A mathematical framework for forcing turbulence applied to horizontally homogeneous stratified flow

It is often desirable to study turbulent flows at steady state even if the flow has no inherent source of turbulence kinetic energy. Doing so requires a forcing schema, and various methods applicable to laboratory experiments or numerical simulations have been studied extensively for turbulence that is isotropic and homogeneous in three dimensions. A review of existing schemata for simulations is used to form a framework for more general forcing methods. In this framework, the problem of developing a forcing method 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 methods for simulating horizontally homogeneous and isotropic, vertically stratified turbulence. They are implemented in a pseudo-spectral large-eddy simulations and their characteristics are analyzed. The framework is then used to characterize existing laboratory experiments. While no exact analogy can be drawn between forcing in esoteric pseudo-spectral simulations and forcing in physical experiments, there are many similarities. It is suggested that the forcing framework can be applied to predict and systematically test the effects of configuration choices made in the design of simulations and laboratory experiments. VC 2011 American Institute of Physics. [doi:10.1063/1.3599704]