相关论文: New equilibrium solution branches of plane Couette…

Symmetry reduction by the method of slices is applied to pipe flow in order to quotient the stream-wise translation and azimuthal rotation symmetries of turbulent flow states. Within the symmetry-reduced state space, all travelling wave…

We study the structure of stationary channel flows predicted by the regularized 13-moment equations. Compared with the previous work [P. Taheri et al., Phys. Fluids, 21 (2009), 017102], we focus on gases whose molecules satisfy the general…

We show possibility of the Plane Couette (PC) flow instability for Reynolds number Re>Reth=140. This new result of the linear hydrodynamic stability theory is obtained on the base of refusal from the traditionally used assumption on…

A novel method to estimate unsteady aerodynamic force coefficients from pointwise velocity measurements is presented. The methodology is based on a resolvent-based reduced-order model which requires the mean flow to obtain physical flow…

We study the nonlinear stability of plane Couette and Poiseuille flows with the Lyapunov second method by using the classical L2-energy. We prove that the streamwise perturbations are L2-energy stable for any Reynolds number. This…

This work employs for the first time invariant solutions of the Navier-Stokes equations to study the interaction between finite-size particles and near-wall coherent structures. We consider horizontal plane Couette flow and focus on…

We propose a novel framework for approximating the statistical properties of turbulent flows by combining variational methods for the search of unstable periodic orbits with resolvent analysis for dimensionality reduction. Traditional…

In this paper, we provide a classification of steady solutions to two-dimensional incompressible Euler equations in terms of the set of flow angles. The first main result asserts that the set of flow angles of any bounded steady flow in the…

Resolvent analysis is a powerful tool for modeling and analyzing turbulent flows and in particular provides an approximation of coherent flow structures. Despite recent algorithmic advances, computing resolvent modes for flows with more…

The normal-mode analysis of the Reynolds-Orr energy equation governing the stability of viscous motion for general three-dimensional disturbances has been revisited. The energy equation has been solved as an unconstrained minimization…

Reduced-order models were derived for plane Couette flow using Galerkin projection, with orthonormal basis functions taken as the leading controllability modes of the linearised Navier-Stokes system for a few low wavenumbers. Resulting…

We introduce a class of high order accurate, semi-implicit Runge-Kutta schemes in the general setting of evolution equations that arise as gradient flow for a cost function, possibly with respect to an inner product that depends on the…

In the study of equilibrium solutions for partial differential equations there are so many equilibria that one cannot hope to find them all. Therefore one usually concentrates on finding individual branches of equilibrium solutions. On the…

We propose a new analyzing method, which is called the tautological flow method, to analyze the integrability of partial difference equations (P$\Delta$Es) based on that of partial differential equations (PDEs). By using this method, we…

This paper provides a pedagogical introduction to the classical nonlinear stability analysis of the plane Poiseuille and Couette flows. The whole procedure is kept as simple as possible by presenting all the logical steps involved in the…

Regular patterns of turbulent and laminar fluid motion arise in plane Couette flow near the lowest Reynolds number for which turbulence can be sustained. We study these patterns using an extension of the minimal flow unit approach to…

The state of a single-species monatomic gas from near-equilibrium to highly nonequilibrium conditions is investigated using analytical and numerical methods. Normal solutions of the Boltzmann equation for Fourier flow (uniform heat flux)…

Lie symmetry analysis is applied to study the nonlinear rotating shallow water equations. The 9-dimensional Lie algebra of point symmetries admitted by the model is found. It is shown that the rotating shallow water equations are related…

We present here two new techniques to solve the one-dimensional random flight. The first one is an expansion in the number of collisions. The second one is the obtention of a Fourier series. This second technique can be applied to an…

Exact solutions are obtained for the steady flow of a power-law fluid between parallel plates with partial slip conditions and uniform cross flow. The problem is properly formulated and similarities are exploited. The exact solutions are…