Abstract
Dynamical behavior of a localized linear array of vortices is investigated by numerical simulations. The physical setup consists of a thin fluid layer (electrolyte) enclosed in a rectangular box and the vortices are locally driven by electromagnetic forces in the vicinity of a long lateral wall. The numerical model is used to simulate 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: a stable unit-type flow with a group of four vortices and an irregular flow including large-scale motion. Fourier decomposition of the streamfunction shows that the mode of twice the wavelength of the forcing scale is prominent in the primary instability and a large-scale mode (uniform along the periodic direction) appears in the secondary instability. The mutual interaction between the unstable modes is shown to play an important role in dynamical behavior in the regime of transition to turbulence.
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