"On the effect of boundary conditions on the
multifractal statistics of incompressible turbulence"
In an earlier paper, the multifractal spectrum has been related to the
history and dynamics of the Navier-Stokes flow in an infinite domain.
The effect of boundary conditions is now included. The difficulty
of distributing the effect of boundary conditions among the wavelet
components of the velocity and pressure fields is overcome through
the use of Green's functions. The wavelet transforms of Green's
functions for the diffusion and Poisson equations are calculated,
and are found to be wavelets and combinations of wavelets. In consequence,
the integral equation for the velocity field in the (Gaussian) wavelet
representation is easily modified, and the formal construction of D_q
proceeds as in the case of free turbulence.
IMA Conference on Multiscale Stochastic Processes
Analyzed using multifractals and wavelets,
Cambridge UK, March 29-31, 1993.
Unpublished. The main results appear in appendix to my
Jacques Lewalle, email@example.com