Numerical simulation on internal wave attractors

Internal waves in the steady stratified fluid propagate along the characteristic, whose angle with the vertical direction is determined by the wave frequency, float frequency and some other factors. The characteristics being reflected at boundaries keep the wave frequency as well as the angle with the vertical direction. In a closed container with one oblique boundary, the energy of the internal waves concentrate or diverse due to the reflections of characteristic by the boundaries. A limited circle, which is called internal wave attractor, might be formed in the concentrating case. This phenomenon has been observed in the water tank experiment, and verified by linear theory and numerical simulation. In this paper, we simulate the (1, 1) and (2, 1)-attractors using a nonlinear non-hydrostatic circulation model, MITgcm, and discuss the dependence of their characteristics on initial conditions. For a stable (1, 1)-attractor, strong shear current was generated around the limit circle. When reducing the slop of oblique boundary in a range, the structure of the attractor will not change greatly, but induce a quicker shrinkage of phase space due to the increase of linearity. For a (2, 1)-attractor, a part of the wave energy dissipated at the node between the two circuits and thus convergence of it needs more time. At the position of the node, current velocity is always zero. But the mixing is strong, and the buoyancy oscillates periodically with large amplitude.