A Cartesian Immersed Boundary Method to Simulate Stably Stratified Turbulent Flows

Abstract

Turbulent katabatic (downslope) flow under stable stratification over a cool surface remains a poorly understood subject, which finds application in geophysical flows. This work investigates an immersed boundary (IB) formulation within a multi-graphics-processing-unit (GPU) parallel incompressible flow solver to impose velocity and heat flux boundary conditions to simulate fundamental katabatic flows. Prandtl\u27s analytical solution for laminar katabatic flow is used to develop an IB formulation to impose heat flux boundary conditions, and to assess its formal order of accuracy. Direct numerical simulation of turbulent katabatic flow is then performed to investigate the applicability of proposed schemes in the turbulent regime. Results from first order statistics show that turbulent katabatic flow simulations are sensitive to the specifics of the IB formulation, and IB schemes that work well for the laminar regime do not readily apply to the turbulent regime. A reconstruction scheme is proposed that performs well in both the laminar and turbulent regime