On the Stability of Turbulent Density-Stratified Shear Flow

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  • 1 Laboratory of Fluid Mechanics, Department of Civil Engineering, Delft University of Technology, Delft, The Netherlands
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Abstract

The linear stability of the solutions to the equations for the vertical. turbulent diffusion of buoyancy and momentum is examined, including the interaction between buoyancy field and velocity field through the gradient Richardson number. The turbulent transports are modelled as gradient transports, and the eddy diffusivity and eddy viscosity are assumed to depend on the gradient Richardson number. A sufficient condition for stability is shown to be Prt ⩾ 0.5, where Prt, is the turbulent Prandtl number (the ratio of eddy viscosity to eddy diffusivity), which condition seems to be always satisfied in real, stratified flows. This result refutes certain arguments found in the literature, which are in favor of the possibility of in- stability.

Abstract

The linear stability of the solutions to the equations for the vertical. turbulent diffusion of buoyancy and momentum is examined, including the interaction between buoyancy field and velocity field through the gradient Richardson number. The turbulent transports are modelled as gradient transports, and the eddy diffusivity and eddy viscosity are assumed to depend on the gradient Richardson number. A sufficient condition for stability is shown to be Prt ⩾ 0.5, where Prt, is the turbulent Prandtl number (the ratio of eddy viscosity to eddy diffusivity), which condition seems to be always satisfied in real, stratified flows. This result refutes certain arguments found in the literature, which are in favor of the possibility of in- stability.

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