Sparsity of Fourier mass of passively advected scalars in the Batchelor regime

Series
PDE Seminar
Time
Tuesday, October 8, 2024 - 3:30pm for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Manh Khang Huynh – Georgia Tech – mhuynh41@gatech.eduhttps://sites.google.com/view/hmkhang24/home
Organizer
Gong Chen

In this paper we propose a general dynamical mechanism that can lead to the failure of the Batchelor's mode-wise power spectrum law in passive scalar turbulence and hyperbolic dynamics, while the cumulative law remains true. Of technical interest, we also employ a novel method of power spectral variance to establish an exponential radial shell law for the Batchelor power spectrum. An accessible explanation of the power spectrum laws via harmonic analysis is also given.