Abstract
The physical characteristics of a certain class of stable perturbations of an idealized oceanic current regime are investigated theoretically and compared with some observed features of the Gulf Stream. The mathematical model envisages an idealized two-layer fluid with a deep lower layer which remains essentially in static balance. The upper layer, under equilibrium conditions, is characterized by a region of uniform geostrophically balanced flow (hence non-uniform thickness); adjoining this is a second region of uniform thickness which is at rest. Under disturbed conditions, the kinematic (shear) boundary which delineates the two regions is subject to transverse excursions (or meandering) associated with the vertical displacement of the interface between the upper and lower layers. Only those disturbances whose energy is confined to the region of the shear boundary are investigated. Two classes of these shear boundary waves occur: inertio-gravitational and quasi-geostrophic waves. Stable modes for both classes are found to exist over the range of 0.1 to 10 in the internal Froude number. There does exist a limited range of wave lengths for stable waves; the range being dependent upon the internal Froude number. Moreover, it is only those flow regimes for which the internal Froude number exceeds unity that stationary meanders in the stream are possible. Although the free perturbations are dynamically stable, they are of dispersive character (the phase speed being wave length dependent). This implies that a general disturbance of the current boundary (as represented by the combination of many different modes) cannot remain of permanent form. This aspect together with the possibility of resonant coupling with the atmosphere can lead to a growth of the disturbance with time as observed for Gulf Stream meanders. The analysis shows that it is the quasi-geostrophic modes which have characteristics which are most consistent with those observed for the meanders of the Gulf Stream.
Duxbury, Alyn C. (1963). An investigation of stable waves along a velocity shear boundary in a two-layer sea with geostrophic flow regime. Doctoral dissertation, Texas A&M University. Texas A&M University. Libraries. Available electronically from
https : / /hdl .handle .net /1969 .1 /DISSERTATIONS -172684.