Wave number space dynamics of enstrophy cascade in a forced two-dimensional turbulence

Abstract

Enstrophy cascade in two‐dimensional turbulence is studied numerically together with dynamics of a passive scalar and the first Lyapunov vector. (i) the vorticity field is decomposed into elliptic (e) and hyperbolic (h) regions by using Weiss’ conditional sampling method. The k −1 law of the enstrophy spectrum associated with the h region extends with the dissipation wave number, while the jumplike spectrum associated with the e region does not. Asymptotic recovery of the k −1 law is thereby suggested in the inviscid limit. Weiss’ decomposition is also applied to the enstrophy spectral flux to elucidate the interaction between e and h regions. (ii) Temporally intermittent nature of the enstrophy cascade is revealed on the (k‐t) plane by tracing the wave number with active transfer. Active(inactive) periods are related with a higher(lower) enstrophy dissipation rate. (iii) the wave number characteristic to the enstrophy spectrum of the first Lyapunov vector is also traced on the (k‐t) plane. When the peak wave number lies in the inertial subrange, enstrophy dissipation is likely to be large.