Mode coupling, energy transfer, and saturation models of Kelvin-Helmholtz-instability-driven turbulence

Turbulence driven by instability saturates, apart from decay by quasilinear flattening, in a way fundamentally different from the common assumption that all the unstable mode energy cascades to small scales. The difference arises from the nonlinearity that transfers unstable mode energy to the large-scale linearly stable modes, as is shown here for Kelvin-Helmholtz-instability-driven turbulence in both 2 and 3 dimensions. In addition to the traditional diagnostic of scale-interaction between flow and magnetic fields, nonlinear energy transfer between non-orthogonal eigenmodes of shear flow, for the first time, is computed. Examination of three-eigenmode interactions exposes two dominant channels of energy transfer between the unstable and stable modes, which are labeled jointly as discrete modes here. These discrete modes at different wavenumbers interact, channeling nearly 50% of nonlinear energy transfer to the stable modes; the other 40% is transferred when continuum (c) modes mediate three-wave process. A small percentage of total energy transfer is lost to small-scale cascade via c-c mode interactions. With these, a truncated set of equations capturing the dominant energy balance is derived and a solution using a statistical closure approximation is sought.