Viscous Flows of Stably Stratified Fluids Over Barriers

H. J. Haussling David W. Taylor Naval Ship Research and Development Center, Bethesda, Md. 20084

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Abstract

Numerical techniques for integrating the time-dependent Navier-Stokes equations, which have proven useful in the study of homogeneous viscous flows, have been extended to handle the flow of a stably stratified viscous fluid over an infinitely long ridge. Almost-steady-state solutions have been computed for various values of the Reynolds and Richardson numbers with two different far-field velocity profiles. A periodic solution is indicated in one case. Results show that the stratification tends to inhibit the development of recirculatory flow regions on the lee slope of the ridge but to encourage the formation of such regions on the upstream slope and downstream from the ridge (rotors). With increasing stratification the drag on the surface first decreases and then increases. A velocity shear tends to offset the upstream effects of stratification.

Abstract

Numerical techniques for integrating the time-dependent Navier-Stokes equations, which have proven useful in the study of homogeneous viscous flows, have been extended to handle the flow of a stably stratified viscous fluid over an infinitely long ridge. Almost-steady-state solutions have been computed for various values of the Reynolds and Richardson numbers with two different far-field velocity profiles. A periodic solution is indicated in one case. Results show that the stratification tends to inhibit the development of recirculatory flow regions on the lee slope of the ridge but to encourage the formation of such regions on the upstream slope and downstream from the ridge (rotors). With increasing stratification the drag on the surface first decreases and then increases. A velocity shear tends to offset the upstream effects of stratification.

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