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

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 field is decomposed into wavelet coefficients, which 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.

Structure of sheared and rotating turbulence: Multiscale statistics of Lagrangian and Eulerian accelerations and passive scalar dynamics.

The acceleration statistics of sheared and rotating homogeneous turbulence are studied using direct numerical simulation results. The statistical properties of Lagrangian and Eulerian accelerations are considered together with the influence of the rotation to shear ratio, as well as the scale dependence of their statistics. The probability density functions (pdfs) of both Lagrangian and Eulerian accelerations show a strong and similar dependence on the rotation to shear ratio.

Small-scale anisotropic intermittency in magnetohydrodynamic turbulence at low magnetic Reynolds numbers.

Small-scale anisotropic intermittency is examined in three-dimensional incompressible magnetohydrodynamic turbulence subjected to a uniformly imposed magnetic field. Orthonormal wavelet analyses are applied to direct numerical simulation data at moderate Reynolds number and for different interaction parameters. The magnetic Reynolds number is sufficiently low such that the quasistatic approximation can be applied.

Influence of initial mean helicity on homogeneous turbulent shear flow.

Helicity statistics are studied in homogeneous turbulent shear flow. Initial mean helicity is imposed on an isotropic turbulence field using a decomposition of the flow into complex-valued helical waves. The initial decay of the turbulent kinetic energy is weakened in the presence of strong mean helicity, consistent with an analytic analysis of the spectral tensor of velocity correlations.

Energy dissipating structures produced by walls in two-dimensional flows at vanishing viscosity.

We perform numerical experiments of a dipole crashing into a wall, a generic event in two-dimensional incompressible flows with solid boundaries. The Reynolds number (Re) is varied from 985 to 7880, and no-slip boundary conditions are approximated by Navier boundary conditions with a slip length proportional to Re(-1). Energy dissipation is shown to first set up within a vorticity sheet of thickness proportional to Re(-1) in the neighborhood of the wall, and to continue as this sheet rolls up into a spiral and detaches from the wall.

Intermittency and scale-dependent statistics in fully developed turbulence.

Fully developed homogeneous isotropic turbulent fields, computed by direct numerical simulation, are compared to divergence-free random fields having the same energy spectrum and either the same helicity spectrum as that of the turbulent data, or vanishing helicity. We show that the scale-dependent velocity flatness quantifies the spatial variability of the energy spectrum. The flatness exhibits a substantial increase at small scales for the turbulent field, but remains constant for the random fields.

Decaying two-dimensional turbulence in a circular container.

We present direct numerical simulations of two-dimensional decaying turbulence at initial Reynolds number 5 x 10(4) in a circular container with no-slip boundary conditions. Starting with random initial conditions the flow rapidly exhibits self-organization into coherent vortices. We study their formation and the role of the viscous boundary layer on the production and decay of integral quantities.

Geometrical alignment properties in Fourier- and wavelet-filtered statistically stationary two-dimensional turbulence.

In this paper we compare the geometrical alignment properties of Fourier- and wavelet-filtered statistically stationary two-dimensional turbulence. The goal is to study the preferential alignment angle of vorticity gradient with respect to the compressing eigenvector of the rate-of-strain tensor, and use this quantity as a measure of how the two filtering methods affect the small scale geometric structure of the flow. The principal result is that for the case of the incoherent part obtained through wavelet filtering the probability density function of this angle is flat, meaning that this field is effectively unstructured and therefore dynamically passive.