Based on the shallow water theory, the problem on radial spreading of incompressible liquid over a horizontal surface with account for the presence of vegetation has been studied. Some exact as well as approximate analytical solutions have been obtained that describe various cases, stages, and possible regimes of the process of spreading. A comparison of the results obtained with experimental data is made.
Similar content being viewed by others
References
H. E. Huppert, Gravity currents: a personal perspective, J. Fluid Mech., 554, 299–322 (2006).
P. Ya. Polubarinova-Kochina, Concerning some unsteady-state motions of "shallow water," Prikl. Mat. Mekh., 24, Issue 6, 783–794 (1957).
H. E. Huppert, The propagation of two-dimensional and axisymmetric viscous gravity currents over a rigid horizontal surface, J. Fluid Mech., 121, 43–58 (1982).
V. Sh. Shagapov and G. R. Galiaskarova, Dynamics of accumulation of negative-buoyancy blowouts into the atmosphere in windless weather, J. Eng. Phys. Thermophys., 75, No. 2, 292–299 (2002).
Kh. M. Gamzaev, Modeling oil fi lm spreading over the sea surface, Prikl. Mekh. Tekh. Fiz., 50, No. 2, 127–130 (2009).
C. Ng and C. C. Mei, Roll waves on a shallow layer of mud modeled as a power-law fl uid, J. Fluid Mech., 263, 151–183 (1994).
V. V. Ostapenko, Numerical simulation of wave fl ows caused by coming down of a shore landslide, Prikl. Mekh. Tekh. Fiz., 40, No. 4, 109–117 (1999).
V. V. Ostapenko, Hyperbolic Systems of Conservation Laws and Their Application to the Theory of Shallow Water [in Russian], Izd. NGU, Novosibirsk (2004).
S. H. Davis and L. M. Hocking, Spreading and imbibition of viscous liquid on a porous base II, Phys. Fluids, 12 (7), 1646–1655 (2000).
L. P. Thomas, B. M. Marino, and P. F. Linden, Lock-release inertial gravity currents over a thick porous layer, J. Fluid Mech., 503, 299–319 (2004).
M. J. Spannuth, J. A. Neufeld, J. S. Wettlaufer, and M. Grae Worster, Axisymmetric viscous gravity currents fl owing over a porous medium, J. Fluid Mech., 622, No. 1, 135–144 (2009).
V. Sh. Shagapov and S. A. Gil′manov, Liquid spreading over a surface accompanied by its absorption by ground, Prikl. Mekh. Tekh. Fiz., 51, No. 5, 88–94 (2010).
L. D. Landau and E. M. Lifshits, Theoretical Physics, 5th edn., Vol. VI, Hydrodynamics [in Russian], Fizmatlit, Moscow (2006).
J. J. Stoker, Water Waves [Russian translation], INL, Moscow (1959).
S. D. Smith, Wind stress and turbulence over ice fl oe, J. Geophys. Res., 77, No. 21, 3886–3901 (1972).
I. A. Repina and A. S. Smirnov, Heat and momentum exchange between the atmosphere and ice according to observational data obtained in the region of the Franz Josef Land, Izv. Akad. Nauk, Fiz. Atmosf. Okeana, 36, No. 5, 672–680 (2000).
V. V. Ostapenko, Simulated equations of the shallow water theory admitting the propagation of discontinuous waves over a dry river bed, Prikl. Mekh. Tekh. Fiz., 48, No. 6, 22–43 (2007).
L. G. Loitsyanskii, Mechanics of Liquids and Gases [in Russian], Nauka, Moscow (1970).
G. I. Barenblatt, V. M. Entov, and V. M. Ryzhik, Motion of Liquids and Gases in Natural Beds [in Russian], Nauka, Moscow (1984).
K. S. Basniev, Oil-Gas Hydromechanics [in Russian], Inst. Komp. Issled., Moscow–Izhevsk (2005).
L. I. Sedov, Similarity and Dimensionality Methods in Mechanics [in Russian], Nauka, Moscow (1972).
G. I. Barenblatt, Similarity, Self-Similarity, and Intermediate Asymptotics [in Russian], Gidrometeoizdat, Leningrad (1982).
G. B. Whitham, Linear and Nonlinear Waves [Russian translation], Mir, Moscow (1977).
A. G. Petrov, Analytical Hydrodynamics [in Russian], Fizmatlit, Moscow (2009).
P. N. Svirkunov, Unsteady-state axisymmetrical motions in the shallow water theory approximations, Prikl. Mat. Mekh., 60, Issue 3, 520–522 (1996).
G. I. Barenblatt, Concerning some unsteady-state motions of liquid and gas in a porous medium, Prikl. Mat. Mekh., 5, Issue 1, 67–68 (1952).
N. A. Slezkin, Dynamics of Viscous Incompressible Liquid [in Russian], Gostekhizdat, Moscow (1955).
H. Lamb, Hydrodynamics [Russian translation], GITTL, Moscow (1947).
Author information
Authors and Affiliations
Corresponding author
Additional information
Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 88, No. 3, pp. 609–622, May–June, 2015.
Rights and permissions
About this article
Cite this article
Shagapov, V.S., Gil′manov, S.A. A Contribution to the Theory of Spreading of Liquid-Containing Ejections Over a Horizontal Surface. J Eng Phys Thermophy 88, 630–644 (2015). https://doi.org/10.1007/s10891-015-1231-5
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10891-015-1231-5