Observations reveal that shear instability-induced turbulences occur in the ocean interior, particularly in the stratified shear flows. Studies further reveal that the resulted diffusivity depends on more parameters than the single Richardson number (Ri), indicating that the widely used Ri-dependent diffusivity parameterizations need to be improved. Therefore, we proposes an energy-constrained framework and hence a profile parameterization for both the turbulent kinetic energy dissipation rate (ε) and vertical diffusivity (κ) of the Kelvin–Helmholtz (KH) instability-induced turbulence, for the regime of 0<Ri<0.25. The energy-constrained framework posits ε as proportional to available kinetic energy and turbulence evolution time scale. κ is determinable by background flow velocity, buoyancy frequency, shear, and Richardson number. Notably, unlike conventional methods that parameterize for single grid points layer by layer, our approach parameterizes the turbulence mixing for the grid points within the turbulent vertical penetration layer by giving a profile of diffusivity. Therefore, it is termed the energy-constrained profile parameterization (EPP). EPP aligns well with both large eddy simulation results and available turbulence observations in the equatorial Pacific, outperforming existing parameterizations.

profile parameterization,,energy-constrained,shear instability,mixing,ocean mixing,model