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Momentum and Energy Transfer in the Oceanic Law of the Wall Region

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  • 1 NOAA/NOS/CS Coastal Survey Development Laboratory, Silver Spring, Maryland
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Abstract

The law of the wall for turbulent boundary layer flow provides an analytic solution for the velocity profile and predictions of the bed shear stress. Most formulations and usages of the law of the wall require knowledge of the physical configuration of the seabed, which is input to the theory in the form of the z0 length scale, the putative height above the bed where the logarithmic velocity profile goes to zero. Models of current–wave interaction and sediment transport attempt to predict the value of z0 by modeling a physical length scale active near the bed, that is, the wave boundary layer height and height of particle saltation. Recent work with flow through forest canopies has put forth a different approach where the effect of drag on individual trees is to reduce the mean velocity momentum and increase the rate of dissipation of turbulent kinetic energy. Simulations with momentum-energy closure models show that a z0 is developed that depends on the amplitude of the drag coefficient and the areal extent of the drag elements. Applications of this technique to oceanographic models of sediment transport and wave–current interaction are possible by accounting for a momentum sink and enhanced energy dissipation due to these processes. Oceanic measurements of velocity profiles will not be able to demonstrate the validity of this approach. Direct measurements of energy dissipation and turbulence structure functions will be required to validate the approach.

Corresponding author address: Dr. Thomas F. Gross, NOAA/NOS/CS/CSDL/OP, 1315 East–West Highway, Silver Springs, MD 20910.

Email: tom.gross@noaa.gov

Abstract

The law of the wall for turbulent boundary layer flow provides an analytic solution for the velocity profile and predictions of the bed shear stress. Most formulations and usages of the law of the wall require knowledge of the physical configuration of the seabed, which is input to the theory in the form of the z0 length scale, the putative height above the bed where the logarithmic velocity profile goes to zero. Models of current–wave interaction and sediment transport attempt to predict the value of z0 by modeling a physical length scale active near the bed, that is, the wave boundary layer height and height of particle saltation. Recent work with flow through forest canopies has put forth a different approach where the effect of drag on individual trees is to reduce the mean velocity momentum and increase the rate of dissipation of turbulent kinetic energy. Simulations with momentum-energy closure models show that a z0 is developed that depends on the amplitude of the drag coefficient and the areal extent of the drag elements. Applications of this technique to oceanographic models of sediment transport and wave–current interaction are possible by accounting for a momentum sink and enhanced energy dissipation due to these processes. Oceanic measurements of velocity profiles will not be able to demonstrate the validity of this approach. Direct measurements of energy dissipation and turbulence structure functions will be required to validate the approach.

Corresponding author address: Dr. Thomas F. Gross, NOAA/NOS/CS/CSDL/OP, 1315 East–West Highway, Silver Springs, MD 20910.

Email: tom.gross@noaa.gov

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