minimum period of oscillation of about 4 min can be derived, according to Nyquist theorem, from the Fourier transform analyses of time series of data. Since the period of the Brunt-Vaisala (BV) frequency is in the range of ∼5–13 min in the lower and middle atmospheres, it can be derived easily by using the time series of the vertical wind velocity. Determining the BV frequency is essential to calculate the Richardson number (Ri) as it is related to the Kelvin-Helmholtz instability (KHI) by the following equation.

[7] The condition for the onset of KHI is

equation image

where N is the BV frequency and dU/dz is the vertical shear in wind speed, which is given by

equation image

where u, v, and w are the zonal, meridional, and vertical wind velocities, respectively. In the present work, following Revathy et al. [1996], N is calculated for every 2 h by Fourier transformation of the time series of vertical wind velocity collected every 2 h with 112 s as a sampling interval. Then the height profiles of Ri are calculated for every 2 h by using equations (1) and (2). It is found that the condition (1) is satisfied in a thin layer, with a width of less than 0.5 km in height, located near the tropopause height of 16.5 km (above the Tropical Easterly Jet [TEJ]) during the whole observational period. More details of this KHI layer are provided in the following sections.

3. Observations and Results

[8] Figure 1 shows the time-height (3.6–20 km) contour plots of zonal, meridional and vertical wind velocities measured by the MST radar over Gadanki and their associated vertical shears. Figures 1a and 1b show the contour plots of zonal wind velocity (u, m/s) and its associated vertical shear (du/dz, (m/s)/150 m), respectively. Similarly, Figures 1c and 1d show the same for the meridional wind velocity, and Figures 1e and 1f show that for the vertical wind velocity. It may be observed in Figure 1a that the zonal wind shows maximum easterly wind speed of about 35 m/s from 1700 to 0100 LT and in the last 1 h in the heights of ∼15–16.5 km. The easterly wind speed of more than 30 m/s, occurred near the tropopause height over the Indian tropical region, is associated with the tropical easterly jet (TEJ), which is a semipermanent component of the Indian southwest monsoon, occurring every year during June–September [Koteswaram, 1958]. From the nearby radiosonde stations of Bangalore (12.96°N, 77.58°E) and Karaikal (10.91°N, 79.83°E), it is found that the tropopause height was located at ∼16.5 km, which is just above the TEJ region. Further, it is observed that the TEJ strength shows large variations within a day from about 35 m/s during 1700–0100 LT to less than ∼20 m/s in the next 5 h, and again it increases to a value of ∼30 m/s in the last hour of observation. The meridional component shows strong southerly winds in the height region of ∼15.5–16.5 km. The time evolution of this strong southerly meridional wind is found to be similar to the zonal easterly wind (TEJ) during the whole present observation period, indicating that the zonal and meridional winds are related to each other in the heights of 15–17 km [Koteswaram, 1958]. It is clear that there was no convective activity in the atmosphere during this period as the vertical wind velocity (Figure 1e) shows small values within ±0.3 m/s at all the heights.

Figure 1.

Height (3.6–20 km) versus time (112 s time interval) contour plots of (a) zonal wind velocity, (c) meridional wind velocity, and (e) vertical wind velocity and (b, d, f) their vertical shears, respectively, at each height (in 150 m height intervals corresponding to radar height resolution) measured by MST radar over Gadanki at 1700–0840 LT on 2–3 June 2005.

[9] It may be observed from Figure 1b that there exists a layer (∼0.5 km width in height) of strong vertical shear in the zonal wind speed just above the TEJ at ∼16.5 km. The shear is obtained by taking a difference (wind velocity at an higher height minus the wind velocity at a lower height) between the zonal wind velocities measured at two successive height levels and then dividing this difference by the height interval (radar resolution) of 150 m. The observed strong vertical shear of more than 0.02 s−1 is more than the Brunt-Vaisala (BV) frequency, which is on the order of 0.0011–0.0033 s−1 corresponding to the BV period of 15–5 min in the tropical lower and middle atmospheres. This indicates that this narrow height region is unstable to any disturbances passing through it. Similar unstable layers are found also in the heights of ∼18 and ∼19 km (Figure 1b). Similar to the zonal wind, the meridional wind also shows unstable shear regions in the heights of 16–19 km (Figure 1d). However, in the vertical winds (Figure 1f), the shear is very small at all the times and heights and hence there is no well-defined unstable layers as observed for the horizontal winds.

[10] Figure 1a shows that when the TEJ strength decreased to less than 20 m/s during 2200–0200 LT, it shows an oscillation with periodicity of ∼30 min. Similar oscillation is also found in the first 2 h when the strength of the TEJ was larger. The noted oscillations in the zonal wind velocity appeared also in the meridional (Figure 1c) and vertical (Figure 1e) wind velocities during the observation periods of 1700–1900 and 2200–0100 LT. Filtering analyses of the winds (observation of downward phase propagation not shown here) indicate that there is a wave with periodicity of ∼30 min, propagating from below the height of 3.6 km to above the tropopause height. However, there is some discontinuity in the wave-propagation characteristics in the strong shear region of 16–17 km. Above the tropopause height (∼16.5 km), the amplitude decreases with height, indicating that a significant amount of energy of the upward propagating, internal-atmospheric gravity waves has been dissipated in the strong unstable shear region located at ∼16.5 km during these two periodic intervals of 1700–1900 and 2200–0200 LT.

[11] In addition to the well-formed persisting layers of strong shears in the zonal and meridional winds, an intermittently occurring, unstable shear layers with downward propagation are also observed in the heights of 10–15 km during 1700–2100 and 2200–0300 LT in both the zonal (Figure 1b) and meridional winds (Figure 1d). The height of the shear layer in the meridional wind was nearly constant at 14 km until 0600 LT, whereas in the zonal wind it showed downward propagation until 0300 LT of 3 June. It is expected that these strong unstable shear layers can cause attenuation to the vertically propagating gravity waves, leading to deposition of some of the momentum and energy of the waves. This would in turn lead to generation of turbulence in the atmospheric medium and hence a strong reflectivity and an enhancement in the Doppler width of the received radar echoes when the incident electromagnetic waves are scattered by this turbulent medium.

[12] To illustrate this point of view, Figure 2 shows signal-to-noise ratio (SNR) in decibel (dB) units of the echoes received by the MST radar. As expected, well-defined layers of enhanced SNR exist near the heights of 16.5, 18 and 19 km, corresponding to the strong unstable wind-shear layers as observed in the horizontal winds (Figures 1b and 1d), for both the polarizations of zenith beams Zx and Zy (Figures 2a and 2b). Further, there are intermittent downward propagating layers of enhanced SNR, corresponding to the unstable shear layers as observed for the horizontal winds (Figures 1b and 1d), in the heights of 10–14 km during the time intervals of 1700–2100 and 2200–0300 LT. Similarly, the beams tilted in the zonal (Figures 2c and 2d) and meridional (Figures 2e and 2f) directions also show similar features as observed for the vertical beams. As a support of this observation, Fritts et al. [2003] argued that the layers of atmospheric medium associated with gravity wave (GW) breaking are more transient in nature. This is due to continuous vertical progression of GW phase, GW breaking, and the associated turbulence occurring within ∼1 GW period. Further, they stressed that the occurrence of transient turbulent layers associated with GW breaking is in response to both (1) the localized turbulence generated at an early stage of the evolution and (2) the structure of the more nearly homogeneous turbulence (along the GW phase) during the decay stages of the waves. Moreover, Fritts et al. [2003] noted that GW breaking involves an overturning of the stable thermal structure of the atmosphere, evolving on a timescale of a GW period or less and resulting in turbulence and mixing that closely associate to and move with the unstable phase of the GW. The occurrence of turbulence primarily within the most unstable phase of both the high- and low-frequency GWs seems to support the arguments for weak mixing and a large turbulent Prandtl number arising owing to GW breaking [Fritts and Dunkerton, 1985; Coy and Fritts, 1988; McIntyre, 1989]. Earlier works also pointed out that a broad spectrum of gravity waves will have a range of saturation altitudes [Fritts, 1979; Weinstock, 1982; Dunkerton, 1982]. In addition, in the present work, the observation of distinct layers of SNR with weaker strengths occurred above 18 km (above the tropopause) for the off-zenith beams is because of the aspect sensitivity of the scatterers in these layers. Further, all the beams (Figure 2) show downward propagating layers of enhanced SNR in the heights of 14–16 km during the last 3 h.

Figure 2.

Height (3.6–20 km) versus time (112 s time interval) contour plots of SNR of received echoes by MST radar for (a) beam-tilted zero zenith (Zx polarization), (b) zero zenith (Zy polarization, (c) 10° toward the east, (d) 10° toward the west, (e) 10° toward the north, and (f) 10° toward the south directions for the same period of observation as that in Figure 1.

[13] An another important feature observed is that, in the height region of 11–14 km, there are three to four distinct layers of enhanced SNR occurred only for the transmitting beams tilted in the zx (Figure 2a), north (Figure 2e), and south (Figure 2f) directions but not for the zy (Figure 2b), east (Figure 2c) and west (Figure 2d) directions. It may be noted that for the zx, north, and south beam positions, the antennae were aligned along the geographic meridian, whereas for the zy, east and west beams, they were aligned along the geographic zonal direction. This would indicate that there exist layers of polarized refractive index structures in the height region of 11–14 km. The characteristics of the polarization may be associated with distinct microphysical properties of the scattering medium. It is tempting to suggest that there are polarized refractive index structures with electrical vectors oriented along the geographic meridian, existing at least in the heights of 11–14 km. Below this height range, probably, the large clutter signals from the nearby mountains mask or make it difficult to distinctly observe these polarized layers. Attempts will be taken in the near future to get more information on these polarized layers. We claim that this is the first report on the polarized refractive index structures existing in the lower atmosphere. As the exact causative mechanism for the existence of these polarized refractive index structures is not known presently, more studies are required to explain this phenomenon in detail. It may be noted that if the polarized refractive index structures, existing in the heights of 11–14 km, are due to instrumental (radar related) effects, then these effects should be observed in all the height ranges, which is not the present case. The instrumental effects are therefore ruled out.

[14] Sometimes, polarized gravity waves can lead to get strong and distinct signals in a particular direction but that depends on the particular orientation of the gravity wave vector. However, even between the two zenith beams polarized in the meridional and zonal directions, the observation of distinct layers of enhanced echoes in only one beam, in which the electrical vectors are aligned along the meridian, indicates that the scattering medium itself is polarized and it is not due to the polarized nature of the internal atmospheric gravity waves. Further, the corresponding Doppler spectral widths (Figure 3) do not show any kind of turbulent layers in this height region (11–14 km), indicating that these distinct scattering layers are not associated with any dynamical phenomena like dissipation of internal atmospheric gravity waves, vertical shear in the wind velocities (Figure 1), etc. Moreover, as the SNR strength is comparable between the zenith (zx) and meridional beams, it is suggested that the polarized scattering layers existing in this height region of 11–14 km are less aspect sensitive in nature in the meridional plane. As the dynamical phenomena and instrumental effects are ruled out, the only mechanism that is left out is the microphysical properties of the scattering layers, which may be the cause of the polarization characteristics of the scatterers. But what makes the scatterers to become polarized is an outstanding question to be addressed in detail in the near future. One possible mechanism is that a specific orientation, due to the electric field of global electric circuit (GEC), of electric dipole moments of water molecules dispersed in the atmosphere can lead to more scattering of the incident electromagnetic waves with electric field oriented in that specific direction. The physical importance of the existence of polarized layers is that sometimes it can lead to wrong interpretation as if the gravity waves got dissipated in a particular horizontal direction because of the existence of critical levels for the waves propagating in that direction. Hence it is imperative that a proper distinction be made between the actual highly turbulent layers existing because of the dissipation of the waves and the polarized atmospheric-scattering structures.

Figure 3.

(a–f) Same as Figure 2 but for the spectral widths.

[15] The close correspondence between the layers of enhanced Doppler spectral width (Figure 3), SNR (Figure 2) and strong vertical shears (Figure 1) indicates that these layers are associated with turbulent layers induced probably by partial dissipation of the upward propagating internal atmospheric gravity waves [Grimshaw, 1975; Weinstock, 1982]. To strengthen this point of view, Figures 4a4f show time (1700–0830 LT) versus period of oscillation (in minutes) contour plots of Morlet wavelet power spectrum [Torrence and Compo, 1998] of the vertical wind velocity determined in the heights of 20, 19, 18, 17, 16.5, and 16 km, respectively, and Figures 4g4l show that for 14, 12, 10, 8, 6, and 4 km, respectively. Similarly, Figures 5 and 6 show the power spectra of the zonal and meridional wind velocities, respectively. The thick dotted lines near the ends of the observation periods denote “cone of influence” (COF) of the Morlet wavelet power spectrum, indicating that outside of which it needs careful interpretation as it may lead to wrong conclusions. Thick contour lines indicate that inside which the spectral power is more than the statistical 95% confidence level. It can be noted on the top of each plot (i.e., at each height) the variance (m/s)2 of the time series of the wind velocity (m/s) at that height. The values inside the contour plots are equal to this variance times 2 to the power of the value of the corresponding color code value (i.e., power = variance*2c, where c is the value of the corresponding color code of the color bar).

Figure 4.

Period of oscillation (minutes) versus time (112 s time interval) contour plots of power spectrum (Morlet wavelet analysis) of vertical wind velocity in the heights of (a) 20 km, (b) 19 km, (c) 18 km, (d) 17 km, (e) 16.5 km, (f) 16 km, (g) 14 km, (h) 12 km, (i) 10 km, (j) 8 km, (k) 6 km, and (l) 4 km for the same period of observation as that in Figure 1.

Figure 5.

(a–l) Same as Figure 4 but for zonal wind velocity.

Figure 6.

(a–l) Same as Figure 5 but for meridional wind velocity.

[16] It may be observed in the vertical wind velocity spectrum that in the heights of 4–10 km (Figures 4i4l) there is significant power near the periodicity of 8–15 min, existing intermittently during the whole observational period. However, in the height of 12 km (Figure 4h), the 8–15 min periodicity band is almost disappeared and sporadically occurred the higher frequency oscillations with periodicity of less than 8 min. In the heights of 8 and 10 km, the occurrence of significant power during the first 1 h (1700–1800 LT) is noticeable as it comprises a wide periodicity band of 8–30 min. Further, significant ∼30–60 and ∼30 min periodic oscillations are occurred at almost all the heights from 4 to 10 km during ∼2300–0100 and 0200–0400 LT, respectively. However, at the height of 12 km, the 30–60 min periodicity band has been changed into the 15–40 min periodicity band (probably because of the Doppler shifting effect of the background horizontal winds), which existed for a few hours around 2300 and 0300 LT of 2 and 3 June, respectively. At the height of 14 km (Figure 4g), there is a shift in the periodicity of gravity waves toward the higher frequencies with period of oscillation less than ∼12 min, occurred intermittently during the whole period of observation.

[17] At the height of 16 km (Figure 4f), the intensity as well the occurrence statistics of these high-frequency (less than 15 min periodicity) gravity waves is found to be maximum. Here the spectral band is wide ranging from a few minutes to more than 30 min of periodicity. Within 0.5 km width in height at 16.5 km (Figure 4e), these high-frequency gravity waves are dissipated almost for the whole period of observation, indicating that the strong vertical shear in the horizontal winds existing at 16.5 km would have acted as a critical layer for the upward propagating high-frequency gravity waves. Again, within 0.5 km at 17 km (Figure 4d), these high-frequency gravity waves have appeared again and both the intensity and frequency of occurrence of these waves increased with height up to the present observation limit of 20 km (Figure 4a). It seems that these upward propagating (phase propagation not shown here) high-frequency gravity waves are generated from the strong vertical shear layer located at ∼16.5 km, where it is found that the Richardson number (Ri) is less than 0.25 (Kelvin-Helmholtz instability (KHI) condition satisfied) for almost the whole period of observation (see Figure 10b). This value of Ri indicates that the layer (width of ∼0.5 km) at 16.5 km is dynamically unstable and large turbulence is generated there owing to the strong vertical shear in the horizontal winds. The layers of strong SNR (Figure 2) and Doppler widths (Figure 3) of the echoes observed with MST radar at this height of 16.5 km indicate that they are associated with dynamically unstable shear regions (KHI condition satisfied). Also it is observed that this strong shear layer has dissipated a significant amount of the energy of the upward propagating gravity waves with 16–30 min periodicity band during ∼2300 and 0300 LT. This is indicated in the observation of insignificant amplitude of oscillations with these periodicities above 17 km. The filtering analyses (not shown) of these oscillations in all the height regions indicate that they might have propagated from below 3.6 km (lower limit fixed by the MST radar).

[18] In the zonal winds, it is rare (except at 10 and 12 km) even up to 14 km (Figures 5g5l) to observe significantly strong spectral amplitudes of high-frequency gravity waves. However, around 16 km, there is a significant enhancement in the spectral power for the periodicity range of up to ∼30 min during the whole observational period. Similar to the vertical winds at 16.5 km (Figure 4e), one can notice the almost disappearance of these spectral powers in the zonal wind within a narrow height range of 0.5 km (Figure 5e). Again, similar to the vertical winds (Figure 4), there is an enhancement with height up to 20 km of both the intensity and frequency of occurrence of high-frequency gravity waves with periodicities less than 15 min. Similar above mentioned features observed for the zonal wind are also observed for the meridional winds (Figure 6). One difference is that the meridional wind spectra do not show significant spectral amplitudes at 17 km. This is because in the meridional winds, the thickness of the strong vertical shear region is more, extending up to 17 km (Figure 1e).

[19] It is interesting to find where the resonance condition (wave dissipation) would occur for different frequencies of upward propagating gravity waves in the high-frequency band of 4–60 min. The resonance condition (critical layer) can occur in the heights where

equation image

where C is the phase velocity of the gravity waves and U is the background wind velocity. While it is easier to measure directly the background wind velocity, it is difficult to determine directly the phase velocity of the gravity waves of different frequencies using an MST radar at a single location. So to determine the Doppler-shifted phase velocities of the gravity waves, the following relations are used [Fritts, 1985, equation (17)].

[20] Assuming that the wave motions are monochromatic and hydrostatic,

equation image

where |u′| and |u′z| are the absolute values of perturbation in gravity wave amplitude and its vertical shear, respectively, and N is the Brunt-Vaisala frequency. It is warned that although u′z = N implies a convective instability condition, the minimum of the wave-perturbed ‘N’ rather than the maximum shear determines the unstable portion of the wavefield [Fritts, 1985; Orlanski and Bryan, 1969]. By determining these perturbation values at different frequencies in the frequency band of 4–60 min in the heights of 3.6–20 km with 150 m height resolution, the corresponding Doppler-shifted phase speeds (C-U) of gravity waves are determined. The results are shown in Figures 7, 8, and 9 for the zonal, meridional, and vertical velocities, respectively. Only the small values within −0.5–0.5 of (C-U) are plotted as they represent the waves that are nearer to dissipation [Lindzen, 1985]. With a time band of 2 h, Figure 7 shows the height profiles of (C-U) for the zonal wind velocity. Figures 7e7h correspond to 1700–1900, 1900–2100, 2100–2300, and 2300–0100 LT, and similarly Figures 7a7d correspond to 0100–0300, 0300–0500, 0500–0700, and 0700–0900 LT of 2–3 June 2005. An important observation is that all the heights up to 16 km are conducive to wave dissipation, and above 16 km there are no wave dissipation conditions for the high-frequency band of 4–15 min periodicity during the whole observation period (Figures 7a7h). This would indicate that these high-frequency waves, propagated from below 4 km, have faced the critical levels of absorption at different heights up to 16 km and almost all the waves might have been dissipated by this height range. Above this height (16 km), there is no wave dissipation. This is one of the reasons for the enhancement of wave amplitudes with height above 16.5 km as shown in Figure 5 for these high-frequency gravity waves. Further, this would indicate that the occurrence of these waves in the lower stratosphere is due to the strong turbulence (the Kelvin-Helmholtz instability) occurred in a narrow height range of 0.5 km at 16.5 km. We can see similar features also in the other wind components in Figures 8 and 9 for the meridional and vertical winds, respectively.

Figure 7.

Two-hourly height profiles (3.6–20 km) of critical levels (values of C-U within −0.5–0.5 m/s, where C is the phase speed and U is the background wind speed) of high-frequency (4–50 min periodicity) gravity waves in zonal wind for the same period of observation as that in Figure 1. Profiles are for local times on 2–3 June 2005: (a) 0100–0300, (b) 0300–0500, (c) 0500–0700, (d) 0700–0900, (e) 1700–1900, (f) 1900–2100, (g) 2100–2300, and (h) 2300–0100.

Figure 8.

(a–h) Same as Figure 7 but for meridional wind.

Figure 9.

(a–h) Same as Figure 8 but for vertical wind.

[21] The conditions, however, are different in the case of the other periodicity band of 20–60 min. The critical layers occurred sporadically with less frequency in heights for the lower-frequency gravity waves and concentrated mostly in the troposphere for all the three wind components. One can easily associate the distinctly enhanced SNR (Figure 2) and Doppler spectral width (Figure 3) of the echoes observed in all the six beam directions, in the heights of 10–12 and 13–14 km at ∼1900–2000 LT, with the critical layers (Figures 79), which indicates that dissipating gravity waves can induce turbulence. Similarly, it is easier to associate the distinctly enhanced SNR (Figure 2) and Doppler spectral widths (Figure 3) occurred in the heights of 12–16 km during the midnight hours of 2200–0200 LT with the critical layers (Figures 79). For example, one can notice that there is an enhanced Doppler spectral width of the echoes, observed in the meridional off-zenith beams (Figures 3e and 3f), around the heights of ∼4.5 and 6 km during 1900–2300 LT. Correspondingly, there exist the critical levels of the gravity waves, associated with the meridional winds for the whole periodicity range of ∼4–60 min (Figures 8f and 8g) around these two height regions. Further, around 2300–0100 LT, a weak spectral width (Figures 3e and 3f) is observed at ∼6 km, and correspondingly, the critical level around this height is found to disappear (Figure 8h). Moreover, at ∼10 km, there is an enhanced spectral width in almost all the beam directions (Figure 3) during 1900–2300 LT, which is in correspondence to the existence of critical levels in the vertical (Figures 9f and 9g) and zonal winds (Figures 7f and 7g). After this period, the spectral width does not show any distinct enhancement in the vertical beam at this height of ∼10 km (Figures 3a and 3b) and also there are no critical levels of gravity waves existing in the vertical wind (Figure 9). Sometimes, it may be difficult to find coherence between the critical levels of gravity waves, existing in the different wind components. For that, one has to keep in mind that here we are dealing with high-frequency gravity waves (with periodicity of less than an hour) which are, in general, highly intermittent in nature with respect to both the space and time.

4. Discussion

[22] Using a theory based on nonlinear interactions among many gravity wave modes, Weinstock [1982] showed that a broad spectrum of gravity waves will have a range of saturation amplitudes and hence a range of saturation altitudes instead of a single altitude. This theory can explain the present observed downward propagating features of the unstable vertical shears in the horizontal winds (Figure 1), SNR (Figure 2), and Doppler spectral widths (Figure 3) of all the three wind components in the heights of 10–14 km during the observation periods of 1700–2100 and 2200–0300 LT of 2–3 June 2005. These downward-propagation characteristics might have been resulted from breaking of the upward propagating gravity waves at successive height levels, agreeing with the theoretical expectations [Weinstock, 1982]. Earlier, the same explanation was proposed also by some others [Jones and Houghton, 1972; Breeding, 1972]. They examined the large-amplitude internal gravity waves that can cause changes in the mean winds even in the absence of any initial shear. These changes may then introduce a sufficient shear or even a critical level to cause an absorption or a “self-destruction” of the propagating gravity waves.

[23] In the present observation, there is a concern for the leaking of upward propagating internal-atmospheric gravity waves (15–40 min periodicity) above an unstable-shear layer located near the tropopause during 1700–2100 and 2200–0300 LT. This can be explained on the basis that an unstable shear layer can Doppler shift the upcoming waves and hence becomes less efficient in filtering out these waves [Jones and Houghton, 1971]. Using a numerical model, Jones and Houghton [1971] showed that the mean-flow acceleration existing near a critical unstable-shear layer can Doppler shift an internal-gravity wave frequency, thus allowing more penetration of the wave energy than expected from a linear theory. Also, Jones [1969] showed that, using the geometrical optics approximation that precludes the large amplitude effects, which are almost certainly taking place during observations, a local acceleration in a mean flow can cause a shift in the frequency of a wave packet relative to a fixed reference frame [Jones, 1969]. However, in another condition [McIntyre and Weissman, 1978], in order to propagate away from a critical shear layer, the Doppler-shifted frequency of the waves needs to be less than the BV frequency when the background atmosphere is uniformly stratified. However, when the background is not uniformly stratified, the conditions required for the generation and propagation of the internal atmospheric gravity waves are that the Ri be less than 0.25 in a shear region and greater than 0.25 in a farther but away from the shear region [Sutherland et al., 1994; Sutherland and Peltier, 1994, 1995; Sutherland, 1996, 2006], which is in agreement with the present observation (Figure 10b). Figure 10a shows the height profile (3.6–19 km) of the Brunt-Vaisala frequency; calculated by following the method of Revathy et al. [1996], and using the vertical velocities measured by the MST radar. Figure 10b shows the corresponding height profile of Richardson number determined using the calculated BV frequency.

Figure 10.

(a) Height profiles of Brunt-Vaisala frequency (N, rad/s) calculated using the measurements of vertical velocity by MST radar over Gadanki. The horizontal bars denote standard deviation about the mean. (b) Corresponding Richardson number.

[24] For an internal wave on the scale of KH billows to be generated by KH instability, when the background is not uniformly stratified, the stratification over the depth of the shear layer must be sufficiently weak and that the flow needs to be highly unstable. Using nonlinear numerical simulations, Sutherland [2006] examined the effect of Rayleigh wave–internal wave coupling in a semi-infinite shear flow that is stratified some distance away from the shear, when the unstable Kelvin-Helmholtz shear layer is localized. Further, he showed by examining the profiles of wave-induced mean flow that if the bulk Richardson number is of the order of unity, then a significant amount of momentum can be extracted by waves from a shear layer as a consequence of transport by the waves. The hypothesis is that this coupling can affect the excitation of internal waves from a finite-depth shear layer that is KH unstable. There is an another possibility that an interaction between a gravity wave and a critical level can lead to an excitation of waves that can propagate above the critical level and a KH-unstable-layer through nonlinear interactions near the critical level [Fritts, 1979; Nault and Sutherland, 2008]. Other later studies found that upward propagating waves can get overreflected when the frequency and horizontal wave number of the incident waves match closely to those of the most unstable modes in the shear layer.

[25] Another important aspect of the present observation is that it is possible for the occurrence of high-frequency (less than 15 min periodicity) gravity waves, at almost all the times, up to a few kilometers below and well above a dynamically unstable layer located near the tropopause. It is suspected that this strong-shear layer at ∼16.5 km with Richardson number less than 0.25 (Figure 10b) has generated these high-frequency gravity waves that have propagated even above 20 km and only a few kilometers below this layer [McIntyre and Weissman, 1978; Fritts, 1982; Sutherland, 2006]. Earlier, high-resolution numerical simulations have shown the radiation of large-amplitude internal gravity waves from the flanks of a jet flow in fluids having variable squared-BV-frequency (N2) [Sutherland et al., 1994; Sutherland and Peltier, 1994]. According to them, both the linear and nonlinear mechanisms in different parameter regimes can explain the direct excitation of large-amplitude gravity waves from shear layers. Using a numerical simulation model, Fritts [1982] studied of nonlinear excitation of gravity waves from an unstable shear layer. He found that one of the modes (B1 mode of Fritts [1982]) excited through nonlinear interaction of two KH modes, propagates well above and weakly (evanescent mode) below an unstable-shear layer, which is in agreement with the present observations. Numerical simulations [Sutherland and Peltier, 1994; Sutherland, 1996; Tse et al., 2003] also show that under two Richardson number criteria, that is, Ri < 0.25 inside the shear and Ri > 0.25 outside the shear, the internal waves generated by the KH instability will have such a large amplitude and be excited for such long times that significant drag can be induced in a mixing region. These waves themselves can transport momentum far from a source, crossing even a critical layer existing in a second nearby stably stratified shear layer [Smyth and Moum, 2002]. This report is particularly helpful in interpreting the present observation of high-frequency gravity waves, generated from a strong unstable shear region at ∼16.5 km, even up to the highest radar-limiting height of 20 km in spite of the presence of multiple shear layers in both the zonal and meridional winds (Figure 1). Sutherland [2006] explained that if a well-stratified region lies immediately above a shear layer, then the “direct excitation” of internal waves during the linear-growth phase is the dominant mechanism for the wave generation, which is in agreement with the present observation (Figure 10). Here one can easily note that the sharp enhancement of the Brunt-Vaisala frequency at ∼17 km (Figure 10a), which is just above the strong-unstable shear layer with Ri < 0.25, occurred (Figure 10b) within a narrow height region of 16.5–17 km (Figure 1b). However, in the “indirect mechanism,” the fluid is stratified sufficiently far above a shear layer and that the KH instability in the shear layer gets only weakly influenced by the far-field stratification. As a result, the flow passes over growing shear-unstable waves and the nonlinearly developed billows move up and down, leading to generation of internal waves in a manner similar to topographic wave generation [Sutherland, 1996]. Further, it is also possible that internal waves can be generated when a shear-induced mixing region collapses [Buhler et al., 1999].

[26] Another theory is based on the forcing of large-scale internal gravity waves by shear-unstable and stratified-free shear layers through nonlinear interaction between different unstable modes with different horizontal wave numbers, when they reach finite amplitudes in the shear layer [Scinocca and Ford, 2000]. Here the generation of these large-scale internal waves (i.e., larger than the horizontal scale of eddies that form initially in the shear layer) is considered to be arising only from the dynamical action of the eddies present in the shear layer. The dynamical adjustment, that is required to remove the horizontal pressure gradients arising between a patch of eddies formed in the unstable shear layer and the surrounding flow, can lead to the excitation of the gravity waves. This adjustment process is called a “mixed-layer collapse” by Buhler et al. [1999]. Further, it was proposed that a vortex pairing (and wavelength doubling) of the most rapidly growing KH modes also can lead to excitation of waves through nonlinear mechanisms [McIntyre and Weissman, 1978; Davis and Peltier, 1979]. As another possibility, Chimonas and Grant [1984] argued that a resonant interaction among two similar wavelength KH modes and one unstable mode of much longer wavelength can lead to excitation of large-scale gravity waves.

5. Conclusions

[27] We have examined the characteristics of high-frequency (periodicity range of 5–60 min) gravity waves in the troposphere and lower stratosphere by continuously operating an MST radar at Gadanki (a tropical station in India) for about 16 h. During this observational period, there were two incidences of vertical propagation of internal-atmospheric waves with periodicity of 15–30 min through a strong wind-shear region located near the tropopause level at ∼16.5 km. These waves are identified as propagating vertically upward from below 3.6 km, which is the lower limit fixed by the technical specifications of the MST radar operation. At ∼16.5 km, which is just above the tropical easterly jet core, there is a strong wind shear (exceeding 0.02 per second) region (width of ∼0.5 km in height) with Richardson number less than 0.25, indicating the possible existence of the Kelvin-Helmholtz instabilities. During these two incidences, the upward propagating waves are not totally dissipated while passing through the strong wind-shear region at ∼16.5 km. Some leakages of the wave energy to higher heights above the shear layer are observed, which is suspected to be due to the effect of Doppler shifting on the frequencies of the upward propagating waves through wave-critical level interaction in the unstable shear region. Further, the downward propagation characteristics of the strong wind shears and the associated distinctly enhanced SNR and Doppler spectral width of the echoes, occurred in the 10–14 km height region during these two incidences of the passage of the waves, are explained on the basis of initial strong-amplitude gravity waves having broader spectrum and variable saturation heights. The occurrence of high-frequency gravity waves with periodicity of ∼5–15 min up to a few kilometers below and well above the strong wind-shear region is explained on the basis of generation of unstable waves from a dynamically unstable wind-shear region composed of KH instabilities. Further, it is found the existence of critical levels at almost all the heights of 4–16 km for the 4–15 min periodicity band during the whole observation period and sporadically in heights and time for the rest of the frequency band of gravity waves. Between 16 and 20 km, it is rare to find the critical levels. Moreover, the present observations also show that the high-frequency gravity waves, generated from the shear region at ∼16.5 km, propagate to even above 20 km without significant attenuation, which is because of the absence of critical levels in the lower stratosphere. The distinct enhancements observed in the SNR and Doppler spectral widths of the received echoes by the MST radar during the observation period are associated with these critical levels. These critical levels exist particularly in the zonal and meridional winds, indicating that the breaking gravity waves lead to these enhancements in the SNR and spectral widths. The present observation of high-frequency gravity waves that propagate vertically upward well above 20 km into the stratosphere and weakly downward below up to a few km, from a strong wind-shear region located immediately below a highly stratified layer near the tropopause, is in accordance with the “direct mechanism” explained by Sutherland [2006] through nonlinear numerical simulation studies. For the first time, the MST radar observations showed existence of layers of polarized refractive-index structures in the heights of 10–15 km, which may be associated with distinct microphysical properties of the scatterers.


[28] This work is supported by the Department of Space, Government of India. We acknowledge with sincere thanks the kind help extended by M. N. Rajeevan, Scientist at NARL, Gadanki, in preparing this manuscript. The dedicated work of the scientific and technical staff who operate the MST radar at NARL, Gadanki, is duly acknowledged. We are indebted to the reviewers and the Editor Steven Ghan, whose comments helped to significantly improve the quality of the manuscript.