Magnetohydrodynamic wave generation due to seabed disturbances in a running stream

This study focuses on wave generation resulting from a sudden seabed displacement occurring over an infinitesimal time interval within a flowing stream of an electrically conducting field-free fluid under the influence of an external magnetic field. Our goal is to analyze how the external magnetic field influences the wave patterns produced by disturbances at the ocean floor in a fluid of finite depth in the presence of a uniform current. The fluid is subjected to a uniform magnetic field applied above the air–water interface. Adopting linear wave theory, the problem is formulated as an initial boundary value problem. By applying the Laplace–Fourier transform technique, an analytical expression for the surface elevation is derived in the form of an integral. This expression is then evaluated asymptotically for both large distances and long times using the method of stationary phase and Bleistein's approach. Numerical results for the asymptotic form of the free surface elevation are presented in several figures, highlighting the effects of varying current speeds, Alfvén velocities, and different types of ground displacement. The graphical representations reveal that the presence of a magnetic field and current speed significantly alters the wave dynamics. For validation, the results are compared with earlier calculations in the limiting case where the magnetic field is absent. The study aims to provide a useful tool for predicting wave behavior generated by sudden ocean floor disturbances.