Atmospheric pressure-driven surface wave propagation in a compressible ocean including static compression

The surface waves generated by a moving atmospheric pressure field are calculated, including both the effects of compressibility and static background compression of the ocean. The solution is found by using the Laplace transformation in time and the Fourier transformation in space. The Laplace transform is inverted analytically, and the Fourier transform is inverted numerically to obtain the solution in the time domain. The impact of ocean compressibility and static compression on the three wave modes, namely the wave locked with the pressure field and the two free waves propagating in opposite directions, induced by an initial pressure field, is demonstrated. The inclusion of compressibility of the water reduces the phase speed of the waves. Although the complexity of the mathematical problem increases when static compression is included, we show that its impact on phase speed is as significant as compression alone. Further effects are observed as a result of compressibility. The free surface near the initial centre of the pressure field oscillates, and the phase of this oscillation changes when static compression is included. Also, acoustic-gravity modes are excited, dominated by the first mode. The evolution of waves over time shows the significant impact of the compressibility of the water.