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A maximum entropy approach to the interaction between small and large scales in two‐dimensional turbulence
Author(s) -
Verkley Wim T. M.,
Severijns Camiel A.,
Zwaal Boudewijn A.
Publication year - 2019
Publication title -
quarterly journal of the royal meteorological society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.744
H-Index - 143
eISSN - 1477-870X
pISSN - 0035-9009
DOI - 10.1002/qj.3554
Subject(s) - enstrophy , turbulence , statistical physics , principle of maximum entropy , wavenumber , entropy (arrow of time) , length scale , scale (ratio) , physics , mathematics , mechanics , vorticity , thermodynamics , vortex , statistics , quantum mechanics , optics
A numerical model of a fluid dynamical system is necessarily limited to scales of motion down to a given minimum length‐scale. All interactions with smaller scales have to be dealt with in some approximate way by methods that are called parametrizations. The problem can be studied particularly well in a system that is geophysically relevant yet relatively simple and therefore amenable to very high‐resolution modelling: two‐dimensional turbulence. By using spectral models with high and low spatial resolutions and concentrating on the energy and enstrophy and their time‐derivatives as functions of wavenumber, we study the process of interaction between small and large scales. We show that this interaction can be modelled quite well by representing the small scales by means of a probability density function that is based on the principle of maximum entropy and on constraints on their energy and enstrophy as well as their time‐derivatives. Two sets of constraints are discussed and assessed in terms of the performance of their corresponding parametrizations.