We investigate a Cartesian-mesh immersed-boundary formulation within an incompressible flow solver to simulate laminar and turbulent katabatic slope flows. As a proof-of-concept study, we consider four different immersed-boundary reconstruction schemes for imposing a Neumann-type boundary condition on the buoyancy field. Prandtl’s laminar solution is used to demonstrate the second-order accuracy of the numerical solutions globally. Direct numerical simulation of a turbulent katabatic flow is then performed to investigate the applicability of the proposed schemes in the turbulent regime by analyzing both first- and second-order statistics of turbulence. First-order statistics show that turbulent katabatic flow simulations are noticeably sensitive to the specifics of the immersed-boundary formulation. We find that reconstruction schemes that work well in the laminar regime may not perform as well when applied to a turbulent regime. Our proposed immersed-boundary reconstruction scheme agrees closely with the terrain-fitted reference solutions in both flow regimes.
This is an author-produced, peer-reviewed version of this article. The final, definitive version of this document can be found online at Boundary-Layer Meteorology, published by Springer. Copyright restrictions may apply. The final publication is available at doi: 10.1007/s10546-017-0252-3
Umphrey, Clancy; DeLeon, Ray; and Senocak, Inanc. (2017). "Direct Numerical Simulation of Turbulent Katabatic Slope Flows with an Immersed-Boundary Method". Boundary-Layer Meteorology, 164(3), 367-382.