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Low Reynolds number turbulence in wall-bounded shear flows \emph{en route} to laminar flow takes the form of oblique, spatially-intermittent turbulent structures. In plane Couette flow, these emerge from uniform turbulence via a…
In this visualisation the instantaneous local velocity is expressed in terms of four components to capture the development of and interactions between coherent structures in turbulent flows. It is then possible to isolate the terms linked…
A new approach to the old-standing problem of the anomaly of the scaling exponents of nonlinear models of turbulence has been proposed and tested through numerical simulations. This is achieved by constructing, for any given nonlinear…
We present a systematic analysis of statistical properties of turbulent current and vorticity structures at a given time using cluster analysis. The data stems from numerical simulations of decaying three-dimensional (3D)…
In this article we consider a damped version of the incompressible Navier-Stokes equations in the whole three-dimensional space with a divergence-free and time-independent external force. Within the framework of a well-prepared force and…
The Navier-Stokes (NS) equations as a turbulence model have been widely applied in lots of fields. The NS equations contain such a fundamental assumption that all small physical/artificial disturbances could be neglected. Is this assumption…
Inertial-range features of turbulence are investigated using data from experimental measurements of grid turbulence and direct numerical simulations of isotropic turbulence simulated in a periodic box, both at the Taylor-scale Reynolds…
In the present work, we investigate a numerical one-dimensional solver to the Navier-Stokes equation that retains all terms, including both pressure and dissipation. Solutions to simple examples that illustrate the actions of the nonlinear…
A theory for the evolution of a metric $g$ driven by the equations of three-dimensional continuum mechanics is developed. This metric in turn allows for the local existence of an evolving three-dimensional Riemannian manifold immersed in…
We propose a simple statistical model of three-dimensionally anisotropic, intermittent, strong Alfv\'enic turbulence, incorporating both critical balance and dynamic alignment. Our model is based on log-Poisson statistics for Elsasser-field…
We present the results of a search of log-periodic corrections to scaling in the moments of the energy dissipation rate in experiments at high Reynolds number (2500) of three-dimensional fully developed turbulence. A simple dynamical…
A new transient regime in the relaxation towards absolute equilibrium of the conservative and time-reversible 3-D Euler equation with high-wavenumber spectral truncation is characterized. Large-scale dissipative effects, caused by the…
We use the mapping between Burgers' equation and the problem of a directed polymer in a random medium in order to study the fully developped turbulence in the $N$ dimensional forced Burgers' equation. The stirring force corresponds to a…
The effects of turbulent dynamic range on scalar mixing in stably stratified turbulence are investigated by an adaptation of the theoretical passive scalar modelling arguments of Beguier et al. (1978) and demonstrated statistically using…
Turbulent compressible flows are traditionally simulated using explicit time integrators applied to discretized versions of the Navier-Stokes equations. However, the associated Courant-Friedrichs-Lewy condition severely restricts the…
We survey the recent advance in the rigorous qualitative theory of the 2d stochastic Navier-Stokes system that are relevant to the description of turbulence in two-dimensional fluids. After discussing briefly the initial-boundary value…
In many astrophysical environments, mixing of heavy elements occurs in the presence of a supersonic turbulent velocity field. Here we carry out the first systematic numerical study of such passive scalar mixing in isothermal supersonic…
A phenomenological model for the inertial range scaling of passive-scalar turbulence is developed based on a bivariate log-Poisson model. An analytical formula of the scaling exponent for three-dimensional passive-scalar turbulence is…
The extent to which statistical equilibrium theory is applicable to driven dissipative dynamics remains an important open question in many systems. We use extensive direct numerical simulations of the incompressible two-dimensional (2D)…
On the basis of the Navier-Stokes equations we develop the statistical theory of many space-time correlation functions of velocity differences. Their time dependence is {\em not} scale invariant: $n$-order correlations functions exhibit…