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.

Width of Hyperbolic Tangent 12

Width of Hyperbolic Tangent 11

Width of Hyperbolic Tangent 10

Width of Hyperbolic Tangent 9

Width of Hyperbolic Tangent 8

Width of Hyperbolic Tangent 7

Width of Hyperbolic Tangent 6

Additional PROGRESSIVE Tests Compared to Width of 6