Effects of a spanwise magnetic field on the exact coherent states in a channel flow

Abstract

The primary objective of this study is to examine the effect of a uniformly constant spanwise magnetic field on exact coherent states and their structures in channel flow. Exact coherent states represent nonlinear solutions to the Navier–Stokes equations, bearing significant importance in the prediction and control of flow with and without magnetic field. Despite the recent extensive research which have reported the influences of magnetic fields with respect to fluid dynamics, the specific effect of a spanwise magnetic field on the exact coherent states remain ambiguous. To investigate the influence of magnetic field on exact coherent states in channel flow, our study encompasses Reynolds numbers ranging from 3000 to 10 000, with variations in the size of computational domains. High-precision direct numerical simulations, coupled with a Fourier–Chebyshev spatial pseudospectra discretization, are employed to solve the governing equations under the assumption of low magnetic Reynolds number. Starting from laminar flow, we utilize a bisection method on the amplitude of perturbations to track the exact coherent states in the channel. In a smaller computational domain 2π × 2.4 × 2, the spanwise magnetic field expedites the self-sustaining process of exact coherent structures, accelerating the transition from streamwise vortices to streamwise streaks. In a larger computational domain, the exact coherent states are bifurcated from relative periodic orbit solutions to traveling wave solutions. Furthermore, as the spanwise computational domain expands, localization coherent structures persist and steadily propagate downstream in the channel.