Abstracts - KTH Mechanics

154
Study of anisotropy in purely stratified and purely rotating
turbulence by orthogonal wavelets
Lukas Liechtenstein ∗ and Kai Schneider †
Rotating or stratified turbulence develops coherent structures which are generally
known as cigars and pancakes, respectively. This self organization of the flow is widely
observed in direct numerical simulations of homogeneous anisotropic turbulence 1 as
well as in laboratory experiments 2 .
The iso-surfaces of vorticity for a stratified (left) and rotating flow (right) shown
in Fig.1 illustrate the strongly anisotropic character of these coherent structures. A
quantitative analysis of their anisotropy has up to now not been performed, partly due
to the difficulty in defining a coherent structure. Attempts have been made by using
statistical measures, such as directional correlation length scales or directional Rossby
and Froude numbers 3 . However, a scaling law including the parameters determining
the anisotropy, namely f the Coriolis parameter, N the Brunt-Vaisala frequency and
ν the kinematic viscosity, have not been found.
An objective way to define coherent structures has been introduced 4 using an
orthogonal wavelet decomposition of vorticity. The coherent flow is reconstructed
from few strong wavelet coefficients, while the incoherent flow corresponding to the
majority of weak coefficients is uncorrelated and noise like. In the present paper
we apply the orthogonal wavelet decomposition to extract coherent vortices out of
rotating or stratified turbulence calculated by decaying DNS with Reynolds numbers
of Reλ ≈ 150. The orthogonal wavelet decomposition of a 3D-flow field creates by
definition coefficients with seven pre-defined directions. Due to this characteristic of
the coefficients, we then quantify the anisotropy of the coherent vortices by studying
the energy distribution and higher order moments in wavelet coefficient space.
Figure 1: Iso-surfaces of coherent vorticity for |ω| = 3.70,σ =0.92 computed at
resolution 256 3 . Left: stratified case, represented by 2.12 % of the wavelet coefficients.
Right: rotating case, represented by 2.25 % of the wavelet coefficients.
∗ MSNM-CNRS, IMT Château-Gombert, 38 rue Joliot Curie, F-13451 Marseille, FRANCE
† MSNM-CNRS & CMI Univ.de Provence, 39 rue Joliot Curie, F-13453 Marseille, FRANCE
1 see e.g. Liechtenstein et al., Journal of Turbulence 6, 24 (2005).
2 see e.g. C. Morize et al, Phys. Fluids 17 095105 (2005)
3 Godeferd and Staquet, J. Fluid Mech., 486, 115 (2003)
4 Farge et al, Phys. Rev. Lett., 87(5), 054501-1 (2001)