Baroclinic instability of density current along a sloping bottom and the associated transport process

Abstract

Abstract. Numerical experiments with a three-dimensional nonhydrostatic ocean model have been carried out to investigate the dynamic processes of downslope density current and associated transport of dense water, focusing on the effects of bottom slope for the range of slope inclination S from 0 to 0.04. Bottom slope has two effects on baroclinic instability of the flow. One is the stabilizing effect due to the topographic/3 effect and to offshoreward increase in water depth. The other is the destabilizing effect due to steepened inclination of isopycnal surface, which increases available potential energy. Since the destabilizing effect over the upper slope overcomes the stabilizing one in the early stage, unstable waves develop more rapidly with increasing S. Nonlinear energy conversion due to Reynolds stresses also affects the flow stability and then the growth rate of instability increases linearly with S in this stage. After the unstable waves have finite amplitudes in the mature stage the stabilizing effect of bottom slope becomes dominant, especially over the lower slope. Thus vigorous unstable eddies are confined to the upper slope region in steep slope cases, while they cover the whole slope region in gentle slope cases, and this difference in the eddy field causes a drastic change in downslope transport of dense water. In gentle slope cases, efficiency of the transport becomes higher with increasing S since the destabilizing effect overcomes the stabilizing one as a whole. On the contrary, the efficiency becomes lower with increasing S in steep slope cases since the stabilizing effect surpasses the destabilizing one. As a result, the most effective transport is realized in the case with S -0.005. Although the transport due to eddies in steep slope cases becomes weak over the lower slope, it is still larger than that due to the bottom Ekman current since the eddy transport occurs in the bottom layer with a thickness of 100 -200 m, which is 4 -8 times the Ekman layer thickness.

Transport and modification processes of dense shelf water revealed by long‐term moorings off Sakhalin in the Sea of Okhotsk

“…The generation of eddies and associated offshore dense water transport by baroclinic instability over the continental shelf and slope with the application of negative buoyancy forcing have been studied numerically by Kikuchi et al [1999], Gawarkiewicz [2000], and Tanaka and Akitomo [2001], among others. Over the northwest shelf, Shcherbina et al [2004a] found indications of baroclinic instability of the polynya rim current [ Gawarkiewicz and Chapman , 1995] from late February to early May 2000 at their western mooring (see Figure 1 for the location).…”

Faroe Bank Channel Overflow: Mesoscale Variability*

“…Numerical work shows that eddies influence the descent rate of plume water (Tanaka 2006;Seim et al 2010) and that the dissipation rate of turbulent kinetic energy, which can be related to the vertical mixing, may change with a factor of 2-10 as an eddy passes . The latter is supported by the observations presented here, as the Richardson number oscillates between critical and noncritical values (Fig.…”

“…Comparable mesoscale variability is observed in other overflow regions [e.g., the Denmark Strait Overflow (DSO; Smith 1976) and the Filchner Overflow (Darelius et al 2009)], as well as in laboratory experiments (Smith 1977;Cenedese et al 2004;Wå hlin et al 2008) and numerical models (Jiang and Garwood 1996;Tanaka and Akitomo 2001;Ezer 2006) simulating dense plumes on sloping topography. A number of generation mechanisms has been suggested, often related to baroclinic instabilities (Smith 1976;Swaters 1991), vortex stretching (Lane-Serff and Baines 1998; Spall and Price 1998), or the bathymetry (Nof et al 2002;Pratt et al 2008), but as of today no consensus or clear understanding of the origin and nature of these oscillations exist.…”

“…They increase the descent rate of the plume (Tanaka and Akitomo 2001;Seim et al 2010), possibly because growing baroclinic instabilities represent a loss of momentum from the overflow to the overlying ambient (Kida et al 2009). Eddies may also increase entrainment, through either enhanced vertical mixing or horizontal stirring (Voet and Quadfasel 2010).…”

Tidally induced diapycnal mixing in the Kuril Straits and its role in water transformation and transport: A three‐dimensional nonhydrostatic model experiment

“…Therefore we took into account the effect of a planetary‐vorticity gradient by adopting the β‐plane approximation. The model has been constructed using that of Tanaka and Akitomo [2001] as a basis, but with the following governing equations and settings: where u = ( u , v , w ) are “internal mode velocities” in the ( x , y , z ) directions, respectively; U = ( U , V , W ) is a barotropic tidal flow; k is a unit vector along the z axis; p is pressure; ρ is density variation; and C represents potential temperature θ or salinity S . The equation of state is that recommended by UNESCO [ Jackett and McDougall , 1995].…”