Farge (Ecole Normale Superieure) and Kai Schneider (Univesite
methods to analyze and compute turbulent flows
is characterized by its nonlinear and multiscale behaviour,
self-organization into coherent structures and a generic randomness.
The number of active spatial and temporal scales involved increases
with the Reynolds number, therefore it soon become prohibitive for
numerical simulation. However, observations show that for a given flow
realization these scales are not homogeneously distributed, neither in
space nor in time, which corresponds to the flow intermittency.
To be able to benefit from this property, a suitable representation of
flow should reflect the lacunarity of the fine scale activity, in both
space and time.
A prominent tool for multiscale decompositions are wavelets. A wavelet
a well localized oscillating smooth function, i.e. a wave packet, which
dilated and translated. The thus obtained wavelet family allows to
decompose a flow field into scale-space contributions from which it can
perfectly reconstructed. Note that for finer scales the physical support
of the basis functions is decreasing. The flow intermittency is
in the sparsity of the wavelet representation, i.e. only few
the strongest ones, are necessary to represent the dynamically active
of the flow.
The Coherent Vortex Simulation (CVS) approach we have proposed is based
the wavelet filtered Navier-Stokes equations. At each time step the
turbulent flow is split into two orthogonal parts, one corresponding to
coherent vortices which are kept, and the other to an incoherent
flow which is discarded.
In the talk we will present first applications of the CVS filter to data
computed by Direct Numerical Simulation (DNS) at high resolution (up to
2048^3 grid points). We will show that the coherent flow can be
represented by few wavelet modes only, which are sufficient to fully
reproduce the vorticity probability density function (PDF) and the
spectrum. The discarded incoherent background flow, which is
gaussian and decorrelated, corresponds to the turbulent enstrophy but
has a negligible contribution to the energy.
Finally, we present simulations of a time-developing turbulent mixing
layer where the CVS filter is applied at each time step. The results
CVS preserves the nonlinear dynamics of the flow, and that discarding
incoherent modes is sufficient to model turbulent dissipation.
Related publications can be downloaded from the following web page: