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Home > News > Thesis defense > 2019 thesis defense

PhD defense ECL

Aleksandr Eremin

mardi 5 novembre 2019 à 14h00, amphi 203, bâtiment W1 à l’ECL

Aleksandr Eremin

Numerical implementation of the wave-turbulence closure in a rotating channel

A problem of turbulence in a rapidly rotating channel is investigated. The rapid rotation means that nonlinearity is dominated by rotation suggesting application of wave-turbulence theory.
The first part of the work is devoted to study of the wave-turbulence closure (WTC) model. We express the velocity field as a combination of inertial waveguide modes. In its turn, confinement implies discretization of the wall-normal component of the wave vector. The nonlinear transfer is dominated by resonant interactions of wave-vector triads. Viscosity is present via modal damping, which is the sum of two components: volumetric and wall damping.
The time evolution of the turbulence occurs in two phases: volumetric damping takes over initially dominating wall damping at time referred to as critical time. The critical time is insensitive to both
wall- and volumetric-damping coefficients, but varies significantly with the third parameter of the problem, which is the initial spectral width. Evolution of the spectra reveals the development of an inertial range whose exponent is found to be almost independent of the problem parameters. The transfer of energy parallel to the channel walls is found to be more efficient than in the cross-channel direction.
Comparison of the DNS and WTC model requires consistent initialization and construction of the spectral matrix at later times. For the latter, limited in number of realizations, we apply a method of averaging over annular regions in place of ensemble average. The results of comparison indicate that nonlinearity is not small enough and further reduction of the Rossby number would be needed to reach the regime of applicability of the wave-turbulence theory which is not achievable with the computer power available.

Jury :
S. Chibarro, Maître de Conférences, Institut d’Alembert, Paris
S. Galtier, Professeur, LPP, Palaiseau
B. Favier, CR CNRS, IRPHE, Marseille
N. Mordant, Professeur, LEGI, Grenoble
A. Cadiou, IR CNRS, LMFA, encadrante
F. Godeferd, DR CNRS, LMFA, encadrant
J. Scott, Professeur, LMFA, directeur de thèse


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