The understanding of fluid turbulence has considerably progressed in recent years. The
application of the methods of statistical mechanics to the description of the motion of fluid …

When discussing research in physics and in science more generally, it is common to ascribe
equal importance to the three components of the scientific trinity: theoretical, experimental …

Two decades ago when we wrote Spectral Methods in Fluid Dynamics (1988), the subject
was still fairly novel. Motivated by the many favorable comments we have received and the …

The last decades witnessed a renewal of interest in the Burgers equation. Much activities
focused on extensions of the original one-dimensional pressureless model introduced in the …

We discuss the generation and statistics of the density fluctuations in highly compressible
polytropic turbulence, based on a simple model and one-dimensional numerical …

Stochasticity can play an important role in the dynamics of biologically relevant populations.
These span a broad range of scales: from intra-cellular populations of molecules to …

Here S1 denotes the unit circle, and C, a generic constant. Without loss generality, we can
assume that for all k, fl Fk (x) dx= O. We will den the elements in the probability space Q by …

Even if numerical simulation of the Burgers' equation is well documented in the literature, a
detailed literature survey indicates that gaps still exist for comparative discussion regarding …

A precise characterization of structures occurring in turbulent fluid flows at high Reynolds
numbers is one of the last open problems of classical physics. In this review we discuss …

We are investigating the inviscid limit of the Navier–Stokes equation, and we find previously
unknown anomalous terms in Hamiltonian, Dissipation, and Helicity, which survive this limit …