Boundary Layer, Urban Meteorology and Land-Surface Processes

New similarity model solutions for boundary-layer flows

Alan Shapiro
School of Meteorology,
University of Oklahoma, Norman, OK

14 February 2014, 2:00 PM

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

Following a review of the concept of self-similarity, similarity models are developed for two prototypical problems in geophysical fluid dynamics. The first problem is of unsteady free convection flows over a differentially cooled horizontal surface. The cooling, specified in terms of an imposed negative buoyancy or buoyancy flux, varies laterally as a step function with single step change. As thermal boundary layers develop on either side of the step change, an intrinsically unsteady, boundary-layer-like flow arises in the transition zone between them. The second problem is of wind-induced circulations in shallow coastal waters. The motion is induced in an initially resting sea by the sudden imposition of a surface wind stress. Attention is restricted to a particular form of seabed shape. In both problems the buoyancy frequency and turbulent mixing coefficients are considered constant, and the governing equations are boundary-layer-approximated forms of the Boussinesq equations of motion, thermal energy, and mass conservation. In both problems the similarity scalings yield propagations speeds and trajectories for local extrema in velocity and buoyancy fields, as well as power laws in time for the amplitudes of the local extrema. Of special interest is the impact of stratification and Prandtl number effects on the flows.

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