Stochastic wave radiation by the Gulf Stream: numerical experiments

Abstract

The present work combines two ideas: (i) that transient Rossby waves are excited by meander growth and decay and radiate into the far field; (ii) that the stochastic nature of meander growth, lifetimes and decays is responsible for the observed high values of eddy variances. A simple barotropic model was used analytically through an asymptomatic theory and numerically to explore the fully nonlinear regime. Three questions are addressed. First, in the fully nonlinear limit can a Rossby wave radiation field be excited for which the predicted covariance distributions compare well with the observed ones? Second, can the divergence of the associated eddy vorticity fluxes induce a mean recirculation similar to the deep recirculation gyre observed north of the stream? Third, is the variable thickness of the deep layer due to the main thermocline depth change across the stream and the sloping bottom topography, crucial in driving the deep recirculation gyre? From the results obtained the following was concluded. Over a flat bottom, both theory and the numerical experiments predict a series of circulation cells produced by the nonlinear interactions between the forced and free wave response of the flow. Realistic eddy variances due to Rossby wave radiation into the far field are predicted. However, the induced mean recirculation is much too weak. A bowl-shaped topography that mimics the variable thickness of the deep layer across the stream front was then introduced. In this case, the mean cyclonic circulation follows the closed potential vorticity contours and compares well with that observed. However, this equivalent topography produces a very rapid energy decay away from the southern boundary by inhibiting wave radiation. The fact that one or the other of the two results were achieved, but not both simultaneously. is a clear indication of the limitations of the model used in which the meandering stream is idealized as a southern boundary forcing. A final, interesting result of these simulations is that topographic Rossby waves are preferentially forced in regions where the stream meanders over the sloping relief, corresponding to the regions upstream of the Grand Banks and downstream of Cape Hatteras.