


The linearized shallow-water equation with friction can be written as Ou ση ru, öt ду where r is ...
2) If we now set H(x,y.t)-H0(x,y)+n(x,y,t) and assume that we only have small- amplitude motions with we obtain the linearized shallow-water equations Ot on O a) For the special non-rotating case (f -0 ) with constant depth (Ho - const.) show that the speed of gravity waves is c-VgHo Hint: set v-0 and derive a wave equation for the sea level η b) Given a harmonic wave η(x,t)=Asin(k-or) with amplitude A (again for f-0 and Ho= const.), derive the equation...
Kelvin waves The linearized shallow-water equations for a fluid of constant depth Ho on a f-plane (f-const.) are dr) ot dv ot Эт Assume that there is a continent in the half-plane x20 (that is, the y-axis of the coordinate system is a lateral boundary). Find a wave solution with -0 everywhere (that automatically fulfills the condition of no flow through the boundary. Try a solution of the form n(x,yt) F(x)explily-or) You have to determine the function Fix) and the...