Introduction

Shear flows driven by Kelvin–Helmholtz instabilities such as mixing layers, wakes, and jets are of great interest because of their crucial roles in many practical applications. The simulation of shear flows is based on the numerical solution of the Navier–Stokes (NS) or Euler (EU) equations with appropriate boundary conditions. The important simulation issues that have to be addressed relate to the appropriate modeling of (1) the required open boundary conditions for flows developing in both space and time in finite-size computational domains, and (2) the unresolved subgrid-scale (SGS) flow features.

Appropriate boundary condition modeling is required because, in studying spatially developing flows, we can investigate only a portion of the flow – as in the laboratory experiments, where finite dimensions of the facilities are also unavoidable. We must ensure that the presence of artificial boundaries adequately bounds the computational domain without polluting the solution in a significant way: numerical boundary condition models must be consistent numerically and with the physical flow conditions to ensure well-posed solutions, and emulate the effects of virtually assumed flow events occurring outside of the computational domain. SGS models are needed that ensure the accurate computation of the inherently three-dimensional (3D) time-dependent details of the largest (grid-scale) resolved motions responsible for the primary jet transport and entrainment. At the high Reynolds number of practical interest, direct numerical simulation (DNS) cannot be used to resolve all scales of motion, and some SGS modeling becomes unavoidable to provide a mechanism by which dissipation of kinetic energy accumulated at high wave numbers can occur.