Boundary Layer, Urban Meteorology and Land-Surface Processes

On the lower boundary condition for pressure in numerical simulations of boundary layer flows driven by surface buoyancy variations

Dr. Alan Shapiro
OU School of Meteorology

17 October 2014, 3:00 PM

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

Computational fluid dynamics codes used in studies of atmospheric boundary layer flows commonly solve Boussinesq- or anelastic-approximated governing equations with the pressure or a pressure-like variable diagnosed from a Poisson-type elliptic equation. In many of these codes the lower pressure condition is the inhomogeneous Neumann condition (INC) that results from imposing the impermeability condition in the vertical equation of motion. This INC contains contributions from buoyancy and the vertical stress. However, a simpler lower boundary condition, the homogeneous Neumann condition (HNC) has also found application in some meteorological models and engineering codes. Comparisons of HNC and INC solutions against benchmark solutions have been reported in the engineering literature, primarily for hydrodynamical flows. There one finds intriguing (i.e., contradictory) results, with some investigators reporting only minor differences between the HNC and INC solutions, but others reporting a spurious numerical boundary layer in the HNC solution that seriously degrades the accuracy of quantities of interest (e.g., net force on an obstacle).

The purpose of the present investigation is to assess the accuracy of HNC and INC solutions for circulations driven by thermal perturbations of the lower boundary, a scenario of interest in boundary-layer meteorology. The benchmark solution is an array of counter-rotating thermal convection rolls described analytically by a solution of the linearized steady-state Boussinesq governing equations where the surface buoyancy is a specified square-wave (spatially periodic with step-function waveform). The tests show that for closely spaced step changes both the HNC and INC solutions are in excellent agreement with the analytical solution. However, for the more isolated step changes, the HNC flow breaks down into a chaotic state far removed from the correct solution.

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