The Nonnormality of Coastal Ocean Flows around Obstacles, and Their Response to Stochastic Forcing

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Abstract
The effect of stochastic variability upon the wake downstream of a real headland is investigated. From observations taken at Bass Point, Australia, three sources of stochastic forcing are identified and quantified, these being variability in the wind stress, in the flow incident on the headland, and that generated in the flow by complex reef topography at the headland's tip. These sources of stochastic forcing are found to induce a significant degree of unsteadiness in a nonlinear numerical model of flow around Bass Point that, in the absence of stochastic forcing, simulates steady recirculating flow. The observed stochastic variability of the flow incident on the headland is found to be larger than is necessary to support unsteadiness in the simulated straining zone. The dynamics of the perturbation growth observed in the model are understood by applying the techniques of generalized stability theory to the associated tangent linear model (TLM). The eigenmodes of the TLM confirm that the system is asymptotically stable, but analysis reveals that these eigenmodes are nonorthogonal and hence that the dynamical system is nonnormal. It is found that the model's response to stochastic forcing is not controlled by the least damped eigenmodes of the TLM, but rather by the least damped of its most nonnormal modes. The pseudospectra of the system suggest that the nonnormal modes are excited and sustained by the process of pseudoresonance. The nonnormality of the system permits transient growth of disturbances, because this allows a linear sum of exponentially decaying nonorthogonal modes to grow for a finite period because of eigenmode interference. Only in the absence of forcing do the least damped modes dictate the character of the flow. It is concluded that the subcritical transition to unsteady flow observed in the model may occur in straining coastal ocean circulations in general because of the ubiquity of environmental noise. As a result, nondimensional parameters such as the Reynolds number may only give a probability of transition occurring in nonnormal geophysical systems.

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