Spiral structure of the liquid particles trajectories near free surface of the vortex

Экспериментально и аналитически исследованы характеристики вихревого течения со свободной поверхностью, образующегося в результате вращения активаторного диска, расположенного на дне цилиндрического контейнера, заполненного водой. Получены аналитические выражения, показывающие, что траектории жидких частиц вблизи поверхности вихря представляют собой трехмерные спирали, по которым происходит течение от периферии к центу вихря. Показано, что рассчитанные и визуализированные траектории жидких частиц хорошо согласуются между собой и относятся к классу пространственных логарифмических спиралей. The work is aimed to compare results of analytical and experimental modeling of vortex fluid flow. The compound flow of liquid (water) occurs in a vertical cylindrical container without upper endwall under the action of the disk rotating at the bottom endwall. The two main components of the emerging flow are the toroidal vortex and the vortex with vertical axis. The equations are written in the cylindrical coordinate system dictated by the geometry of the problem. On the basis of the existing analytical expression, which describes the free surface form of the compound vortex in the zero approximation, an approach is developed to describe the trajectories of individual “liquid particles”. The obtained result allows to explore the velocity field structure near the free surface. The obtained expressions indicate that the velocity field near free surface becomes more pronounced in the tangent direction. This result is confirmed in the experimental studies of the compound vortex flow. The analytical forms of liquid particle trajectories near and on the free surface of the compound vortex are obtained. The general particle movement is from the container sidewall along the free surface to its center and further down the spiral-helical line. The images of the visualized particles trajectories both on the free surface (logarithmic spiral) and in the liquid depth are obtained in experiments and testify in favor of the implemented approach to the construction of analytical solution of the liquid particle motion for the vortex flow of the mentioned type. The correspondence of the calculated free surface forms obtained with the help of analytical expressions and those observed in the experiments with different parameters of the vortex flow shows that the developed approach to the problem can be based on a simplified description.

Vortex Stability in a Large-Scale Internal Wave Shear

The effect of a large-scale internal wave on a multipolar compound vortex was simulated numerically using a 3D Boussinesq pseudospectral model. A suite of simulations tested the effect of a background internal wave of various strengths, including a simulation with only a vortex. Without the background wave, the vortex remained apparently stable for many hundreds of inertial periods but then split into two dipoles. With increasing background wave amplitude, and hence shear, dipole splitting occurred earlier and was less symmetric in space. Theoretical considerations suggest that the vortex alone undergoes a self-induced mixed barotropic–baroclinic instability. For a vortex plus background wave, kinetic energy spectra showed that the internal wave supplied energy for the dipole splitting. In this case, it was found that the presence of the wave hastened the time to instability by increasing the initial perturbation to the vortex. Results suggest that the stability and fate of submesoscale vortices in the ocean may be significantly modified by the presence of large-scale internal waves. This could in turn have a significant effect on the exchange of energy between the submesoscale and both larger and smaller scales.