Shear-free, inhomogeneous turbulence in a stably stratified fluid. Part 2. A wave–turbulence decomposition

Abstract

In Hass & Lele (2026 J. Fluid Mech. 1037, A20), we looked at the statistical structure (self-similarity) and entrainment rate of a shear-free turbulent layer bounded by a net zero momentum source layer above and a stable density interface below and found agreement with oscillating grid turbulence experiments. However, interfacial waves supported by the stable stratification make quantification of variances in the near-interfacial region ambiguous. In the present paper we propose a decomposition of the fluctuating fields based on eigenmodes of the linearized equations. Evidence that a linear model is appropriate is provided by the wavenumber–frequency spectra for low Froude number simulations. Using the decomposition, a detailed analysis of the wave–turbulence statistics, including budgets of kinetic and potential energy, is conducted. An energy conversion pathway is uncovered consistent with the internal wave-breaking entrainment mechanism proposed by Hannoun & List (1988 J. Fluid Mech. 189, 211–234), Fernando & Hunt (1997 J. Fluid Mech. 347, 197–234), and McGrath et al. (1997 J. Fluid Mech. 347, 235–261). A locally defined mixing or flux coefficient upper Gamma equals chi divided by epsilon Γ = χ / ϵ $\varGamma =\chi /\epsilon$ scales with the (local) turbulent Froude number in the same way as in homogeneous turbulence simulations where transport is identically zero. Finally, we connect our spatially inhomogeneous simulations to the strongly stratified turbulence theory demonstrating that the parameter regime required by the theory is, in principle, accessible for sufficiently energetic forcing, but is not realized in our simulations.