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

Fluid Dynamics