Related papers: Pattern fluctuations in transitional plane Couette…
Recent studies have brought into question the view that at sufficiently high Reynolds number turbulence is an asymptotic state. We present the first direct observation of the decay of turbulent states in Taylor-Couette flow with lifetimes…
Fluctuation properties of the Langevin equation including a multiplicative, power-law noise and a quadratic potential are discussed. The noise has the Levy stable distribution. If this distribution is truncated, the covariance can be…
Lower branch coherent states in plane Couette flow have an asymptotic structure that consists of O(1) streaks, $O(R^{-1})$ streamwise rolls and a weak sinusoidal wave that develops a critical layer, for large Reynolds number $R$. Higher…
In linearly stable shear flows turbulence spontaneously decays with a characteristic lifetime that varies with Reynolds number. The lifetime sharply increases with Reynolds number so that a possible divergence marking the transition to…
Laminar-turbulent transitions occur at different Reynolds numbers for different flow configurations and different fluids. In order to study quantitatively the similarity among the transition processes of wall-bounded shear flows, a uniform…
A structure consisting of quasi-laminar and turbulent regions in a stripe pattern, which can be found in a transitional plane channel flow, is called `turbulent stripe'. In the previous works, the emergence of this structure was confirmed…
In this essay, we recall the specificities of the transition to turbulence in wall-bounded flows and present recent achievements in the understanding of this problem. The transition is abrupt with laminar-turbulent coexistence over a finite…
We identify a new type of pattern formation in spatially distributed active systems. We simulate one-dimensional two-component systems with predator-prey local interaction and pursuit-evasion taxis between the components. In a sufficiently…
We study a quantum particle coupled to hard-core bosons and propagating on disordered ladders with $R$ legs. The particle dynamics is studied with the help of rate equations for the boson-assisted transitions between the Anderson states. We…
We track the secondary bifurcations of coherent states in plane Couette flow and show that they undergo an incomplete periodic doubling cascade that ends with a crisis bifurcation. We introduce a symbolic dynamics for the orbits and show…
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 present a new application of Lagrangian Perturbation Theory (LPT): the stability analysis of fluid flows. As a test case that demonstrates the framework we focus on the plane Couette flow. The incompressible Navier-Stokes equation is…
The transition from a chaotic to a periodic oscillatory state can be smooth or abrupt in real-world turbulent systems. Although there have been several mathematical studies, the occurrence of abrupt transitions in real-world systems such as…
This article aims to make a detailed analysis of co-flowing plane Couette flows. Particularly, the variation of flow quantities from the turbulent to non-turbulent region is studied. While the enstrophy exhibits a sharp jump, the other…
A simple analytical model for a turbulent flow is proposed, which considers the flow as a collection of localized spatial structures that are composed of elementary "cells" in which the state of the particles (atoms or molecules) is…
Something as simple as Couette and Poiseuille onedimensional flow of a newtonian fluid between infinite parallel walls provides an illuminating example of the contrasting physics of laminar and turbulent flow: the difference between their…
We consider Langevin equation with dichotomously fluctuating diffusivity, where the diffusion coefficient changes dichotomously in time, in order to study fluctuations of time-averaged observables in temporary heterogeneous diffusion…
We prove nonlinear stability for finite amplitude perturbations of plane Couette flow. A bound of the solution of the resolvent equation in the unstable complex half-plane is used to estimate the solution of the full nonlinear problem.The…
The transitional boundary layer flow over a flat plate is investigated. The boundary layer flow is known to develop unstable Tollmien-Schlichting waves above a critical value of the Reynolds number. However, it is also known that this…
In shear flows like pipe flow and plane Couette flow there is an extended range of parameters where linearly stable laminar flow coexists with a transient turbulent dynamics. When increasing the amplitude of a perturbation on top of the…