The nonlinear behavior of varicose disturbances in a simple model of the Gulf Stream

Abstract The behavior of varicose (width-altering) and mixed (sinuous-varicose) disturbances to an equivalent barotropic, f -plane jet is examined using analytical and numerical techniques. Specifically, we show that long waves are subject to nonlinear steepening, and we follow the evolution of such disturbances past the point of wave-breaking using the method of contour dynamics. Depending on the potential vorticity structure of the model, quantified by a parameter r , and on the amplitude of the initial wave, a variety of effects are produced including undular bores, ejected filaments, detaching eddies, and aneurisms. Most significantly, we show that r values in the range thought appropriate to the Gulf Stream produce detached eddies similar in appearance to "warm outbreaks". Measurements of the propagation speed of Gulf Stream width values using satellite imagery support the prediction of wave steepening at long wavelengths.

[1]  W. R. Holland,et al.  A parameter study of the mixed instability of idealized ocean currents , 1980 .

[2]  D. A. Brooks,et al.  Gulf Stream meanders off North Carolina during winter and summer 1979 , 1983 .

[3]  P. Richardson.  Gulf Stream Rings , 1983 .

[4]  T. Rossby,et al.  The Structure and Transport of the Gulf Stream at 73°W , 1985 .

[5]  M. Stern.  Lateral Wave Breaking and “Shingle” Formation in Large-Scale Shear Flow , 1985 .

[6]  N. Zabusky,et al.  Nonlinear Waves and Coherent Vortex Structures in Barotropic β-plane Jets , 1987 .

[7]  Warm outbreaks of the Gulf Stream into the Sargasso Sea , 1986 .

[8]  L. Polvani.  Geostrophic Vortex Dynamics , 1988 .

[9]  J. Larsen,et al.  Florida Current Volume Transports from Voltage Measurements , 1985, Science.

[10]  T. Joyce,et al.  Gulf Stream velocity structure through inversion of hydrographic and acoustic Doppler data , 1988 .

[11]  L. Pratt,et al.  Dynamics of Potential Vorticity Fronts and Eddy Detachment , 1986 .

[12]  A. Robinson,et al.  On the Time-Dependent Meandering of a Thin Jet , 1984 .

[13]  David G. Dritschel,et al.  The repeated filamentation of two-dimensional vorticity interfaces , 1988, Journal of Fluid Mechanics.

[14]  Norman J. Zabusky,et al.  Regularization of contour dynamical algorithms. I. tangential regularization , 1983 .

[15]  D. Watts.  Gulf Stream Variability , 1983 .

[16]  L. Pratt.  Meandering and Eddy Detachment According to a Simple (Looking) Path Equation , 1988 .

[17]  Michael A. Spall,et al.  Gulf Stream Simulations and the Dynamics of Ring and Meander Processes , 1988 .

[18]  S. Meacham,et al.  Vortices in shear , 1989 .

[19]  A. Beckmann.  Vertical Structure of Midlatitude Mesoscale Instabilities , 1988 .

[20]  J. Apel,et al.  Mesoscale Eddies Detached from Spatially Growing Meanders in an Eastward-Flowing Oceanic jet Using a Two-Layer Quasi-Geostrophic Model , 1981 .

[21]  David G. Dritschel,et al.  Contour surgery: a topological reconnection scheme for extended integrations using contour dynamics , 1988 .

[22]  F. Vukovich,et al.  Observations of the intrusion of a narrow warm tongue into the Sargasso Sea using satellite and in situ data , 1978 .

[23]  L. Pratt,et al.  Dynamics of vorticity fronts , 1985, Journal of Fluid Mechanics.