Master thesis defence by Jes Ravnbøl – Niels Bohr Institute - University of Copenhagen

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Master thesis defence by Jes Ravnbøl

Stochastic cascade models of two and three dimensional turbulence

Supervisor: Peter Ditlevsen

Abstract:
In the thesis, a pair of simple stochastic cascade models of 2 and 3 dimensional turbulence have been proposed and investigated. The two models are similar in structure, but differ with respect to their conserved integrals. The 2D model conserves energy and enstrophy like quantities in the unforced, inviscid limit, where as the 3D model conserves energy and helicity like quantities in the unforced, inviscid limit.

It has been shown from numerical simulations that the 3D model has an inertial range with a direct cascade of energy, and an energy spectrum displaying kolmogorov scaling.
Similarly, it has been shown from simulations, that the 2D model has two inertial ranges and two cascades: A direct cascade of enstropy and an inverse cascade of energy. The energy spectrum of the 2D model also shows Kolmogorov scalings for both the energy and enstrophy cascades.

Neither the 2D nor the 3D model show intermittency corrections to the scaling exponents of the structure functions.