Principles of Instability Saturation: Stable Perturbations in Hydrodynamic, Magnetized, and Thermal-Diffusion-Destabilized Shear Flows*

An overview of general instability-saturation principles, building on fusion plasma turbulence modeling, is presented. Various flow instabilities are shown to saturate via large-scale stable perturbations, instead of via a widely-assumed small-scale energy cascade. Hydrodynamic 3D Kelvin–Helmholtz instability (KHI) nonlinearly excites linearly stable perturbations, namely, eigenmodes conjugate to the inviscid KHI [1]. They are more efficient in 3D than in 2D in transporting momentum and energy from fluctuations to the mean flow. In 3D, they suppress vortex stretching and drive zonal jets. Magnetized KHI in 2D and 3D also saturate by exciting linearly stable perturbations, which sequester magnetic energy at large scales [2], drive a large-scale dynamo, and transport momentum [3] and turbulent energy via nonlinear mode coupling [4]. Double-diffusive centrifugal instability---where buoyancy forces opposing the unstable angular momentum gradient are tempered by thermal diffusion in stellar interiors---also saturates by exciting linearly viscously-damped zonal flows. An analytical closure model, based on nonlinear interactions among two unstable modes and zonal flow, predicts turbulent transport rates of momentum and heat, to which full nonlinear numerical simulations agree [5].