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Gravity Waves Due to a Point Disturbance in a Plane Free Surface Flow of Stratified Fluids

Mei, C. C. and Wu, T. Yao-tsu (1964) Gravity Waves Due to a Point Disturbance in a Plane Free Surface Flow of Stratified Fluids. Physics of Fluids, 7 (8). pp. 1117-1133. ISSN 0031-9171. doi:10.1063/1.1711351.

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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 Love's equations. The effect of density stratification p_0(y) and the gravity effect are characterized by two flow parameters σ = −(dp_0∕dy)∕p_0 and λ = gL∕U^2, where λ^(1/2) may be regarded as the internal Froude number if L assumes a characteristic value of σ^(−1). Two special cases of σ and λ are treated in this paper. In the first case of constant σ (and arbitrary λ) an exact mathematical analysis is carried out. It is shown that the flow is subcritical or supercritical according as λ > or < (1/2), in analogy to the corresponding states of channel flows. In addition to a potential surface wave, which exists only for λ > (1/2), there arises an internal wave which is attenuated at large distances for λ > (1/4) and decays exponentially for λ < (1/4). In the second example an asymptotic theory for large λ is developed while σ(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.

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Additional Information:© 1964 American Institute of Physics. Received 20 April 1964; final manuscript received 8 June 1964. This work was supported by the U. S. Office of Naval Research under Contract Nonr-220(35). We are grateful to Professor Yih for enlightening discussions of this topic.
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Office of Naval Research (ONR)Nonr-220(35)
Issue or Number:8
Record Number:CaltechAUTHORS:20120830-161623975
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Official Citation:Gravity Waves due to a Point Disturbance in a Plane Free Surface Flow of Stratified Fluids C. C. Mei and T. Yao-tsu Wu, Phys. Fluids 7, 1117 (1964), DOI:10.1063/1.1711351
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:33741
Deposited On:30 Aug 2012 23:48
Last Modified:09 Nov 2021 21:37

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