Spectral analysis of the nonlinear terms in stratified wall turbulence*

The quadratic nonlinearity in the Navier-Stokes equations redistributes energy across scales and plays a central role in the dynamics of wall turbulence. Introducing stable stratification can have a qualitative impact on the flow, even in the weakly stratified regime. In this work, we adapt a recent spectral analysis of the nonlinear terms that was performed for isothermal flows (Morra et al., J. Fluid Mech. (2021), vol. 907, A24) to include the influence of buoyancy. The data are obtained from direct numerical simulations of channel flow, for multiple Richardson numbers. We report the cross-spectral densities of the nonlinear terms, both in the momentum and scalar transport equations. The results are discussed with reference to the dynamics of the underlying stratified flow.