Observations demonstrate that turbulent processes in the planetary boundary layer (PBL) are largely organized into "coherent structures" which have a significant impact on turbulent transport in the atmosphere. Traditionally, linear stability theory has been used as a guide to understanding the transition of flows from laminar to turbulent. In some situations, however, the predictions drawn from linear stability analysis are at odds with observations, in terms of both the conditions for instability and the coherent structures which naturally arise. Recently, a closer correspondence with observations has been achieved for some shear flows using a non-modal stability analysis known as Optimal Perturbation Theory. However, optimal perturbation analysis has not yet been applied thoroughly to the important problem of Kelvin-Helmholtz (KH) instability -- a common form of shear flow instability in the PBL. In this talk I will give an overview of optimal perturbation theory, review the previous work on this problem, show how this work can be generalized and provide some preliminary results, highlighting some of the unexpected new results from this analysis.

Committee members: Keith Julien, James Meiss, James Curry, Joe Werne (CORA), Dave Fritts (CORA)

This is a 3-D visualization of the initial perturbation which experiences the greatest increase, after 5 advective time units, of total energy, in an unbounded linear shear flow with linear density stratification. The background shear is in the x direction. Shown here is the vertical vorticity; light blue is positive, dark blue is negative. This shows that the optimal perturbation configuration is an array of vortex rolls, tilted against the shear and aligned in the streamwise (x) direction.