A control algorithm for statistically stationary large-eddy simulations of thermally stratified boundary layers

Abstract

Large-eddy simulations (LESs) of thermally stratified atmospheric boundary layers (ABLs) typically involve imposed heating or cooling at the ground surface, leading to slowly varying temperature distributions in the domain. While for some applications an interpretation of the resulting fields as quasi-stationary is possible, there are certain applications for which the slow temporal variations are a serious drawback. An example occurs when using LES for a systematic analysis of effects of large wind farms on atmospheric heat fluxes, where analysis of stationary statistics greatly facilitates understanding. In order to obtain statistically stationary temperature fields in LES of thermally stratified boundary layers, in this article we introduce a control algorithm, and test its effectiveness for various levels of surface heating and cooling. The method uses a ‘proportional-integral’ (PI) control algorithm, designed to keep constant the horizontally averaged temperature in a computational fringe layer placed above the ABL region of interest. For flows driven by a geostrophic wind, another controller is used to adjust the mean flow angle within the ABL at a specified height to achieve a prescribed direction. This is done by controlling a source term (in the form of an additional Coriolis force) in the momentum equations. This term is deactivated once the statistics become stationary and the flow aligns with the desired direction. Together, these two control schemes enable very long-time simulations of thermally stratified heated or cooled boundary layers displaying fully stationary distributions of mean velocity and temperature.