The effect of velocity field forcing techniques on the Karman–Howarth equation

Abstract

Many velocity field forcing methods exist to simulate isotropic turbulence, but no in-depth analysis of the effects that these methods have on the generated turbulence has been performed. This work contains such a detailed study. It focuses on Lundgren’s linear and Alvelius’ spectral velocity forcing methods. Based on the constraints imposed on their associated forcing terms, these two are representative of the numerous forcing methods available in the literature. This study is conducted in the context of the Karman–Howarth equation, which, as a consequence of velocity forcing, has a source term appended to it. The expressions for the forcing method-specific Karman–Howarth source terms are derived, and their effect on key turbulent metrics, e.g. structure functions and spectra, is investigated. The behaviour of these source terms determines the state to which all turbulent metrics evolve, allowing for the differences noted between linearly and spectrally forced turbulent fields to be explained.