相关论文: Invariant Sets and Explicit Solutions to a Third-O…

Modeling fluid turbulence using a 'skeleton' of coherent structures has traditionally progressed by focusing on a few canonical experiments, such as pipe flow and Taylor-Couette flow. We here consider an alternative canonical experiment,…

Invariant solutions of the Navier-Stokes equations play an important role in the spatiotemporally chaotic dynamics of turbulent shear flows. Despite the significance of these solutions, their identification remains a computational…

We investigate the nonlinear dynamics of turbulent shear flows, with and without rotation, in the context of a simple but physically motivated closure of the equation governing the evolution of the Reynolds stress tensor. We show that the…

In the context of fluid flows, the coupled Ostrovsky equations arise when two distinct linear long wave modes have nearly coincident phase speeds in the presence of background rotation. In this paper, nonlinear waves in a stratified fluid…

We present a reduced system of 7 ordinary differential equations that captures the time evolution of spatial gradients of the velocity and the temperature in fluid elements of stratified turbulent flows. We show the existence of invariant…

Three-dimensional direct numerical simulations of an incompressible open square cavity flow are conducted. Features of the permanent (non-linear) regime together with the linear stability analysis of a two-dimensional steady base flow are…

Modelling fluid turbulence using a `skeleton' of coherent structures has traditionally progressed by focusing on a few canonical laboratory experiments such as pipe flow and Taylor-Couette flow. We here consider the stratified inclined…

Turbulent dynamical systems characterized by both a high-dimensional phase space and a large number of instabilities are ubiquitous among many complex systems in science and engineering. The existence of a strange attractor in the turbulent…

Stability of inviscid shear shallow water flows with free surface is studied in the framework of the Benney equations. This is done by investigating the generalized hyperbolicity of the integrodifferential Benney system of equations. It is…

This article provides a reduced-order modelling framework for turbulent compressible flows discretized by the use of finite volume approaches. The basic idea behind this work is the construction of a reduced-order model capable of providing…

Consider the dynamics of turbulent flow in rivers, estuaries and floods. Based on the widely used k-epsilon model for turbulence, we use the techniques of centre manifold theory to derive dynamical models for the evolution of the water…

Exact solutions for laminar stratified flows of Newtonian/non-Newtonian shear-thinning fluids in horizontal and inclined channels are presented. An iterative algorithm is proposed to compute the laminar solution for the general case of a…

In this paper, we train turbulence models based on convolutional neural networks. These learned turbulence models improve under-resolved low resolution solutions to the incompressible Navier-Stokes equations at simulation time. Our study…

This work builds upon recent work exploiting the notion of structured singular values to capture nonlinear interactions in the analysis of wall-bounded shear flows. In this context, the structured uncertainty can be interpreted in terms of…

Modelling sediment transport in environmental turbulent fluids is a challenge. This article develops a sound model of the lateral transport of suspended sediment in environmental fluid flows such as floods and tsunamis. The model is…

When turbulent flow is laden with negatively buoyant particles, their mean distribution over the direction of gravity can induce stable density gradients that penalize turbulent fluctuations. This effect is studied numerically for…

Being able to account for the missing mixing in stellar radiative zones is a key step toward a better understanding of stellar evolution. Zahn (1974) argued that thermally diffusive shear-induced turbulence might be responsible for some of…

Over the past decade, the edge of chaos has proven to be a fruitful starting point for investigations of shear flows when the laminar base flow is linearly stable. Numerous computational studies of shear flows demonstrated the existence of…

We consider the dynamics of a vertically stratified, horizontally-forced Kolmogorov flow. Motivated by astrophysical systems where the Prandtl number is often asymptotically small, our focus is the little-studied limit of high Reynolds…

A dynamical systems approach to turbulence envisions the flow as a trajectory through a high-dimensional state space transiently visiting the neighbourhoods of unstable simple invariant solutions (E. Hopf, Commun. Appl. Maths 1, 303, 1948).…