Boundary Layer, Urban Meteorology and Land-Surface Processes

A Boundary-Layer Scaling for Turbulent Katabatic Flow

Dr. Alan Shapiro

OU School of Meteorology

06 September 2013, 2:00 PM

National Weather Center, Room 5600
120 David L. Boren Blvd.
University of Oklahoma
Norman, OK

Scaling relationships are proposed for the turbulent katabatic flow of a stably stratified fluid down a uniformly cooled planar slope – the turbulent analogue of a Prandtl-type slope flow. By exploiting the structure of the governing differential equations in their boundary-layer form, we deduce scaled equations that involve only two non-dimensional parameters: the Prandtl number and a Reynolds number based on viscosity, diffusivity, Brunt–Väisälä frequency, and a surface buoyancy or buoyancy flux. An important property of the scaling hypothesis is that the slope angle is not an independent parameter, but only enters the problem through the Reynolds number and the scales for the dependent and independent variables. Preliminary validation tests of the scaling hypothesis are conducted using data from direct numerical simulations.

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