in which R, is a particle Reynolds number. 



dU 







and 



R^ = -^ , (A-93) 



d V 



R^ = ^ (l-n)^n ^ - 0.17 / _ CA-94} 



c 



o 



is a critical Reynolds number whose value is of the order 70 if the mean 

 values of the ranges indicated by equation (A-89) are taken. The fact 

 that the term (l-nj^n varies only slightly for 0.4 < n < 0.5 has been 

 used in establishing equation (A-94) . 



Thus, for values of Rj >> R^ the flow resistance is purely 

 turbulent and with 3 related to the physical characteristics of the 

 porous material through equation (A-88) with Sq taken as 2.7, the 

 problem of determining f may be considered resolved. 



b. Limitation of the Solution . The basic assumption made in the 

 derivation of the equations for the propagation of long waves in a 

 porous medium was that the waves be long relative to the depth. Whereas 

 this assumption in the context of long waves over a rough bottom was 

 equivalent to the negligible effect of vertical fluid accelerations, the 

 important term to consider in the context of waves propagating in a 

 porous medium is the term expressing the resistance to vertical flow in 

 equation (A-69) . 



For the simple case of a progressive wave in a porous medium the 

 solution for the horizontal velocity component given by equation (A-78) 

 is 



g n k a ., 



+ -ikx ,. „p, 



u = + ■ — e , CA-95) 



CO v^S-if 

 and from the continuity equation one may therefore obtain: 



g n k a h ., 



■ + o ,, z, -ikx ^. „^. 



w+ = -1 ^^ "■ F"^ ® ' ^^-^^^ 



o 



and the vertical resistance will contribute to the pressure distribution 

 by an amount 



122 



