A spectral framework for constraining anisotropic eddy viscosity - I

Abstract

Eddy viscosity is employed throughout the majority of numerical fluid dynamical models, and has been the subject of a vigorous body of research spanning a variety of disciplines. It has long been recognized that the proper description of eddy viscosity uses tensor mathematics, but in practice it is almost always employed as a scalar due to uncertainty about how to constrain the extra degrees of freedom and physical properties of its tensorial form. This talk will introduce techniques from outside the realm of geophysical fluid dynamics that allow us to consider the eddy viscosity tensor using its eigenvalues and eigenvectors, establishing a new framework by which tensorial eddy viscosity can be tested. This is made possible by a careful analysis of an operation called tensor unrolling, which casts the eigenvalue problem for a fourth-order tensor into a more familiar matrix-vector form, whereby it becomes far easier to understand and manipulate. New constraints are established for the e...