318 CAMERON AND PRITCHARD [CHAP. 1 5 



we consider the estuary as a geometrically simple, elongated indenture in the 

 coastline with a river entering the upper end. A rectilinear, right-hand co- 

 ordinate system is located with the origin at the landward end of the estuary. 

 The #-axis is directed horizontally along the estuary toward the sea, the y-a,xis 

 horizontally across the estuary, and the z-axis vertically upward. 



The x-, y- and z-components of the velocity vector u are designated by u x , 

 u y and u z , respectively. Further, we designate the specific volume by a, the 

 hydrostatic pressure by p, and the x-, y- and z-components of the angular 

 velocity of the earth by Q x , &y and Q z . Neglecting the molecular viscous 

 stresses (for reasons to be explained later), the longitudinal or x-component of 

 the equation of motion is expressed by 



du x Bu x Bu x du z dp „ „ 



Bt Bx By Bz Bx 



The corresponding lateral or ^-component is given by 



BUy 8Uy 8Uy BUy Bp „ ~ , . 



-ZT + Uz-TT + Uy-^ + Uz-^ = -a-f-2[Q z u x -Q x Uz\ (2) 



Bt Bx By Bz By 



These equations apply to the instantaneous velocity field. Our observational 

 evidence is at present insufficient to deal with the instantaneous distribution 

 of properties, and it is necessary to treat these equations in such a way that 

 mean values of the various parameters may be employed. 



For this purpose, the instantaneous velocity u is considered to be composed 

 of three terms : 



(a) A time mean velocity, u, obtained by averaging over one or more tidal 

 cycles. This mean velocity may vary slowly over time intervals longer than the 

 period of averaging. 



(b) An oscillatory velocity, U, which is here assumed to vary according to a 

 simple harmonic function of the tidal period. 



(c) A velocity deviation, u', which results from those turbulent fluctuations 

 having a time scale smaller than the period employed in the averaging process. 



The x-, y- and z-components of the instantaneous velocity are then given by 



u x = u x +U x + u' x (3a) 



Uy = Uy+Uy + U'y (3b) 



u z = Ug+Uz + u'z. (3c) 



Here the tidal velocity terms are given by simple harmonic functions of the 

 type 



U x = V ox cos <p x . (4) 



The term U ox is the amplitude of the longitudinal component of the tidal 

 current, and cp x represents the sum of an angular time argument of tidal period 

 plus a phase angle. Similar expressions apply to the lateral and vertical com- 



