APPENDIX A 

 GOVERNING EQUATIONS AND TILEIR SOLUTION 



1 . Long Waves over a Rough Bottom. 



To derive the approximate equations governing the propagation of 

 long waves over a rough bottom we take the basic equations expressing 

 conservation of mass and momentum for an incompressible fluid. In two 

 dimensions these equations read CSchlichting, 1960) 



3U 



8W 

 Sz 



CA-1) 



DU 

 Dt 



dx dz 



(A-2) 



DW 

 Dt 



3£. 



Pg 



(A-3] 



in which U and W are the horizontal and vertical velocity components, 

 respectively; p is the fluid density, p is the pressure, and g is the 

 acceleration due to gravity. The coordinate system is defined in 

 Figure A-1 and only the horizontal shear stress, t, is retained in the 

 horizontal momentum equation. 



7 / / / ^ ^ / ^ ^ ^ / / / ■ 



Figure A-1. Definition sketch. 



105 



