" A filtering and wavelet formulation for incompressible turbulence"

by
Lewalle, J.

ABSTRACT

Gaussian filtering and Hermitian wavelet transforms lead to a new presentation of the Navier-Stokes equations by adding an independent variable. The diffusive part takes the form of an invariant translation toward smaller scales. The filtered pressure term is spatially local and is a superposition of generalized stresses at all scales larger than the scale of observation. Dominant contributors to the stresses are identified in the wavelet domain. The wavelet representation of Navier-Stokes is derived from the filtered version, and has a simple algebraic structure similar to its Fourier counterpart. All nonlinear terms are shown to involve spatial transport; within this scheme, spectral transfer involves triplets of scales, covering the entire spectrum with a concentration on nearby scales, consistently with cascade models. The physical content of the equations is interpreted anew from this perspective, and several lines of application are discussed.