We revisit the issue of whether thermal fluctuations are relevant for incompressible fluid
turbulence and estimate the scale at which they become important. As anticipated by …

Adaptive Galerkin numerical schemes integrate time-dependent partial differential equations
with a finite number of basis functions, and a subset of them is selected at each time step …

We present an overview of the current status in the development of a two-point spectral
closure model for turbulent flows, known as the local wavenumber (LWN) model. The model …

The long-time solutions of the Galerkin-truncated three-dimensional, incompressible Euler
equation relax to an absolute equilibrium as a consequence of phase space and kinetic …

The effects of Mach number on the spectra and statistics of stationary compressible
homogeneous shear turbulence (HST) are studied using numerical simulations in a …

Finite-dimensional, inviscid equations of hydrodynamics, obtained through a Fourier-
Galerkin projection, thermalize with an energy equipartition. Hence, numerical solutions of …

In many simulations of turbulent flows, the viscous forces ν∇ 2 u are replaced by a
hyperviscous term− ν p (−∇ 2) pu to suppress the effect of viscosity at the large scales. In …

We undertake a systematic, direct numerical simulation of the twodimensional, Fourier-
truncated, Gross–Pitaevskii equation to study the turbulent evolutions of its solutions for a …

The flux reconstruction (FR) approach offers a flexible framework for describing a range of
high-order numerical schemes; including nodal discontinuous Galerkin and spectral …

We show, by using direct numerical simulations and theory, how, by increasing the order of
dissipativity (α) in equations of hydrodynamics, there is a transition from a dissipative to a …