GRAVITY WAVES DUE TO A POINT DISTURBANCE IN A PLANE FREE SURFACE FLOW OF STRATIFIED FLUIDS.
CALIFORNIA INST OF TECH PASADENA HYDRODYNAMICS LAB
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The fundamental solution of the gravity waves due to a two-dimensional point singularity submerged in a steady free surface flow of a stratified fluid is investigated. A linearized theory is formulated by using Loves equations. The effect of density stratification and the gravity effect are characterized by two flow parameters sigma and lambda. Two special cases of sigma and lambda are treated in this paper. In the first case of constant sigma and arbitrary lambda an exact mathematical analysis is carried out. It is shown that the flow is subcritical or supercritical according as lambda or 12 in analogy to the corresponding states of channel flows. In addition to a potential surface wave, which exists only for lambda 12 there arises an internal wave which is attenuated at large distances for lambda 14 and decays exponentially for lambda 14. In the second example an asymptotic theory for large lambda is developed while sigma y may assume the profile roughly resembling the actual situation in an ocean where a pronounced maximum called a seasonal thermocline occurs. Internal waves are now propagated to the downstream infinity in a manner analogous to the channel propagation of sound in an inhomogeneous medium. Author