A Solution to the Oscillation of Lake Water Generated by Wind

Abstract

The usual solution of equation of motion of lake water generated by wind is mathematically true under the boundary condition that the component current normal to the vertical lake wall is zero along the coast, only when the tractive force of wind is zero at the coast. When the tractive force of wind is uniform all over the lake surface, the solution is not correct under the given boundary condition.
In the present paper, the author treats the problem of this latter case. He transforms the usual equation into a equation which contains the total flow S. In that case, the order of the differential equation coincides with the number of boundary conditions, so a solution of the equation can be obtained.
The obtained result is as follows: where _??_= the surface elevation or depression from the mean water level T= the tractive force of the wind per unit area of the lake surface, and it is uniform forO<X<a t= time both coasts of the lake _??_= the depth of the lake f= constant number Lastly the author investigates the ca_??_ Resonance Effect.