Decaying quasi-two-dimensional viscous flow on a square domain

A comparison is made between experimental, numerical and analytical results for the two-dimensional flow on a square domain. The experiments concern the flow at the interface of a two-layer stratified fluid, evoked by either stirring the fluid with a rake, or by injecting additional fluid at the interface. Two numerical simulations were performed with initial conditions and boundary conditions that correspond approximately with those met in the experiments. The analytical results concern the calculation of the lowest modes of a decaying Stokes flow on a square domain. At late times, the experimental and numerical flows resemble the fundamental mode of the Stokes flow. The damping of small-scale structures by viscous diffusion plays an important role even if the initial Reynolds number is high. In particular, viscous diffusion is likely to be responsible for the appearance of an almost linear relationship between vorticity and stream function in the experiments and the simulations.