Transport and mixing of density in a continuously stratified shear layer

Abstract

Scalar transport and mixing by active turbulence in a high Reynolds number inhomogeneous stratified shear layer are investigated using three-dimensional Direct Numerical Simulation. Two density profiles are considered: (i) two layers of homogenous fluid with different density, namely the two-layer case, and (ii) a continuously stratified background ambient, namely the J_d case. The evolution of the mixing layer includes shear instability, formation of Kelvin–Helmholtz rollers, transition to turbulence, fully developed active turbulence, and, finally, decay toward a laminar state. In the J_d case, internal gravity waves carrying momentum and energy are observed to propagate away from the shear layer. Although different during the initial evolution, the eddy diffusivity and mixing efficiency when plotted as a function of buoyancy, Reynolds number takes similar values between the two cases later in time during the stage when turbulence decays. During this stage, the mixing efficiency computed based on the buoyancy flux is approximately 0.35, while the mixing efficiency estimated from the scalar dissipation is approximately 0.4. Parameterization of the eddy diffusivity in terms of Reynolds numbers and gradient Richardson number is also discussed.

Keywords:

• stratified shear layer
• turbulence
• internal waves

Acknowledgement

We are grateful for the support provided by ONR N000140710133, program monitor Ron Joslin, and ONR N000140810504, program monitor Scott Harper.