Continental Shelf Waves 



Bt 



- fO, . g 3^ = , 



Bt r r 30 



A(,hu-J. ^(hu-,)+ r^(^.c,)= 



(1) 



(2) 

 (3) 



Here f 

 gravity, 



2fi 



sin 6'q (-0.59x10-1 sec'i for Australia), g is the acceleration of 

 -h(r,i/') the equation of the sea bottom, and 



V 



^-cp 



(4) 



where z = I(r,v'',t) is the sea-level distortion and ^(r.^.t) is the negative of 

 the atmospheric pressure fluctuations measured in centimeters of water. From 

 Eq. (4) we note that r, is a measure of the deviation of the sea-level behavior 

 from exact barometric behavior. It is thus our purpose to derive an equation for 

 fj and examine its magnitude relative to cp. 



We assume that the driving force 

 plane wave, viz., 



is of the form of an eastward moving 



= (Pq exp[i(kr cos - wt)] 



(5) 



where ^ ^ is a constant of order 10 cm. The choice of Eq. (5) as a model for the 

 ordinary weather systems which progress across mid-Australia is motivated by 

 two facts: (a) the weather systems essentially progress from west to east, and 

 (b) for a specified season and at any given station the power spectrum of the daily 

 mean atmospheric pressure fluctuations, which have an amplitude of about 10 cm, 

 has a single, albeit broad, maximum (1). In particular, the spectrums for "win- 

 ter" (April- September) and "summer" (October- March) are peaked at 9 days 

 {..'^ = 0.81 X 10" ^ sec" ^ ) and 5 days ( - ^ = 1.45 x 10" ^ sec' ^ ) respectively. As a 

 typical example, the winter spectrum of the atmospheric pressure at Sydney is 

 given in Fig. 1. In this figure the product of frequency and spectral energy den- 

 sity has been plotted against the logarithm of frequency. 



Fig. 1 - Winter spectrum of the daily mean atmos- 

 pheric pressure at Sydney. The vertical lines rep- 

 resent the lowest mode eigenfrequencies -- j ^^^ (m = 5, 

 6, .... 20) for 1= i^. 



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