## 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[−2*π*(R_{c} − 0.25)^{1/2}], where R_{c} is the Richardson number at the critical level [*Eliassen and Palm*, 1961]. On the basis of linear theory and the condition that the ratio || > 1 ( = 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/8^{1/2} 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.