Numerical Forcing of Horizontally-Homogeneous Stratified Turbulence

It is often desirable to study simulated turbulent flows at steady state even if the flow has no inherent source of turbulence kinetic energy. Doing so requires a numerical forcing scheme and various methods have been studied extensively for turbulence that is isotropic and homogeneous in three dimensions. A review of these existing schemes is used to form a framework for more general forcing methods. In this framework, the problem of developing a forcing scheme in Fourier space is abstracted into the two problems of (1) prescribing the spectrum of the input power and (2) specifying a force that has the desired characteristics and that adds energy to the flow with the correct spectrum. The framework is used to construct three forcing schemes for horizontally homogeneous and isotropic, vertically stratified turbulence. These schemes are implemented in large-eddy simulations and their characteristics analyzed. Which method is “best” depends on the purpose of the simulations, but the framework for specifying forcing schemes enables a systematic approach for identifying a method appropriate for a particular application