Idealized KH Billow Initialization using Tanh Lateral Displacements

Here a small-amplitude initial distortion to the shear layer is used to encourage KH billow formation with hyperbolic tangent excursions in the lateral direction. Two billows are used and the tanh excursions are aligned (i.e. not staggered along the billow length) A sequence of runs was performed where the width of the tanh function was progressively reduced from about one billow spacings to about one half billow spacing. More precisely, the billow spacing is 12.56 units and the tanh width is varied over the range 12:6 at unit increments. The Reynolds number is 2500 and the Richardson number is 0.05.

The results show a remarkable transition from an array of connecting vortices to a single concentrated tube as the lateral distortion becomes more abrupt (reducing tanh width). A single tube is most pronounced when the tanh width approaches 1/2 the billow spacing. The final animation is similar to the one above it, but the amplitude of the initial disturbance was reduced by a factor of 10. This case has very low levels of initial helicity and also evolves into the desired single tube configuration. It also exhibits the zig-zag pattern of the billow cores seen in the larger simulations.