Self-organization of decaying quasi-two-dimensional turbulence in stratified fluid in rectangular containers

Abstract

Laboratory experiments on decaying quasi-two-dimensional turbulence have been performed in stratified fluid inside containers with length-to-width ratios $\delta$ up to 5. The Reynolds number $Re$ of the horizontal flow, based on the r.m.s. velocity of the initial flow field and the half-width $H$ of the container, was typically between 1000 and 3000. The turbulence was generated by towing an array of vertical cylinders through the container which was filled with a two-layer stratified fluid. By varying the grid configuration a different amount of angular momentum could be added to the initial flow. The evolution of the flow was visualized by two-dimensional particle tracking velocimetry. The observed decay has been investigated with the emphasis on the final states as function of $\delta$, $Re$ and the angular momentum initially added to the flow. In addition, numerical simulations were carried out for decaying two-dimensional turbulence on rectangular domains with $\delta\,{=}\,2$ and 3. In these runs zero net angular momentum was added to the initial flow field. The numerical study focused on the final states as a function of $\delta$ and $Re$. The numerically obtained final states appeared to agree with the experimental observations. Furthermore, they indicate a clear difference between the predictions of quasi-stationary final states from statistical-mechanical theories and the final states as found in the numerical simulations.