Abstract
The results of experiments on the motion of a plate rigidly fastened to a dynamometric trolley performed in the water channel of Moscow State University are presented. The wave wake behind the body and the flow ahead of it in a finite-depth fluid were investigated at near-critical velocities of the motion and small planing angles. The observations show that a steady periodic wave wake occurs together with a nose wave of fixed shape, while in the case of detached rear waves the waves are excited ahead of the planing plate. The well-known Russell formula for the solitary wave amplitude is experimentally confirmed. It is shown that, accurate to small parameters, it coincides with Lavrent’ev’s results. The experimental conditions are numerically simulated using the XFlow™ software package. The results of the experiments performed in the water channel are in agreement with the numerical results.
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References
E. V. Filatov and A. Yu. Yakimov, “Drag of a plate planing on the shallow water with formation of waves,” Fluid Dynamics 53 (5), 608–615 (2018).
S. Russell, “Report on waves”, Brit. Ass. Rep. (1844).
V. I. Bukreev and A. V. Gusev, “Waves ahead of a vertical plate in a channel,” Fluid Dynamics 23 (1), 71–77 (1999).
S. Chen and G. Doolen, “Lattice Boltzmann method for fluid flows,” Annu. Rev. Fluid Mech. 30, 329–364 (1998).
S. Succi, “The lattice Boltzmann equation for fluid dynamics and beyond,” Oxford University Press, pp. 82–84 (2001).
Xflow, a new software package fir modeling the physical processes associated with hydrogasdynamics and heat and mass transfer. URL: https://doi.org/www.cadmaster.ru/magazin/articles/cm_60_13.html
M. A. Lavrent’ev and B. V. Shabat, Methods of Theory of Functions of a Complex Variable (Nauka, Moscow, 1973) [in Russian].
Yu. L. Yakimov, “An approximate formula for extension on the conformal mapping of a domain having a narrow region,” Sib. Mat. Zh. 3 (6), 956–960 (1962).
L. N. Sretenskii, Theory of Wave Motions of Fluids (Nauka, Moscow, 1977) [in Russian].
M. S. Longuet-Higgins and J. D. Fenton, “On the mass, momentum, energy and circulation of a solitary wave. II,” Proc. Roy. Soc. London. A 340, 471–493 (1974).
Funding
The study was carried out with the support of the Russian Foundation for Basic Research (project no. 16-08-00807).
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The Authors declare no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.
Russian Text © The Author(s), 2019, published in Izvestiya RAN. Mekhanika Zhidkosti i Gaza, 2019, No. 5, pp. 52–58.
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Filatov, E.V., Yakimov, A.Y. Wave Formation ahead of a Planing Plate. Fluid Dyn 54, 640–646 (2019). https://doi.org/10.1134/S0015462819050033
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DOI: https://doi.org/10.1134/S0015462819050033