Related papers: Visualizing the geometry of state space in plane C…
The paper considers a two-dimensional flow in a channel, which consists of straight inlet and outlet branches and a circularly 90-degree curved bend. An incompressible viscous fluid flows through the elbow under the action of a constant…
The equations in conservative form for nonlinear waves modeling on a liquid film flowing down a vertical plane have been investigated. It has been found that in the computational domain extended along the transverse axis the equations with…
We study the size of large-scale motions in turbulent plane Couette flows at moderate Reynolds number up to $Re_\tau$ = 500. Direct numerical simulation domains were as large as $100\pi\delta\times2\delta\times5\pi\delta$, where $\delta$ is…
Turbulent plane-Couette flow suspended with finite-size spheroidal particles is studied using fully particle-resolved direct numerical simulations. The effects of particle aspect ratio on turbulent arguments and particle statistics are…
Turbulence -- ubiquitous in nature and engineering alike [1-5] -- is traditionally viewed as an intrinsically inertial phenomenon, emerging only when the Reynolds number (Re), which quantifies the ratio of inertial to dissipative forces…
In this paper, we study the global existence and low Mach number limit of strong solutions to the 2-D full compressible Navier-Stokes equations around the plane Couette flow in a horizontally periodic layer with non-slip and isothermal…
The subject of this work is the instability mechanism of simple shear flows, like Hagen-Poiseuille pipe flow, which is a long-standing problem in fluid mechanics [1,2]. A possible analogy with phenomenological theory of ideal plasticity in…
We investigate the linear stability of shears near the Couette flow for a class of 2D incompressible stably stratified fluids. Our main result consists of nearly optimal decay rates for perturbations of stationary states whose velocities…
The roll streak structure (RSS) is ubiquitous in shear flow turbulence and is fundamental to the dynamics of the self-sustaining process (SSP) maintaining the turbulent state. The formation and maintenance of the RSS in wall-bounded shear…
The instability of a streak and its nonlinear evolution are investigated by direct numerical simulation (DNS) for plane Poiseuille flow at Re=3000. It is suggested that there exists a traveling-wave solution (TWS). The TWS is localized…
Turbulent-laminar intermittency, typically in the form of bands and spots, is a ubiquitous feature of the route to turbulence in wall-bounded shear flows. Here we study the idealised shear between stress-free boundaries driven by a…
We present a pseudo-spectal Navier-Stokes solver for plane parallel flows (Couette/Poiseuille), that has been developed on the MATLAB programming language. The code performs direct numerical simulations (DNSs) of turbulence in 3 dimensions…
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…
In this paper, we establish the inviscid damping and enhanced dissipation estimates for the linearized Navier-Stokes system around the symmetric flow in a finite channel with the non-slip boundary condition. As an immediate consequence, we…
We consider the incompressible Navier--Stokes equations with periodic boundary conditions and time-independent forcing. For this type of flow, we derive adjoint equations whose trajectories converge asymptotically to the equilibrium and…
Recent research has shed light on the role of coherent structures in forming layers when stably stratified turbulence is forced with horizontal shear (Lucas, Caulfield & Kerswell, J. Fluid Mech., vol. 832, 2017, pp. 409-437). Here we extend…
We compute the solutions of Prandtl's and Navier-Stokes equations for the two dimensional flow induced by a rectilinear vortex interacting with a boundary in the half plane. For this initial datum Prandtl's equation develops, in a finite…
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).…
This paper investigates the generation of free-surface waves in a liquid layer driven by linear instabilities in Couette-Poiseuille (quadratic) shear flows. The base velocity profiles are characterized by a curvature parameter, and…
The incompressible Navier-Stokes equations and static Euler equations are considered. We find that there exist infinite non-trivial regular solutions of incompressible static Euler equations with given boundary conditions. Moreover there…