Mysak 



observed wave speed at the east coast. However, the solution does not yield any 

 information about the variation of sea level behavior with latitude. Also, Robin- 

 son's mathematical representation of the forcing atmosphere pressure variations 

 is questionable in view of the fact that at midlatitudes ordinary weather systems 

 tend to progress eastward rather than northward. 



To overcome these two shortcomings of the theory, we consider in this 

 paper the following problem: the response of the sea surface to a plane-wave 

 pressure distribution which progresses eastward across a circular continent 

 with a sloping sheK which sharply drops off to water at constant depth. 



The solution to this problem (given in the next section), when applied to the 

 Australian stations where an anomalous sea level behavior has been observed, 

 does in general predict the observed behavior, provided the forcing frequency 

 lies in a small neighborhood of an eigenfrequency. However, the behavior is 

 indeterminate when the forcing frequency is equal to an eigenfrequency, since 

 both viscosity and nonlinear effects have been neglected. In view of this short- 

 coming, we also obtain the solution (given in the third section) for the same 

 geometry and driving force as used in the next section but with bottom friction 

 incorporated into the equations of motion. The solution given in these next two 

 sections also predicts the existence of circularly traveling shelf waves which in 

 the case of the southern hemisphere, move in the observed direction, namely, 

 counterclockwise. However, the theoretical wave speeds are somewhat less 

 than the observed, especially for the values of the parameters which apply to 

 the east coast. In the fourth section the geometry of the model is modified so 

 as to include a finite-slope continental slope region. The unforced solution for 

 this geometry does give a west coast wave speed which lies well within the error 

 bounds of the observed speed; however, there is still a significant discrepancy 

 between the theoretical and observed speeds for the case of the east coast. In 

 view of the fact that the theory does not take into account the intense current and 

 associated stratification which is present off the east Australian coast (6,7), this 

 discrepancy is, perhaps, not too surprising. In the last section the change in 

 wave speeds due to deep-sea stratification (idealized by a two-layer model) and 

 a uniform, upper-layer deep-sea current is determined. 



We mention here that this paper is primarily intended to serve as an intro- 

 duction to the theory of continental shelf waves; a more complete treatment will 

 be published elsewhere. 



FORMULATION OF PROBLEM AND ITS SOLUTION 



Governing Equations 



In view of the nature of the phenomena we are considering, we shall use the 

 equations of linear shallow-water theory with the addition of the Coriolis param- 

 eter. Therefore, in terms of a cylindrical polar coordinate system (r. ^ , z ) cen- 

 tered at the origin of the continent with z measured vertically upward from the 

 undistorted sea surface, the adjusted sea level fi(T,4i,t) and velocity components 

 J. ( r , i//, t ) and u , ( r , V^ t ) satisfy the equations 



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