A note on cascade flux laws for the stochastically-driven nonlinear Schrödinger equation
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arXiv
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| Format: | Preprint |
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2023
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| _version_ | 1866929272682184704 |
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| author | Bedrossian, Jacob |
| author_facet | Bedrossian, Jacob |
| contents | In this note we point out some simple sufficient (plausible) conditions for `turbulence' cascades in suitable limits of damped, stochastically-driven nonlinear Schrödinger equation in a $d$-dimensional periodic box. Simple characterizations of dissipation anomalies for the wave action and kinetic energy in rough analogy with those that arise for fully developed turbulence in the 2D Navier-Stokes equations are given and sufficient conditions are given which differentiate between a `weak' turbulence regime and a `strong' turbulence regime. The proofs are relatively straightforward once the statements are identified, but we hope that it might be useful for thinking about mathematically precise formulations of the statistically-stationary wave turbulence problem. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2306_03251 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | A note on cascade flux laws for the stochastically-driven nonlinear Schrödinger equation Bedrossian, Jacob Analysis of PDEs In this note we point out some simple sufficient (plausible) conditions for `turbulence' cascades in suitable limits of damped, stochastically-driven nonlinear Schrödinger equation in a $d$-dimensional periodic box. Simple characterizations of dissipation anomalies for the wave action and kinetic energy in rough analogy with those that arise for fully developed turbulence in the 2D Navier-Stokes equations are given and sufficient conditions are given which differentiate between a `weak' turbulence regime and a `strong' turbulence regime. The proofs are relatively straightforward once the statements are identified, but we hope that it might be useful for thinking about mathematically precise formulations of the statistically-stationary wave turbulence problem. |
| title | A note on cascade flux laws for the stochastically-driven nonlinear Schrödinger equation |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2306.03251 |