Dependence of small-scale energetics on large scales in turbulent flows

Abstract

In a turbulent flow, small- and large-scale fluid motions are coupled. In this work, we investigate the small-scale response to large-scale fluctuations in turbulent flows and discuss the implications on large eddy simulation (LES) wall modelling. The interscale interaction in wall-bounded flows was previously parameterized in the predictive inner–outer (PIO) model, where the amplitude of the small scales responds linearly to the large-scale fluctuations. While this assumed linearity is valid in the viscous sublayer, it is an insufficient approximation of the true interscale interaction in wall-normal distances within the buffer layer and above. Within these regions, a piecewise linear response function (piecewise with respect to large-scale fluctuations being positive or negative) appears to be more appropriate. In addition to proposing a new response function, we relate the amplitude modulation process to the Townsend attached eddy hypothesis. This connection allows us to make theoretical predictions on the model parameters within the PIO model. We use these parameters to apply the PIO model to wall-modelled LES. Further, we present empirical evidence of amplitude modulation in isotropic turbulence. The evidence suggests that the existence of nonlinear interscale interactions in the form of amplitude modulation does not rely on the presence of a non-penetrating boundary, but on the presence of a range of viscosity-dominated scales and a range of inertial-dominated scales.