Abstract
The influence of a surface electric charge on the character and properties of wave motion along the free surface of a viscous homogeneous fluid is investigated by analytical asymptotic methods. Expressions describing the dispersion relations of the wave-motion components are obtained. The phase and group velocities of the structures forming wave motion are determined.
REFERENCES
Rayligh (Strutt, J.W.), On waves, Phil. Mag., 1876, vol. 1, pp. 257–259.
Stokes, G.G., On the theory of oscillatory waves, Trans. Cam. Philos. Soc., 1847, vol. 8, pp. 441–455.
Sretenskii, L.N., On waves on the surface of a viscous fluid, Tr. TsAGI, 1941, no. 541, pp. 1–34.
Lamb, H., Hydrodynamics, Cambridge: Univ. Press, 1924.
Whitham, G.B., Linear and Nonlinear Waves, N. Y.: Wiley, 1999.
Lighthill, J., Waves in Fluids, Cambridge: Univ. Press, 1978.
Chandrasekhar, S., Hydrodynamic and Hydromagnetic Stability, Oxford: Clarendon, 1961.
Landau, L.D. and Lifshitz, E.M., Course of Theoretical Physics, vol. 6: Fluid Mechanics, Oxford: Pergamon, 1987.
Kochin, N.E., Kibel, I.A., and Roze, N.V., Theoretical Hydromechanics, Intersci. Publ., 1964, vol. 1.
Levich, V.G., Physicochemical Hydrodynamics, Englewood Cliffs, N.Y.: Prentice-Hall, 1962.
Chashechkin, Yu.D., Transfer of the substance of a colored drop in a liquid layer with travelling plane gravity-capillary waves, Izv., Atmos. Oceanic Phys., 2022, vol. 58, no. 2, pp. 188–197. https://doi.org/10.1134/S0001433822020037
Grzonka, L. and Cieślikiewicz, W., Mass transport induced by nonlinear surface gravity waves, Proc. Copernicus Meetings, Boston, 2023, no. EGU23-16788.
Druzhinin, O.A. and Tsai, W.T., Numerical simulation of micro-bubbles dispersion by surface waves, Algorithms, 2022, vol. 15, no. 4, p. 110.
Kalinichenko, V.A., Regularization of barotropic gravity waves in a two-layer fluid, Fluid Dyn., 2019, vol. 54, no. 6, pp. 761–773.
Kalinichenko, V.A., Standing gravity waves on the surface of a viscous liquid, Fluid Dyn., 2022, vol. 57, no. 7, pp. 891–899.
Abrashkin, A.A. and Bodunova, Yu.P., Spatial standing waves on the surface of viscous fluid, Tr. Nizhegorod. Gos. Tekh. Univ. im. R. E. Alekseeva, Mekh. Zhidk. Gaza, 2011, no. 2 (87), pp. 49–54.
Rudenko, A.I., Two types of waves in a two-layer stratified liquid, Mater. mezhdunar. nach. kof. Aktual’nye proeblemy prikladnoi matematiki i mekhaniki (Proc. Int. Conf. Applied Mathematics, Computational Science and Mechanics: Current Problems), Voronezh, Dec. 12–14, 2022, pp. 1450–1456.
Chashechkin, Yu., Ochirov, A., and Lapshina, K.Yu., Surface waves along the interface of stably stratified liquids, Fiz.-Khim. Kinet. Gaz. Din., 2022, vol. 23, no. 6.
Chashechkin, Yu.D. and Ochirov, A.A., Periodic waves and ligaments on the surface of a viscous exponentially stratified fluid in a uniform gravity field, Axioms, 2022, vol. 11, no. 8, p. 402.
Roach, L.A., et al., Advances in modeling interactions between sea ice and ocean surface waves, J. Adv. Model. Earth Syst., 2019, vol. 11, no. 12, pp. 4167–4181.
Buckley, M.P. and Veron, F., The turbulent airflow over wind generated surface waves, Eur. J. Mech. B: Fluids, 2019, vol. 73, pp. 132–143.
Ersoy, N.E. and Eslamian, M., Capillary surface wave formation and mixing of miscible liquids during droplet impact onto a liquid film, Phys. Fluids, 2019, vol. 31, no. 1, p. 012107.
Il’inykh, A.Y. and Chashechkin, Yu.D., Fine structure of the spreading pattern of a freely falling droplet in a fluid at rest, Fluid Dyn., 2021, vol. 56, no. 4, pp. 445–450.
Chashechkin, Yu.D., Packages of capillary and acoustic waves of a drop impact Vestn. Mosk. Gos. Univ. im. N.E. Baumana, Ser. Estestv Nauki, 2021, no. 1 (94), pp. 73–91.
Chashechkin, Yu.D., Evolution of the fine structure of the matter distribution of a free-falling droplet in mixing liquids, Izv., Atmos. Oceanic Phys., 2019, vol. 55, no. 3, pp. 285–294.
Tonks, L., A theory of liquid surface rupture by a uniform electric field, Phys. Rev., 1935, vol. 48, no. 6, p. 562.
Frenkel, Ya.I., The Tonks theory on liquid surface disruption by constant electric field in vacuum, Zh. Eksp. Teor. Fiz., 1936, vol. 6, no. 4, pp. 348–350.
Taylor, G.I., Disintegration of water drops in an electric field, Proc. R. Soc. London A, 1964, vol. 280, pp. 383–397.
Grigor’ev, A.I., Kolbneva, N.Y., and Shiryaeva, S.O., Nonlinear monopole and dipole acoustic radiation of a weakly charged droplet oscillating in a uniform electrostatic field, Fluid Dyn., 2022, vol. 57, no. 8, pp. 982–997.
Zhuravleva, E.N., et al., A new class of exact solutions in the planar nonstationary problem of motion of a fluid with a free boundary, Theor. Math. Phys., 2020, vol. 202, no. 3, pp. 344–351.
Belonozhko, D.F. and Grigor’ev, A.I., Nonlinear periodic waves on the charged surface of a deep low-viscosity conducting liquid, Tech. Phys., 2004, vol. 49, no. 3, pp. 287–295.
Chashechkin, Yu.D., Foundations of engineering mathematics applied for fluid flows, Axioms, 2021, vol. 10, no. 4, p. 286.
Nayfeh, A.H., Introduction to Perturbation Technique, N. Y.: Wiley, 1993.
Funding
The work was carried out with financial support of the Russian Science Foundation (project 19-19-00598-P “Hydrodynamics and energetics of drops and droplet jets: formation, motion, decay, interaction with the contact surface,” https://rscf.ru/project/19-19-00598/).
Author information
Authors and Affiliations
Corresponding authors
Ethics declarations
The authors of this work declare that they have no conflicts of interest.
Additional information
Publisher’s Note.
Pleiades Publishing remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Ochirov, A.A., Chashechkin, Y.D. Wave Motion in a Viscous Homogeneous Fluid with a Surface Electric Charge. Fluid Dyn 58, 1318–1327 (2023). https://doi.org/10.1134/S0015462823602012
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S0015462823602012