Abstract
We shall discuss the development of low-order models describing nonlinear phenomena in geophysical fluid dynamics (GFD) and turbulence. Difficulties in these fields, as is well known, are caused by the infinite number of degrees of freedom combined with the nonlinearity of equations. One of the possible ways to overcome them is to replace an object of infinite number of degrees of freedom with a finite dimensional one, but described by nonlinear equations analogous to those of fluid dynamics. The question of what this analogy should be was addressed in the pioneering works of Lorenz [1,2] and Obukhov [3,4], and the conclusion was that models pretending to describe fluid dynamics should be quadratically nonlinear finite systems of ordinary differential equations, possessing the energy integral and conserving the phase volume (in the absence of forcing and dissipation), being what Obukhov called the hydrodynamic type systems. Those are the systems this paper deals with and they will be in the form of superpositions of simplest ones, that is composed of similar elementary blocks.
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Gluhovsky, A. (1993). Modeling Turbulence by Systems of Coupled Gyrostats. In: Fitzmaurice, N., Gurarie, D., McCaughan, F., Woyczyński, W.A. (eds) Nonlinear Waves and Weak Turbulence. Progress in Nonlinear Differential Equations and Their Applications, vol 11. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-1-4612-0331-5_10
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DOI: https://doi.org/10.1007/978-1-4612-0331-5_10
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