Boundary Conditions for Spectral Simulations of Atmospheric Boundary Layers

Sammanfattning: An atmospheric boundary layer (ABL) is generally a very high Reynolds number boundary layer over a fully rough surface that is influenced by different external forces. Numerical simulations of ABLs are typically demanding, particularly due to the high Reynolds numbers. Large eddy simulation (LES) where the grid filtered Navier--Stokes equations are solved together with a turbulence model for the subgrid-scale motions is the most accurate and widely used technique to date for ABLs. However, high Reynolds numbers, filtered equations and rough surfaces do not support the simple no-slip boundary conditions together with a feasible grid resolution. A paramount part for the performance of an ABL LES simulation therefore lies in the quality of approximate wall boundary conditions, so called wall models.     The vast majority of LES codes used for ABL simulations rely on spatial discretization methods with low order finite difference approximations for the derivatives in the inhomogeneous wall normal direction. Furthermore, the wall boundary conditions are typically chosen in a mesh-dependent, non-local way, relying on the finite differences formulation.     In this thesis we focus on solving the ABL LES equations with a fully (pseudo) spectral Fourier--Chebyshev code. We present how wall boundary conditions can be formulated through Robin boundary conditions and how to implement these in the normal-velocity normal-vorticity formulation that we solve. A new idea of specifying boundary conditions directly in Fourier space where also the turbulence intensity statistics can be controlled is presented and verified. The present results show that the Robin-type formulation is effective at least in near-equilibrium boundary layers.     The code and boundary conditions were tested in both low and high Reynolds number (open and full) channel flows of neutral and stable stratification. Results were validated with both low to moderate Reynolds number DNS statistics as well as with the logarithmic law. Our results indicate great potential for both the the new boundary condition formulation and the specific code implementation. Further analysis of more complex flow situations will show whether the Robin-type formulation will give similarly good results.