Abstract
An improved Levi-Civita method in which the singularities of the desired function are taken into account by introducing terms containing power singularities is proposed. Results of numerical analysis of the nonlinear problem of a vortex in a bounded flow of an ideal weighable fluid (Fr>1) are given. The following limiting flow regimes are studied: the Stokes waves with one and two crests, emergence of a critical point on the surface, and the detachment of a vortex from a soliton and a uniform flow. It is shown that nonperiodic waves can form in a local zone in the vicinity of the critical point.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
N. Salvesen and C. Kerczek, “Nonlinear aspect of subcritical shallow-water flow past two-dimensional obstructions,”J. Ship Res.,22, No. 4, 203–211 (1978).
S. J. Liao, “A general numerical method for solution of gravity wave problems. Part 2. Steady nonlinear gravity waves,”Int. J. Num. Meth. Fluids,14, No. 10, 1173–1191 (1992).
E. O. Tuck, “Ship-hydrodynamics free-surface problems without waves,”J. Ship Res.,35, No. 4, 277–287 (1991).
D. V. Maklakov,Nonlinear Problems of Potential Flows with Unknown Boundaries [in Russian], Yanus-K, Moscow (1997).
V. P. Zhitnikov and O. I. Sherykhalin, “Soliton-type solutions for subcritical flows of a weighable fluid in the presence of a source and a vortex,” in:High-Speed Hydrodynamics: Proc. of Sci. Seminar (Cheboksary, May 27–June 5, 1996), Chuvash. Univ., Cheboksary (1996), pp. 63–67.
M. I. Gurevich,Theory of Ideal Fluid Jets [in Russian], Nauka, Moscow (1979).
V. P. Zhitnikov, “Gravity waves on a bounded area of a fluid surface,”Prikl. Mekh. Tekh. Fiz.,37, No. 2, 83–89 (1996).
N. M. Sherykhalina, “Development of numerical algorithms for solving hydrodynamic problems with singular points on the free surface and an experimental study of the rate of their convergence,” Ufa (1995). Deposited at VINITI 06.06.95, No. 2550-V95.
J. K. Hunter and J.-M. Vanden-Broek, “Accurate computations for steep solitary waves,”J. Fluid Mech.,136, 63–71 (1983).
J. M. Williams, “Limiting gravity waves in water of finite depth,”Philos. Trans. Roy. Soc. London. Ser. A,302, No. 1466, 139–188 (1981).
W. A. B. Evans and M. J. Ford, “An exact integral equation for solitary waves with new numerical results for some internal properties,”Proc. Roy. Soc. London. Ser. A,452, 373–390 (1996).
D. V. Maklakov, “Jet circulatory flow of a heavy fluid inside or outside a circle,” in:Proc. of the Seminar on Boundary-Value Problems, Kazan', No. 12 (1975), pp. 161–171.
Additional information
Ufa State Technical Aviation University, Ufa 450000. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 41, No. 1, pp. 70–76, January–February, 2000.
Rights and permissions
About this article
Cite this article
Zhitnikov, V.P., Sherykhalina, N.M. & Sherykhalin, O.I. Postcritical regimes in the nonlinear problem of vortex motion under the free surface of a weighable fluid. J Appl Mech Tech Phys 41, 62–68 (2000). https://doi.org/10.1007/BF02465238
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF02465238