Random forcing of three-dimensional homogeneous turbulence

Abstract

A method of using a fully random force to numerically generate statistically stationary homogeneous turbulence has been developed. The forcing is implemented in spectral space where it is concentrated at small wave numbers. Hence, the power input is introduced into the flow at large scales. The randomness in time makes the force neutral, in the sense that it does not directly correlate with any of the time scales of the turbulent flow, and it also makes the power input determined solely by the force-force correlation. This means that it is possible to generate different desirable turbulence states, such as axisymmetric turbulence, where the degree of anisotropy of the forcing can be chosen a priori through forcing parameters. In particular, the total amount of power input from the forcing can be set to balance a desired dissipation at a statistically stationary state. In order to only get a contribution from the force-force correlation to the input power in the discrete equations, the force is determined so that the velocity-force correlation vanishes for each Fourier mode. In direct numerical simulations (DNS) of forced isotropic turbulence, universality of the small scales is shown for the kinetic energy spectrum at different Reynolds numbers and the velocity derivative skewness obtains the value −0.5. The forcing method is used in a large eddy simulation(LES), where it is compared with a simulation of decaying turbulence to show the importance of having a statistically stationary flow if well known inertial laws are to be recovered at moderate Reynolds numbers.