Abstract
Homogeneous heavy fluid flows over an uneven bottom are studied in a long-wave approximation. A mathematical model is proposed that takes into account both the dispersion effects and the formation of a turbulent upper layer due to the breaking of surface gravity waves. The asymptotic behavior of nonlinear perturbations at the wave front is studied, and the conditions of transition from smooth flows to breaking waves are obtained for steady-state supercritical flow over a local obstacle.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
G. B. Witham, Linear and Nonlinear Waves, Wiley, New York (1974).
A. E. Green and P. M. Naghdi, “A derivation of equations for wave propagation in water of variable depth,” J. Fluid Mech., 78, 237–246 (1976).
M. I. Zheleznyak, and E. N. Pelinovskii, “Physicomathematical models for the incidence of a tsunami on a beach,” in: The Incidence of a Tsunami on a Beach (collected scientific papers) [in Russian], Inst. of Appl. Phys., Acad. of Sci. of the USSR (1985), pp. 8–33.
J. A. Battjes and T. Sakai, “Velocity field in a steady breaker,” J. Fluid Mech., 380, 257–278 (1999).
H. G. Hornung, C. Willert, and S. Willert, “The flow field downstream of a hydraulic jump,” J. Fluid Mech., 287, 299–316 (1995).
I. A. Svendsen, J. Veeramony, J. Bakunin, and J. T. Kirby, “The flow in weak turbulent hydraulic jumps,” J. Fluid Mech., 418, 25–57 (2000).
M. S. Longuet-Higgins and J. S. Turner, “An ‘entraining plume’ model of a spilling breaker,” J. Fluid Mech., 63, 1–20 (1974).
I. A. Svendsen and P. A. Madsen, “A turbulent bore on a beach,” J. Fluid Mech., 148, 73–96 (1984).
V. Yu. Liapidevskii, “Structure of a turbulent bore in a homogeneous liquid,” J. Appl. Mech. Tech. Phys., 40, No. 2, 238–248 (1999).
V. Yu. Liapidevskii and V. M. Teshukov, Mathematical Models for the Propagation of Long Waves in an Inhomogeneous Fluid [in Russian], Izd. Sib. Otd. Ross. Akad. Nauk, Novosibirsk (2000).
P. M. Naghdi and L. Vongsarnpigoon, “The downstream flow beyond an obstacle,” J. Fluid Mech., 162, 223–236 (1986).
F. Serre, “Contribution à l’étude des écoulements permanents et variables dans les canaux,” La Houille Blanche, 8, No. 3, 374–388 (1953).
J.-M. Vanden-Broeck, “Free surface flow over an obstruction in a channel,” Phys. Fluids, 30, No. 8, 2315–2317 (1987).
S. Shen, “Forced solitary waves and hydraulic falls in two-layer flow over topography,” J. Fluid Mech., 232, 583–612 (1992).
Z. Xu, F. Shi, and S. Shen, “A numerical calculation of forced supercritical soliton in single-layer flow,” J. Ocean Univ. (Qingdao), 24, No. 3, 309–319 (1994).
J. W. Miles, “Stationary transcritical channel flow,” J. Fluid Mech., 162, 489–499 (1986).
Author information
Authors and Affiliations
Additional information
__________
Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 47, No. 3, pp. 3–11, May–June, 2006.
Rights and permissions
About this article
Cite this article
Liapidevskii, V.Y., Xu, Z. Breaking of waves of limiting amplitude over an obstacle. J Appl Mech Tech Phys 47, 307–313 (2006). https://doi.org/10.1007/s10808-006-0057-5
Received:
Issue Date:
DOI: https://doi.org/10.1007/s10808-006-0057-5