Pattern generation on the ocean''s surface results from complex interactions of the atmospheric wind above, with the natural and man-made disturbance environment below. Waves are ubiquitous at the surface, and in the upper ocean. While wavetrain analysis is the basis for much of what is known about both linear and nonlinear ocean waves, it is poorly suited to the Navy''s desire for an investigation of the transient surface signature of impulsive sources of hydrodynamic and acoustic energy at depth. For this task, LRK Associates, in concert with the University of Illinois at Urbana-Champaign, proposes to apply the analysis techniques and tools of the emerging field of non-normal dynamics and transient growth. This analysis framework yields concrete methods for determining the optimal perturbation that will show greatest growth over specified time. In the context of the surface roughness problem, this means it can predict the form of the pattern that will reach the surface in short times, something wavetrain analysis, with its asymptotic steady-state view, cannot provide. The relevance of non-normal dynamics to the surface pattern generation problem is that the Navier-Stokes equations in both stratified and unstratified shear flows, with appropriate boundary conditions, are frequently non-normal. To analyze the impulse response of such systems without considering the effects of non-normality leads, without doubt, to incorrect, and probably irrelevant, conclusions. LRK Associates believes that a linear non-normal dynamics analysis of the impulsive-source pattern-generation problem will yield considerable physical insight without need for the mathematical complications of nonlinearity. However, should specific evidence for the importance of nonlinearity in this process be discovered, the theoretical framework for a nonlinear, non-normal, transient dynamics analysis is already established.
Keywords: Transient Dynamics, Pattern Generation, Mode Selection, Receptivity, Stratified Compressible Flow
