Transient energy transfer and cascade analysis for stratified turbulent channel flows

Abstract

A comprehensive and fine-grained transient analysis of the kinetic budget equation in the spectral and spatial domains for channel flow subjected to stable stratification is performed, through a series of large eddy simulations (LES) at a bulk Reynolds number of 2200 and for Froude numbers of 0.5, 2.0, 4.5 and 6.8, thereby covering a range of stratification strengths from high to low. The dynamic Smagorinsky eddy viscosity-based sub-grid scale (SGS) model is used for closure. Validation of the methodology is carried out by comparing the turbulent flow LES results to previously published channel flow results. The analysis is focussed on the effect of stratification on the energy cascade process of an initially turbulent flow in a channel configuration. The terms in the kinetic budget equation, in the homogeneous and inhomogeneous directions, are compared for different Froude numbers to assess the effects of weak and strong stratification on turbulent statistics. Transient results are plotted to highlight the role played by different terms in the budget equation and to understand the formation of the gravity waves in the core or outer regions of the wall-bounded flow in the presence of stratification. The energy cascade reveals some interesting observations about the functions of viscous diffusion, pressure diffusion, and inhomogeneous energy transfer in the initial phase of the development of flow, which in turn helps to explain the stationary waves observed in the presence of strong stratification.