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Published on: July 19, 2016
Sign-Indefinite Invariants Shape Turbulent Cascades
Michal Shavit1, Oliver Bühler1, Jalal Shatah1
1<a href="https://ror.org/037tm7f56">Courant Institute of Mathematical Sciences</a>, <a href="https://ror.org/0190ak572">New York University</a>, New York, New York 10012, USA.
Abstract:
We highlight a noncanonical yet natural choice of variables for an efficient derivation of a kinetic equation for the energy density in nonisotropic systems, including internal gravity waves on a vertical plane, inertial, and Rossby waves. The existence of a second quadratic invariant simplifies the kinetic equation and leads to extra conservation laws for resonant interactions. We analytically determine the scaling of the radial turbulent energy spectrum. Our findings suggest the existence of an inverse energy cascade of internal gravity waves, from small to large scales, in practically relevant scenarios.
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