Unsteady, Turbulent Convection into a Homogeneous, Rotating Fluid,with Oceanographic Applications

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  • 1 Departments of Mechanical and Aerospace Engineering, University of Southern California, Los Angeles, California
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Abstract

Turbulent convection into a homogeneous, rotating fluid has been generated in laboratory tanks, for both laterally confined and unconfined domains. When a given experiment was in a solid-body rotation, a source located at the top surface of the water column was activated to release denser saltwater into the underlying, less-dense fluid of total depth H. As a result, a downward propagating 3D turbulent front was formed. Eventually, at a transition depth zc, rotational effects dominated the turbulence and many quasi-2D vortices were generated, which then penetrated downward beneath the upper 3D turbulent layer. Measurements in the confined experiments gave zc ≈ (12.7 ± 1.5) (B0/f3)1/2; the mean diameter (Dv) of the quasi-2D vortices as Dv≈(15.0±1.5) (B0/f3)1/2, their downward speed of propagation (uc) as uc ≈ (1.0 ± 0.1) (B0/f)1/2, and the maximum swirl velocity (uv) of an individual vortex as uv ≈ (4.0 ± 0.4)(B0/f)1/2 (where B0 is the surface buoyancy flux and f the Coriolis parameter). All are in agreement with scaling predictions presented here and in a number of previous publications.

In the unconfined experiments, when zc < H, the vortex columns of the type discussed above “filled out” after reaching the bottom, took on a conical shape, and then underwent a collective baroclinic instability with the resultant larger-scale vortices propagating away from beneath the source. The velocity field of the vortex columns extended throughout the water column and many vortices surrounded the source. The measured diameter (D) of the circle of maximum velocity was consistent with the scaling D/H ≈ (5.2 ± 1)(Ro*)1/2, where Ro*=(B0/f3)1/2/fH=(B0/H2f3)1/2 is a natural Rossby number of the flow based on the characteristic vortex velocity. When zc > H, and the radius of the source (R) was of the same order as the fluid depth, the turbulent layer contacted the bottom directly without forming small-scale vortices, spread horizontally, and eventually baroclinic vortices formed at the edge of the spreading front or gravity current. The diameter of these vortices was consistent with the scaling D/H≈(7.0 ± 1) (Ro*)2/3. Using an extension of the model of O. M. Phillips, it is suggested that this result should be modified by multiplying by a factor (R/H)1/3 when R/H) is large. When zc=H, then (Ro*)1/2 = 0.28, and this constitutes a transition Rossby number between the two regimes. These more extensive results are in agreement with previous theoretical predictions and limited experimental measurements by the authors. Results from the present study have been applied to convective events observed in the Golfe du Lion and the Arctic and a reasonable agreement found, especially when the finite size of the source was taken into account. Furthermore, it is concluded, based on the scaling results found here, that fluid of a density large enough to constitute “bottom water” can only be produced under circumstances that limit mixing with ambient fluid, for example, in an intense vortex column in deep water or under an extensive region of cooling in shallow water. Arguments favoring these possibilities are presented.

Abstract

Turbulent convection into a homogeneous, rotating fluid has been generated in laboratory tanks, for both laterally confined and unconfined domains. When a given experiment was in a solid-body rotation, a source located at the top surface of the water column was activated to release denser saltwater into the underlying, less-dense fluid of total depth H. As a result, a downward propagating 3D turbulent front was formed. Eventually, at a transition depth zc, rotational effects dominated the turbulence and many quasi-2D vortices were generated, which then penetrated downward beneath the upper 3D turbulent layer. Measurements in the confined experiments gave zc ≈ (12.7 ± 1.5) (B0/f3)1/2; the mean diameter (Dv) of the quasi-2D vortices as Dv≈(15.0±1.5) (B0/f3)1/2, their downward speed of propagation (uc) as uc ≈ (1.0 ± 0.1) (B0/f)1/2, and the maximum swirl velocity (uv) of an individual vortex as uv ≈ (4.0 ± 0.4)(B0/f)1/2 (where B0 is the surface buoyancy flux and f the Coriolis parameter). All are in agreement with scaling predictions presented here and in a number of previous publications.

In the unconfined experiments, when zc < H, the vortex columns of the type discussed above “filled out” after reaching the bottom, took on a conical shape, and then underwent a collective baroclinic instability with the resultant larger-scale vortices propagating away from beneath the source. The velocity field of the vortex columns extended throughout the water column and many vortices surrounded the source. The measured diameter (D) of the circle of maximum velocity was consistent with the scaling D/H ≈ (5.2 ± 1)(Ro*)1/2, where Ro*=(B0/f3)1/2/fH=(B0/H2f3)1/2 is a natural Rossby number of the flow based on the characteristic vortex velocity. When zc > H, and the radius of the source (R) was of the same order as the fluid depth, the turbulent layer contacted the bottom directly without forming small-scale vortices, spread horizontally, and eventually baroclinic vortices formed at the edge of the spreading front or gravity current. The diameter of these vortices was consistent with the scaling D/H≈(7.0 ± 1) (Ro*)2/3. Using an extension of the model of O. M. Phillips, it is suggested that this result should be modified by multiplying by a factor (R/H)1/3 when R/H) is large. When zc=H, then (Ro*)1/2 = 0.28, and this constitutes a transition Rossby number between the two regimes. These more extensive results are in agreement with previous theoretical predictions and limited experimental measurements by the authors. Results from the present study have been applied to convective events observed in the Golfe du Lion and the Arctic and a reasonable agreement found, especially when the finite size of the source was taken into account. Furthermore, it is concluded, based on the scaling results found here, that fluid of a density large enough to constitute “bottom water” can only be produced under circumstances that limit mixing with ambient fluid, for example, in an intense vortex column in deep water or under an extensive region of cooling in shallow water. Arguments favoring these possibilities are presented.

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