ANALYSIS OF FIXED AND TOWED OBSERVATIONS OF 

 INTERNAL WAVES 



Importance of the Phase Velocity 



Any small perturbation in an inviscid, incompressible area of the 

 ocean, where currents can be neglected, is determined by the equation 



„ d'^w r, d'^w 9 d^iv I d^w ^ dw\ 



with the boundary conditions 



u) = at z = (2) 



and 



dH dH 



IV = u + i; — where z = H(x,y) (3) 



dx dy 



Equation 1 follows from hydrodynamic equations, the continuity equation, 

 and the incompressibility condition. Surface waves are excluded. 



In the following sections we restrict ourselves to water areas of 

 constant depth: H(x,y) = H = constant. Expanding w into a Fourier series. 



w(x,y,z,t) =\ W^ j^ fzj exp [ilK^x + T]^ y + coj)] 



(4) 



k,i,m 



we get for the vertical dependency W^ jj ^ (z) 



rf^W cM gr-(y2 

 dz'^^^i;^^^ 

 W = at 2 = and 2 = H (5) 



_, 2 - r— + „ ^„ (k2+772) w = 



dz^ dz co^-f^ 



where the indices have been dropped. 



Long waves are characterized by gV » co 2. Furthermore, long waves can 

 be assumed to be long-crested. If they travel in the x direction, we then have 

 /<2 » 772and equation 5 reduces to 



d^W dW 



— + r — +rfW= 



dz^ dz 



W = at e = and 3 = H (6) 



