相关论文: Snakes and ladders: localized solutions of plane C…

Spatially localized exact solutions of plane Couette flow are organized in a snakes-and-ladders structure strikingly similar to that observed for simpler pattern-forming partial differential equations. [PRL 104,104501 (2010)]. We…

We present several new spatially localized equilibrium and traveling-wave solutions of plane Couette and channel flows. The solutions exhibit strikingly concentrated regions of vorticity that are flanked on either side by high-speed…

A specific family of spanwise-localised invariant solutions of plane Couette flow exhibits homoclinic snaking, a process by which spatially localised invariant solutions of a nonlinear partial differential equation smoothly grow additional…

Invariant solutions of shear flows have recently been extended from spatially periodic solutions in minimal flow units to spatially localized solutions on extended domains. One set of spanwise-localized solutions of plane Couette flow…

We consider a 9-PDE (1-space and 1-time) model of plane Couette flow in which the degrees of freedom are severely restricted in the streamwise and cross-stream directions to study spanwise localisation in detail. Of the many steady Eckhaus…

Spatially localized states play an important role in transition to turbulence in shear flows (Kawahara, Uhlmann & van Veen, Annu. Rev. Fluid Mech. 44, 203 (2012)). Despite the fact that some of them are attractors on the separatrix between…

We present an equilibrium solution of plane Couette flow that is exponentially localized in both the spanwise and streamwise directions. The solution is similar in size and structure to previously computed turbulent spots and localized,…

Although the equations governing fluid flow are well known, there are no analytical expressions that describe the complexity of turbulent motion. A recent proposition is that in analogy to low dimensional chaotic systems, turbulence is…

Unsteady spatially localized states such as puffs, slugs or spots play an important role in transition to turbulence. In plane Couette flow, steady versions of these states are found on two intertwined solution branches describing…

We present ten new equilibrium solutions to plane Couette flow in small periodic cells at low Reynolds number (Re) and two new traveling-wave solutions. The solutions are continued under changes of Re and spanwise period. We provide a…

The aim in the dynamical systems approach to transitional turbulence is to construct a scaffold in phase space for the dynamics using simple invariant sets (exact solutions) and their stable and unstable manifolds. In large (realistic)…

Recent work suggests unstable recurrent solutions of the equations governing fluid flow can play an important role in structuring the dynamics of turbulence. Here we present a method for detecting intervals of time where turbulence…

The phenomenon of bursting, in which streaks in turbulent boundary layers oscillate and then eject low speed fluid away from the wall, has been studied experimentally, theoretically, and computationally for more than 50 years because of its…

We present two spanwise-localized travelling wave solutions in the asymptotic suction boundary layer, obtained by continuation of solutions of plane Couette flow. One of the solutions has the vortical structures located close to the wall,…

In shear flows at transitional Reynolds numbers, localized patches of turbulence, known as puffs, coexist with the laminar flow. Recently, Avila et al., Phys. Rev. Let. 110, 224502 (2013) discovered two spatially localized relative periodic…

Plane Couette flow transitions to turbulence for Re~325 even though the laminar solution with a linear profile is linearly stable for all Re (Reynolds number). One starting point for understanding this subcritical transition is the…

The transition to turbulence in plane Couette flow and several other shear flows is connected with saddle node bifurcations in which fully 3-d, nonlinear solutions, so-called exact coherent states (ECS), to the Navier-Stokes equation…

A reduced description of shear flows consistent with the Reynolds number scaling of lower-branch exact coherent states in plane Couette flow [J. Wang et al., Phys. Rev. Lett. 98, 204501 (2007)] is constructed. Exact time-independent…

We discuss how searching for finite amplitude disturbances of a given energy which maximise their subsequent energy growth after a certain later time $T$ can be used to probe phase space around a reference state and ultimately to find other…

Recent progress indicates that highly symmetric recurring solutions of the Navier-Stokes equations, such as equilibria and periodic orbits, provide a skeleton for turbulence dynamics in state-space. Many of these solutions have been found…