Waves on the surface of an ideal incompressible heavy fluid under wind loads

The motion of the half-space of an ideal incompressible fluid is studied in the field of gravity under the action of periodic pressure on its surface. The problem is solved in the approximation of the theory of small-amplitude waves. An analytical solution for the velocity potential, the velocity field, and the form of the free surface are found. An expression of the horizontal force is obtained in the case of a traveling wave.