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

• Published in: Quarterly journal of the Royal Meteorological Society Vol. 140; no. 683; pp. 2017 - 2022
• Main Authors: Sescu, Adrian, Meneveau, Charles
• Format: Journal Article
• Language: English
• Published: Chichester, UK John Wiley & Sons, Ltd 01.07.2014; Wiley; Wiley Subscription Services, Inc
• Subjects: Algorithms; Atmospheric boundary layer; Boundary layer; Boundary layers; Brackish; Control algorithms; Control theory; Convection, turbulence, diffusion. Boundary layer structure and dynamics; Cooling; Coriolis force; Earth, ocean, space; Exact sciences and technology; External geophysics; Geophysics. Techniques, methods, instrumentation and models; Heating; Large eddy simulation; large‐eddy simulations; Marine; Mathematical analysis; Meteorology; Simulation; Statistics; Temperature distribution; thermal stratification; Wind; Wind farms; algorithms; Temperature distribution; large-eddy simulations; Large eddy simulation; Stationary state; thermal stratification; Atmospheric boundary layer; digital simulation
• ISSN: 0035-9009; 1477-870X
• DOI: 10.1002/qj.2266

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.