Energy transfer, Intermittency and Mixing in Shear-Driven Stratified Turbulence

We investigate a stably stratified flow driven by deterministic Kolmogorov forcing that generates horizontal shear, using direct numerical simulations over a broad range of stratification strengths characterized by the Froude number $Fr$. As the stratification is progressively weakened, the flow exhibits a sequence of regimes: a buoyancy-dominated, strongly stratified regime, an intermediate regime characterized by Kelvin--Helmholtz instabilities and enhanced mixing, and a nearly isotropic turbulent regime. A key feature of the intermediate stratification range is the emergence of energetically significant vertically sheared horizontal flows (VSHFs), accompanied by a marked steepening of the reduced one-dimensional perpendicular kinetic energy spectra. The spectral energy transfer remains predominantly forward, although the perpendicular flux becomes negative at large horizontal scales; this apparent upscale transfer reflects anisotropic energy redistribution rather than a true inverse cascade. Strong stratification enhances intermittency, producing increasingly non-Gaussian vertical velocity fluctuations and large kurtosis associated with localized vertical bursts. The energetics-based mixing coefficient remains of order $10^{-1}$ over the parameter range investigated, with a modest enhancement near the Kelvin--Helmholtz instability regime.