Related papers: Symmetry-Constrained Exact Coherent Structures in …
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…
This work is a unified study of stable and unstable steady states of 2D active nematic channel flow using the framework of Exact Coherent Structures (ECS). ECS are stationary, periodic, quasiperiodic, or traveling wave solutions of the…
Several new families of nonlinear three-dimensional travelling wave solutions to the Navier-Stokes equation, also known as exact coherent states, are computed for Newtonian plane Poiseuille flow. The symmetries and streak/vortex structures…
Hairpin vortices are widely studied as an important structural aspect of wall turbulence. The present work describes, for the first time, nonlinear traveling wave solutions to the Navier--Stokes equations in the channel flow geometry --…
The transition to turbulence in plane Poiseuille flow (PPF) is connected with the presence of exact coherent structures. In contrast to other shear flows, PPF has a number of different coherent states that are relevant for the transition.…
Nonlinear traveling waves that are precursors to laminar-turbulent transition and capture the main structures of the turbulent buffer layer have recently been found to exist in all the canonical parallel flow geometries. We study the effect…
Motivated by recent experimental and numerical studies of coherent structures in wall-bounded shear flows, we initiate a systematic exploration of the hierarchy of unstable invariant solutions of the Navier-Stokes equations. We construct a…
We investigate a theoretical framework for modeling fluid turbulence based on the formalism of exact coherent structures (ECSs). Although highly promising, existing evidence for the role of ECSs in turbulent flows is largely circumstantial…
Many exact coherent states (ECS) arising in wall-bounded shear flows have an asymptotic structure at extreme Reynolds number Re in which the effective Reynolds number governing the streak and roll dynamics is O(1). Consequently, these…
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…
Equilibrium, traveling-wave, and periodic-orbit solutions of the Navier-Stokes equations provide a promising avenue for investigating the structure, dynamics, and statistics of transitional flows. Many such invariant solutions have been…
We investigate how symmetry, exact coherent structures (ECSs), and their invariant manifolds organize spontaneous flow reversals in a 2D active nematic confined to a periodic channel. In minimal flow units commensurate with the intrinsic…
We study localised exact coherent structures in plane Poiseuille flow that are relative periodic orbits. They are obtained from extended states in smaller, periodically continued domains, by increasing the length to obtain streamwise…
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 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 pipe flow is still an essentially open area of research, boosted in the last two decades by considerable progress achieved both on the experimental and numerical frontiers, mainly related to the identification and characterization…
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…
Exact coherent states of a linearly stable, plane parallel shear flow confined between stationary stress-free walls and driven by a sinusoidal body force (a flow first introduced by F. Waleffe, Phys. Fluids 9, 883 (1997)) are computed using…
The interaction between shear and double-diffusive convection (DDC) in the diffusive regime (cold fresh water on top of hot salty water) plays an important role in the heat and mass transport of polar region oceans. This study computes…
Nontrivial steady flows have recently been found that capture the main structures of the turbulent buffer layer. We study the effects of polymer addition on these "exact coherent states" (ECS) in plane Couette flow. Despite the simplicity…