A Mathematical Model for the Effects of Internal Waves on Propagation Behavior of Sound in the Sea

The internal waves generation process and sound propagation mechanism have been studied, separately. However, the effects of internal waves on sound waves behaviour is a study field that has not received any attention in our country. Marine environments are generally density stratified continuously or step-like. Layered structure of oceans affect sound propagation. Taking into consideration that some Iranian waters are density stratified and also have some internal waves that can be used in a sound propagation process for many purposes, it is necessary to study internal waves and sound transmission interaction. This paper attempts to discuss the effects of internal waves on underwater sound propagation using a mathematical model and find out how these process are inter dependent. The parameters such as sound speed, buoyancy frequency, displacement variance, relative perturbations in sound propagation associated with vertical displacement and horizontal particle velocity, phase & amplitude function, internal waves phase & amplitude spectrum were computed using Caspian sea data. The parabolic approximation was applied in the wave equation to calculate amplitude spectrum density and phase fluctuations of a plane sound wave propagating through a random field of internal waves in the sea.The rate of sound propagation perturbations due to vertical displacement and particle horizontal velocity shows that horizontal displacement is much lower than vertical one.We found out that wave number and vertical displacement increase with increasing depth and decreasing buoyancy frequency. A maximum in buoyancy frequency and sound propagation fluctuations in associate with vertical displacement is observed near water surface which is due to thermocline and there is a minimum in vertical displacement at same place.