Transverse structure of turbulence in a rotating gravity current

Authors


Abstract

[1] Synoptic, high-resolution, measurements of turbulent kinetic energy dissipation, current velocity and water column stratification across a fast (up to 0.7 m s−1) oceanic saline gravity current are presented. Our data provide, for the first time, a detailed two-dimensional picture of the turbulence structure inside a gravity current. Strong boundary-layer and interfacial turbulence can be distinguished from a quiet core, and a strong asymmetry of mixing near the outer edges of the gravity current is apparent. This asymmetry is mirrored by the computed entrainment velocities, varying approximately by a factor of 5 across the gravity current. It is argued that the asymmetry is due to rotational effects that can be clearly identified also in the velocity and density fields.

1. Introduction

[2] Dense bottom gravity currents affected by the rotation of the Earth are a ubiquitous feature in geophysical flows. In the ocean, gravity currents may be influenced by topographical features such as channels and ridges, a fact that has considerable implications for their dynamics. Well-known examples of topographically constrained gravity currents are the Mediterranean outflow passing through the Strait of Gibraltar [Johnson et al., 1994b; Baringer and Price, 1997a, 1997b], the southern and northern channels of the Red Sea outflow plume [Peters et al., 2005; Peters and Johns, 2005], and the Faroe Bank Channel overflow [Mauritzen et al., 2005].

[3] Among the few direct observations of mixing in oceanic gravity currents, the majority is based on the identification and statistical analysis of overturns in standard CTD profiles, from which dissipation rates and vertical buoyancy fluxes can be estimated [see e.g., Mauritzen et al., 2005; Peters and Johns, 2005; Fer et al., 2004]. An alternative method relies on the observation of the shear microstructure with free-falling profilers from which the dissipation rate of turbulent kinetic energy may be estimated. This method was used e.g. in two campaigns in the Mediterranean outflow [Wesson and Gregg, 1994; Johnson et al., 1994a], and in a study of the Storfjorden overflow in the North Atlantic [Fer, 2006]. These valuable data revealed a number of important characteristics of the vertical structure of naturally occurring gravity currents. However, given the large spatial scales, the large depth, and the strong temporal variability of these overflows, especially due to tidal motions, the spatial and temporal resolution of the microstructure measurements was generally not sufficient to obtain a synoptic and spatially coherent picture of the transverse structure of a rotating gravity current.

[4] Here we present data from an environment that serves as a natural laboratory for rotating gravity currents since it is free from many of the problems described above. Our study site in the Western Baltic Sea is close to an ideal channel, free from tidal fluctuations, and known for the occurrence of strong and quasi-stationary gravity currents during extended periods. This allowed us, for the first time, to obtain a truly synoptic and high-resolution data set of stratification, turbulence (shear-microstructure), and velocity across the whole depth and width of an approximately 10 km wide and vigorously turbulent gravity current. By providing a two-dimensional view across the gravity current, our new data set extends the single-point turbulence measurements obtained by Arneborg et al. [2007] and Sellschopp et al. [2006] at the same location during earlier campaigns.

2. Study Site and Instrumentation

[5] Gravity currents in the Baltic Sea are caused by intermittent inflows of saline North Sea water into the brackish Baltic Sea through a system of narrow and shallow straits called the Belt Sea (see Figure 1). Using one of the possible pathways, saline water masses intermittently pass through the Oere-Sound, and subsequently follow the pathway sketched in Figure 1c [see e.g., Sellschopp et al., 2006]. Influenced by bottom friction and local topography, they are mainly steered through the channel north of Kriegers Shoal, and enter the Arkona Basin further to the east.

Figure 1.

(a) Overview map of North Sea and Baltic Sea. (b) Belt Sea region with the Oere-Sound. (c) Topography of study area at 2 m depth intervals. Dark blue line indicates the simultaneous microstructure and towed ADCP transects across the channel (transect width 11,300 m, measured on 17 November 2005, 08:00–10:45 GMT). Position of the moored ADCP as indicated. Arrows illustrate pathway of dense gravity currents entering from the Sound.

[6] Across this sloping channel simultaneous microstructure and velocity transects were taken on 17 November 2005 from board of two closely operating ships (distance less than 200 m, Figure 1c). From ship A, repeated full-depth shear-microstructure profiles were obtained with a MSS90 profiler from ISW Wassermesstechnik approximately every two minutes (74 profiles), from which 0.5 m binned dissipation rate estimates were computed. In order to simultaneously measure nearly full-depth velocity profiles, a downward-looking 600 kHz acoustic current profiler (ADCP) was equipped with a purpose-built wing, enabling it to be towed and lowered behind ship B, thereby ‘flying’ closely above the interface of the gravity current. In the upper part of the water column, the data from this ADCP were complemented by data from a downward-looking 300 kHz vessel-mounted ADCP. In addition to these shipboard measurements, an upward-looking 600 kHz ADCP was moored near the center of the channel (see Figure 1), in order to check the temporal variability of the gravity current during the ship transects.

3. Velocity and Density Structure

[7] Figure 2 shows the composite velocity transect from the flying and vessel-mounted ADCPs, overlayed with the density structure from the high-precision CTD sensors of the microstructure profiler. Also shown in Figure 2 is the temporal variability and vertical structure of the velocity measured by the bottom-mounted ADCP. These data clearly demonstrate the presence of a strong bottom gravity current with a width of slightly less than 10 km, and a maximum thickness of approximately 13 m, moving down the channel towards the east with a speed of up to 0.7 m s−1. The gravity current is separated from the ambient fluid by a well-defined interface with thickness increasing from about 1 m on the northern flank of the channel towards more than 5 m on the southern flank.

Figure 2.

(a) Along-channel velocity, and σt at 1 kg m−3 intervals. The white line indicates the position of the first bin of the towed and lowered ADCP. Data above this line are derived from the vessel-mounted ADCP. (b) 30 minute low-pass filtered velocities measured by the moored ADCP near the center of the channel (see Figure 1) during the time of the transect shown in Figure 2a.

[8] One of the most remarkable features of the observed gravity current is its small temporal variability during the transect. The corresponding velocity records from the bottom-mounted ADCP displayed in Figure 2b are seen to exhibit only little temporal variability, and vertically averaged current speeds (not shown) vary only by a few percent. This implies that the data obtained during the transects are essentially synoptic.

[9] Several effects of system rotation are visible, of which the most familiar and obvious is the tilt of the interface. To first order, this tilt is consistent with geostrophic velocity estimates, although a frictional retardation of the near-bottom flow is evident in Figure 2. A number of more subtle rotational effects can also be identified. The most remarkable of these are the pronounced spreading and pinching of the pycnocline on the southern and northern flank of the channel, respectively, and the horizontal separation of the plume body into a region with a strong horizontal density gradient (south of approximately 55.12°N), and a region essentially free of horizontal density variations. Both effects are also observable in large scale gravity currents, and have been shown to be related to advection by the cross-channel Ekman transport [see e.g., Johnson and Sanford, 1992; Ezer, 2006]. Surprisingly, it turns out that the vertical thermal wind shear associated with this density gradient is comparable to the observed total shear, suggesting a dominant dynamical impact on the frictional boundary layer that may be similar to that observed in ‘arrested’ Ekman layers in coastal boundary currents [MacCready and Rhines, 1993; [Garrett et al., 1993]. These issues, however, are outside the scope of this short note focusing on turbulence and entrainment, and will be reported elsewhere.

4. Turbulence Structure

[10] The transverse structure of the dissipation rate, ɛ, across the channel obtained from repeated casts of the microstructure profiler is displayed in Figure 3. The key property that makes this turbulence transect rather unique relies on the fact that it has been measured fast enough to be synoptic, and yet at high enough resolution to clearly distinguish between well-defined, spatially coherent turbulence regimes. Clearly visible is a vigorously turbulent gravity current with dissipation rates reaching ɛ ≈ 10−4 W kg−1, separated by a strongly stratified but turbulent interface from the quiescent ambient fluid with dissipation rates several orders of magnitude lower. Turbulence in the gravity current exhibits a rich internal structure that will be discussed in the following.

Figure 3.

Decadal logarithm of the dissipation rate (colors), and contours of σt (for clarity plotted here only at 2 kg m−3 intervals). Roman numbers indicate dynamical regimes discussed in the text. The white line indicates the interface position according to (1).

[11] Most obvious and physically most intuitive are the strongly enhanced dissipation rates in the bottom boundary layer (region I), which can be shown to decrease away from the sediment in good agreement with the law of the wall. Increased near-bottom dissipation rates have also been observed in other gravity currents [Wesson and Gregg, 1994; Johnson et al., 1994a; Peters and Johns, 2005, 2006], and have been attributed to the effect of bottom friction. In the central part of the plume, boundary layer turbulence is separated from the turbulent interface (region II) by the nearly quiescent region III — the core of the plume with very low dissipation rates. This quiet core approximately coincides with the region of maximum speed, a fact that is surprising only at first glance: near the velocity maximum, the shear, and therefore the shear production of turbulent kinetic energy, is small, and turbulence has insufficient energy supply to overcome the relatively weak stratification.

[12] Above this local minimum of turbulence, our data reveal a turbulent interface (region II) with consistently enhanced dissipation levels, often exceeding 10−6 W kg−1. This local maximum of turbulence has also been identified in the same channel in the single-station turbulence measurements presented by Arneborg et al. [2007] and Sellschopp et al. [2006], as well as in other gravity currents observed by Johnson et al. [1994a] and Fer [2006]. Since, in contrast to the bottom boundary layer, interfacial turbulence is associated with a strong density gradient, the contribution of this region to the overall entrainment will be dominant.

[13] A remarkable asymmetry in mixing is apparent between the southern and northern edges of the gravity current. Whereas at the northern edge, the vertical structuring of the dissipation rate as described above persists until the interface intersects with the bottom, at the southern edge (region IV) high dissipation rates can be observed throughout the gravity current. We believe that enhanced mixing in this region is associated with the downwelling-favorable effect of the Ekman transport which has a tendency to destabilize the density field.

5. Entrainment

[14] To arrive at a more quantitative description of entrainment we first note that a bottom gravity current is generally associated with a near-bottom buoyancy deficit monotonically decreasing towards zero with increasing distance from the bottom such that for every buoyancy profile the center of mass can be determined. With this picture in mind, Arneborg et al. [2007] defined the thickness of the gravity current, D, as twice the distance of the center of mass from the bottom, a quantity that is easily computed from

display math

where z = 0 denotes the bottom, b the local buoyancy deficit with respect to the background buoyancy at z → ∞, and G the reduced gravity or effective buoyancy of the plume. This definition leaves the physically attractive possibility to define entrainment on purely energetic arguments as the increase of D (i.e. lifting of the center of mass) due to diapycnal mixing. According to this idea, entrainment is related to the vertically integrated buoyancy flux,

display math

where primes denote fluctuations, and brackets the ensemble average. Then, the entrainment velocity, we, is conveniently defined as the rate of change of the plume thickness, D, due to diapycnal mixing, and, as readily shown, follows from we = 2B/GD; for details see Arneborg et al. [2007]. To obtain a more useful upper integration limit in (2), integrations were performed from the bottom (z = 0) up to a reference level, which is defined here as a straight line located approximately 3 m above the interface of the plume. This choice excludes contributions to (2) from other regions (e.g. the surface mixing layer) that are not related to the gravity current. Clearly, however, the location of the reference level involves some degree of arbitrariness, but since the reference level has been chosen to be located completely inside the essentially non-turbulent region above the interface (see Figure 3), therefore causing only a negligible contribution to the integral (2), this arbitrariness is of very little consequence.

[15] The buoyancy flux appearing in (2) was computed from the estimated dissipation rates assuming a variable mixing efficiency according to Shih et al. [2005], who suggest that the mixing efficiency is a function of the buoyancy Reynolds number, Reb = ɛ/N2ν (ν denotes the molecular viscosity). This avoids an overestimation of the buoyancy flux in weakly stratified but highly energetic regions.

[16] The interface position obtained from (1) is illustrated by the white line in Figure 3, and is seen to coincide with the region of the maximum density gradient. The reduced gravity, G, also following from (1), is shown in Figure 4. Due to the strong density contrast induced by salinity differences exceeding 10 it reaches the comparatively large value of 0.1 m s−2. Note that the constant cross-channel density gradient observed in Figure 2 is mirrored in the nearly constant increase of G in the southern part of the transect.

Figure 4.

Transects of (a) buoyancy deficit, (b) vertically integrated buoyancy flux, and (c) entrainment velocity, we.

[17] The vertically integrated buoyancy flux, B, and the entrainment velocity, we, also displayed in Figure 4, exhibit a remarkable asymmetry across the channel. The maximum value of B near 55.10°N is seen to be associated with the strong mixing region IV discussed in the context of Figure 3, and exceeds the value in the center of the channel by a factor of 2-3. This asymmetry is even more evident in the entrainment velocity, we, which decreases from we ≈ 1.5 × 10−5 m s−1 near the southern flank to we ≈ 0.3 × 10−5 m s−1 in the center, i.e. by a factor of 5. These values should be compared with the range we = (0.5 − 7.5) × 10−5 m s−1 estimated by Arneborg et al. [2007] at 55.11°N in the same section during a 19 h period. The large time variation in entrainment pointed out by these authors may have been caused by the location of that station exactly at the border between regions III and IV. The slightly larger average entrainment is likely due to the larger Froude number (Fr ≈ 0.54) found in their study compared to ours (Fr ≈ 0.4).

6. Conclusions

[18] Our results clearly demonstrate that the assumption of a constant entrainment velocity across a rotating gravity current is a rather coarse approximation. The observed asymmetry is likely related to rotational effects also manifested in the asymmetry of the interface thickness and the generation of a strong across-channel density gradient. This structure is similar to what we have seen during additional observations in similar channels in 2004–2006, and therefore appears to be a stable result.

Acknowledgments

[19] The authors are grateful for the support by the German Research Foundation (DFG) and the German Federal Ministry for the Environment, Nature Conservation and Nuclear Safety through the projects QuantAS-Off and QuantAS-Nat. Lars Arneborg was supported by the Swedish Research Council. We thank the crews of the R/Vs Penck and Stollergrund for their perfect reliability and support. Helpful comments of two anonymous reviewers are greatly appreciated.

Ancillary