A Theory for Multiresolution Signal Decomposition: The Wavelet Representation
IEEE Transactions on Pattern Analysis and Machine Intelligence
Coherent structures in random media and wavelets
Proceedings of a NATO advanced research workshop on New trends in nonlinear dynamics : nonvariational aspects: nonvariational aspects
On the size and smoothness of solutions to nonlinear hyperbolic conservation laws
SIAM Journal on Mathematical Analysis
Composite wavelet bases for operator equations
Mathematics of Computation
Element-by-Element Construction of Wavelets Satisfying Stability and Moment Conditions
SIAM Journal on Numerical Analysis
Wavelet Methods for Second-Order Elliptic Problems, Preconditioning, and Adaptivity
SIAM Journal on Scientific Computing
Adaptive wavelet methods for elliptic operator equations: convergence rates
Mathematics of Computation
Wavelet bases in H(div) and H(curl)
Mathematics of Computation
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In this paper we study the application of divergence-free wavelet bases for the analysis of incompressible turbulent flows and perform several experiments. In particular, we analyze various nominally incompressible fields and study the influence of compressible perturbations due to experimental and computational errors. In addition, we investigate the multiscale structure of modes obtained from the Proper Orthogonal Decomposition (POD) method. Finally, we study the divergence-free wavelet compression of turbulent flow data and present results on the energy recovery. Moreover, we utilize wavelet decompositions to investigate the regularity of turbulent flow fields in certain non-classical function spaces, namely Besov spaces. In our experiments, we have observed significantly higher Besov regularity than Sobolev regularity, which indicates the potential for adaptive numerical simulations.