Generation of beams of three-dimensional periodic internal waves by sources of various types
- 24 Downloads
The energy and force characteristics of periodic internal wave beams in a viscous exponentially stratified fluid are analyzed. The exact solutions of linearized problems of generation obtained by integral transformations describe not only three-dimensional internal waves but also the associated boundary layers of two types. The solutions not containing empirical parameters are brought to a form that allows a direct comparison with experimental data for generators of various types (friction, piston, and combined) of rectangular or elliptic shape. The stress tensor and force components acting on the generator are given in quadratures. In the limiting cases, the solutions are uniformly transformed to the corresponding expressions for the problems in a two-dimensional formulation.
Key wordsstratified fluid internal waves analytical methods exact solution Stokes and internal boundary layers
Unable to display preview. Download preview PDF.
- 1.J. Lighthill, Waves in Fluids, Cambridge Univ. Press, Cambridge (1978).Google Scholar
- 3.A. V. Aksenov, V. A. Gorodtsov, and I. V. Sturova, “Simulation of a stratified ideal incompressible flow over a cylinder,” Preprint No. 282, Institute of Problems of Mechanics, Siberian Division, Russian Academy of Sciences, Moscow (1986).Google Scholar
- 7.Yu. S. Il’inykh, Yu. V. Kistovich, and Yu. D. Chashechkin, “Comparison of the exact solution of one problem of generation of periodic internal waves with experiment,” Izv. Ross. Akad. Nauk, Fiz. Atmos. Okeana, 35, No. 5, 649–655 (1999).Google Scholar
- 8.G. G. Stokes, “On the effect of internal friction of fluids on the motion of pendulums,” Trans. Cambr. Philos., 9, Part 2, 8–106 (1851).Google Scholar
- 13.A. Naifeh, Introduction to Perturbation Techniques, Wiley and Sons, New York (1981).Google Scholar
- 14.Yu. D. Chashechkin and Yu. V. Kistovich, “Classification of three-dimensional periodic fluid flows, ” Dokl. Ross. Akad. Nauk, 395, No. 1, 55–58 (2004).Google Scholar
- 16.L. D. Landau and E. M. Lifshits, Course of Theoretical Physics, Vol. 6: Fluid Mechanics, Pergamon Press, Oxford-Elmsford, New York (1987).Google Scholar
- 17.A. D. McEwan, “Interaction between internal gravity waves and their traumatic effect on continuous stratification,” Bound.-Lay. Meteorol., No. 5, 159–175 (1973).Google Scholar
- 18.Yu. D. Chashechkin, A. Yu. Vasil’ev, and R. N. Bardakov, “Fine structure of beams of three-dimensional periodic internal waves,” Dokl. Ross. Akad. Nauk, 397, No. 3, 404–407 (2004).Google Scholar