A numerical study of scalar gradients in Kelvin-Helmholtz billows
A high resolution numerical technique is used to model the development of a periodically perturbed shear layer imbedded in an initially vertical gradient of a passive scalar. The technique follows the development of the vorticity through an initial linear growth state and well into the nonlinear development of Kelvin-Helmholtz billows, in the zero-viscosity, zero-diffusion limit. The resulting scalar distribution rapidly develops regions of extremely sharp scalar gradients, which wind around the periodically spaced vortical low gradient cores. Vertical cross sections through different parts of the billow structure are presented and compared with rocket measurements of electron density fine structure in the mesosphere. Gradient limits imposed by finite diffusion are calculated, and implications for atmospheric radar observations are discussed.