Applied Math Seminar

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Inverse cascade spectrum of gravity waves in the presence of condensate: Numerical results and analytical explanation

Speaker: Alex Korotkevich, U New Mexico

Location: Warren Weaver Hall 1302

Date: Friday, March 10, 2023, 2:30 p.m.

Synopsis:

Turbulence of gravity waves (waves with domination of gravity force, capillary effects are
neglected) on the surface of sea or ocean is described by Hasselmann's waves kinetic equation. It is
used for wave forecasting: prediction of evolution of waves distribution function dynamics over
time. Some applications of it to practical problems will be discussed in introduction of the talk.
Verification of Hasselmann's waves kinetic equation together with understanding of its range of
applicability are important problems which motivate numerous numerical and laboratory experiments.
In many of such experiments formation of strong long wave background is observed. Also, observed
waves spectra in some cases are different from the ones predicted by the Waves Turbulence Theory
based on Hasselmann's waves kinetic equation and introduced by V.E. Zakharov in late 60's. Results
of massive numerical experiment (arXiv:2211.16567) are considered and explained analytically. We
used scale separation technique together with diffusion approximation in the space of wave vectors
to derive a new inverse cascade spectrum slope which is in good agreement with numerical results.