Inverse Cascade and Rossby Waves in the Kolmogorov Flow on the Beta-Plane View Full Text


Ontology type: schema:Chapter     


Chapter Info

DATE

1998

AUTHORS

B. Villone , B. Legras , U. Frisch

ABSTRACT

Large-scale geophysical flows are subject to the competing effects of quasi-two-dimensional turbulence and Rossby waves. It is well known from phenomenological arguments and numerical simulations that the inverse cascade which characterizes the large-scale dynamics of two-dimensional turbulence can be halted by Rossby wave dispersion. A particular example for which this effect is amenable to a detailed numerical and theoretical understanding is the supercritical large-scale dynamics of the Kolmogorov flow on the β-plane. This flow is governed by the one-dimensional “β-Cahn—Hillird” equation [1], obtained by multiscale technique, with cubic non linearity 1 In the absence of β, the solutions to this equation live essentially within a slow manifold of soliton-like solutions characterized by alternating kinks and antikinks. With periodic boundary conditions of period L, fixed points are obtained with N pairs of regularly spaced kinks and antikinks. These fixed points are unstable saddle points of a Lyapunov functional excepted for the gravest mode N = 1 which is a stable absolute minimum. The temporal evolution is a succession of annihilations of kinks and antikinks, leading eventually to the gravest mode (see, e.g., Ref. [2]). The uniqueness of the final solution is ensured by the existence of a Lyapunov functional. More... »

PAGES

457-460

Book

TITLE

Advances in Turbulence VII

ISBN

978-94-010-6151-3
978-94-011-5118-4

Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/978-94-011-5118-4_114

DOI

http://dx.doi.org/10.1007/978-94-011-5118-4_114

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1038681081


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