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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.
Physical Review Letters
|July 23, 2024
Summary
This study reveals an inverse energy cascade in internal gravity waves, moving energy from small to large scales. This finding simplifies kinetic equations and offers new conservation laws for turbulent systems.
Area of Science:
- Fluid dynamics
- Geophysics
- Plasma physics
Background:
- Nonisotropic systems exhibit complex energy dynamics.
- Understanding wave interactions is crucial for modeling turbulent phenomena.
- Kinetic equations describe energy transfer in complex systems.
Purpose of the Study:
- To derive an efficient kinetic equation for energy density in nonisotropic systems.
- To investigate the role of quadratic invariants in simplifying kinetic equations.
- To determine the scaling of the radial turbulent energy spectrum.
Main Methods:
- Utilized a noncanonical choice of variables for efficient derivation.
- Incorporated a second quadratic invariant to simplify the kinetic equation.
- Analytically determined the scaling of the radial turbulent energy spectrum.
Main Results:
- Developed a simplified kinetic equation for energy density.
- Identified extra conservation laws for resonant interactions.
- Determined the radial turbulent energy spectrum scaling.
Conclusions:
- Internal gravity waves exhibit an inverse energy cascade from small to large scales.
- The findings are relevant for practical scenarios involving wave turbulence.
- The simplified kinetic equation offers new insights into nonisotropic systems.
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