Author: Adrian E. Fraser
Requested Type: Poster
Submitted: 2016-02-15 13:37:21
Co-authors: P.W. Terry, E.G. Zweibel
University of Wisconsin-Madison
1150 University Ave
Madison, WI 53706
Linearly stable modes at all scales can play an important role in instability saturation and turbulent transport. Stable modes at nominal inertial scales provide a mechanism for energy transfer from fluctuations back to the equilibrium, significantly modifying the usual picture of an energy cascade from large instability-driven to small dissipative scales. The importance of turbulent cascades and instability saturation mechanisms in astrophysical and fusion systems motivates investigations of the role of stable modes. This work considers stable modes in Kelvin-Helmholtz (KH) instability to determine their effect on the turbulence.
The KH instability is driven by shear flow. This strong inhomogeneity complicates investigations of the role of stable modes. Previous work focused on weakly inhomogeneous systems where the linear modes are expressed as eigenvectors of the Fourier-transformed governing equations and span the nonlinear solutions. In systems with strong inhomogeneity, e.g. shear, the linear modes are generally eigenfunctions of the linear equations with structure in the direction of the inhomogeneity. The functions may not form a complete basis, leading to the possibility of nonlinear energy transfer to other structures. In this calculation, an eigenvector representation is recovered by considering a two-dimensional system with incompressible flow whose piecewise linear profile localizes the curvature to two points. This allows a description of the strongly inhomogeneous system that is similar to previously studied, weakly inhomogeneous systems where stable modes contributed significantly to saturation. A parameter is evaluated that quantifies the magnitude of energy transfer from unstable to stable modes, and it is concluded that stable modes play an important role in the saturation of the KH instability. This suggests the possible need for a correction to transport models in turbulent systems with strongly sheared flow.