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We present numerical simulations of the three-dimensional Galerkin truncatedincompressible Euler equations that we integrate in time while regularizing thesolution by applying a wavelet-based denoising. For this, at each time step,the vorticity filed is decomposed into wavelet coefficients, that are splitinto strong and weak coefficients, before reconstructing them in physical spaceto obtain the corresponding coherent and incoherent vorticities. Bothcomponents are multiscale and orthogonal to each other. Then, by using theBiot--Savart kernel, one obtains the coherent and incoherent velocities.Advancing the coherent flow in time, while filtering out the noise-likeincoherent flow, models turbulent dissipation and corresponds to an adaptiveregularization. In order to track the flow evolution in both space and scale, asafety zone is added in wavelet coefficient space to the coherent waveletcoefficients. It is shown that the coherent flow indeed exhibits anintermittent nonlinear dynamics and a $k^{-5/3}$ energy spectrum, where $k$ isthe wavenumber, characteristic of { three-dimensional homogeneous isotropicturbulence}. Finally, we compare the dynamical and statistical properties ofEuler flows subjected to four kinds of regularizations: dissipative(Navier--Stokes), hyperdissipative (iterated Laplacian), dispersive(Euler--Voigt) and wavelet-based regularizations.

Wavelet-based regularization of the Galerkin truncated three-dimensional incompressible Euler flows