We briefly describe laboratory experiments demonstrating wind-water solitary wave generation in a wind-water annular tunnel. A mathematical model of this phenomenon is constructed in the context of a shallow-water approximation. The finite-difference algorithm for solving the system is based on regularized shallow-water equations. For the first time, we obtain a numerical solution of the wind-water solitary wave that is qualitatively consistent with the experimental data.
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B. V. Levin and M. A. Nosov, Physics of Tsunamis (Yanus-K, Moscow, 2005) [in Russian].
O. A. Glebova, Al. V. Kravtsov, and N. K. Shelkovnikov, “Experimental and Numerical Study of Wind Solitary Waves on Water,” Izv. Akad. Nauk, Ser. Fiz. 66(12), 1727–1729 (2002).
N. K. Shelkovnikov, “Induced Soliton in a Fluid,” JETP Lett. 82(10), 638–641 (2005).
Al. N. Kravtsov, V. V. Kravtsov, and N. K. Shelkovnikov, “A Numerical Experiment on the Modeling of Solitary Waves on the Surface of a Fluid in an Annular Channel,” Comput. Math. Math. Phys. 44(3), 529–531 (2004).
R. K. Dodd, J. C. Eilbeck, J. D. Gibbon, et al., Solitons and Nonlinear Wave Equations (Academic Press, London, 1982; Mir, Moscow, 1988).
A. N. Volobuev, V. I. Koshev, and E. S. Petrov, Biophysical Principles of Geodynamics (Moscow, 2009) [in Russian].
T. G. Elizarova and O. V. Bulatov, “Regularized Shallow Water Equations and a New Method of Simulation of the Open Channel Flows,” Comput. Fluids 46(1), 206–211 (2011).
O. V. Bulatov and T. G. Elizarova, “Regularized Shallow Water Equations and an Efficient Method for Numerical Simulation of Shallow Water Flows,” Comput. Math. Math. Phys. 51(1), 160–173 (2011).
T. G. Elizarova, A. A. Zlotnik, and O. V. Nikitina, “Simulation of One-Dimensional Shallow-Water Flows using Regularized Equations,” Preprint No. 33 (Keldysh Inst. Appl. Math., Moscow, 2011).
T. G. Elizarova, Quasi-Gas Dynamic Equations and Methods for the Computation of Viscous Flow (Nauchnyi mir, Moscow, 2007) [in Russian]. English Translation: Springer 2009.
Yu. V. Sheretov, Dynamics of Continuous Media in Spatial and Temporal Averaging (RC Dynamics, Moscow-Izhevsk, 2009) [in Russian].
G. I. Marchuk, Mathematical Modeling in the Problem of Environment (Nauka, Moscow, 1982) [In Russian].
Original Russian Text © T.G. Elizarova, M.A. Istomina, N.K. Shelkovnikov, 2012, published in Matematicheskoe Modelirovanie, 2012, Vol. 24, No. 4, pp. 107–116.
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Elizarova, T.G., Istomina, M.A. & Shelkovnikov, N.K. Numerical simulation of solitary wave generation in a wind-water annular tunnel. Math Models Comput Simul 4, 552–559 (2012). https://doi.org/10.1134/S2070048212060051
- wind-water solitary wave
- shallow-water equations
- quasi-gas dynamic equations
- regularized shallow-water equations