Spatio-temporal dynamics of forced periodic flows in a confined domain

Abstract

Nonlinear dynamics of a localized linear array of vortices is investigated by numerical simulations. The setup consists of a thin fluid layer (electrolyte) enclosed in a rectangular box and driven by the injection of homogeneous electric currents in an alternating magnetic field. The spectral model simulates the Navier–Stokes equations in two dimensions with steady forcing and linear bottom friction. The model provides an accurate representation of the evolution of flow pattern. Fourier decomposition of the streamfunction shows that a subharmonic instability occurs in the same symmetry subspace as that of a basic flow in the primary instability regime and a shear flow mode appears in a different symmetry subspace in the secondary instability regime. The exploration of temporal behavior shows that the system produces Hopf-type bifurcations. Chaos and frequency locking due to the mutual interaction between the unstable modes are observed. A general scenario of the dynamics of forced periodic flows is discussed by the amplitude equations, which are modeled using formal group theoretical techniques.