Abstract
In this paper, the peculiarities of wave dynamics of pulses in incompressible stratified media are considered. It is shown that the character of pulse excitation sources of internal gravity waves is determined by the physical formulation of the problems. For the plane case and in the linear setting, two problems of wave generation for an infinitely long source homogeneous along the horizontal axis are considered. The method of asymptotic analysis of far wave field for different excitation source types is proposed for the three-dimensional case. The estimates of the time of settling the limit harmonic excitation at large distances are determined for the harmonic generation source. It is demonstrated that the effect of harmonic excitation concentration in narrow spatial regions is unlikely under conditions of the real ocean.
REFERENCES
Lighthill, J., Waves in Fluids, Cambridge: Cambridge Univ. Press, 1978.
Miropol’sky, Yu.Z., Dynamics of Internal Gravity Waves in the Ocean, Shishkina, O.D., Ed., Atmospheric and Oceanographic Sciences Library, vol. 24, Berlin: Springer, 2001. https://doi.org/10.1007/978-94-017-1325-2
Adcroft, A. and Campin, J.-M., MIT User Manual, Cambridge, Mass.: MIT, 2011.
Özsoy, E., Geophysical Fluid Dynamics II: Stratified / Rotating Fluid Dynamics of the Atmosphere–Ocean, Springer Textbook in Earth Sciences. Geography and Environment, Cham: Springer, 2021. https://doi.org/10.1007/978-3-030-74934-7
Bulatov, V.V. and Vladimirov, Yu.V., Volny v stratifitsirovannykh sredakh (Waves in Stratified Media), Moscow: Nauka, 2015.
Whitham, G.B., Linear and Nonlinear Waves, New York: Wiley, 1974. https://doi.org/10.1002/9781118032954
Gitterman, M., Hydrodynamics of compressible liquids: Influence of the piston effect on convection and internal gravity waves, Phys. A: Stat. Mech. its Appl., 2007, vol. 386, no. 1, pp. 1–11. https://doi.org/10.1016/j.physa.2007.08.020
Staquet, C. and Sommeria, J., Internal gravity waves: From instabilities to turbulence, Annu. Rev. Fluid Mech., 2002, vol. 34, no. 1, pp. 559–593. https://doi.org/10.1146/annurev.fluid.34.090601.130953
Matyushin, P.V., Process of the formation of internal waves initiated by the start of motion of a body in a stratified viscous fluid, Fluid Dyn., 2019, vol. 54, no. 3, pp. 374–388. https://doi.org/10.1134/s0015462819020095
Chai, J., Wang, Z., Yang, Z., and Wang, Z., Investigation of internal wave wakes generated by a submerged body in a stratified flow, Ocean Eng., 2022, vol. 266, p. 112840. https://doi.org/10.1016/j.oceaneng.2022.112840
Ulloa, H.N., De La Fuente, A., and Niño, Ya., An experimental study of the free evolution of rotating, nonlinear internal gravity waves in a two-layer stratified fluid, J. Fluid Mech., 2014, vol. 742, pp. 308–339. https://doi.org/10.1017/jfm.2014.10
Li, T., Wan, M., Wang, J., and Chen, S., Flow structures and kinetic-potential exchange in forced rotating stratified turbulence, Phys. Rev. Fluids, 2020, vol. 5, no. 1, p. 14802. https://doi.org/10.1103/physrevfluids.5.014802
Gervais, A.D., Swaters, G.E., and Sutherland, B.R., Transmission and reflection of three-dimensional Boussinesq internal gravity wave packets in nonuniform retrograde shear flow, Phys. Rev. Fluids, 2022, vol. 7, no. 11, p. 114802. https://doi.org/10.1103/physrevfluids.7.114802
Abdilghanie, A.M. and Diamessis, P.J., The internal gravity wave field emitted by a stably stratified turbulent wake, J. Fluid Mech., 2013, vol. 720, pp. 104–139. https://doi.org/10.1017/jfm.2012.640
Meunier, P., Le Dizès, S., Redekopp, L., and Spedding, G.R., Internal waves generated by a stratified wake: Experiment and theory, J. Fluid Mech., 2018, vol. 846, pp. 752–788. https://doi.org/10.1017/jfm.2018.278
Rees, T., Lamb, K.G., and Poulin, F.J., Asymptotic analysis of the forced internal gravity wave equation, SIAM J. Appl. Math., 2012, vol. 72, no. 4, pp. 1041–1060. https://doi.org/10.1137/110842892
Navrotsky, V.V., Liapidevskii, V.Yu., and Pavlova, E.P., Features of internal waves in a shoaling thermocline, Int. J. Geosci., 2013, vol. 04, no. 05, pp. 871–879. https://doi.org/10.4236/ijg.2013.45081
Voisin, B., Internal wave generation in uniformly stratified fluids. Part 1. Green’s function and point sources, J. Fluid Mech., 1991, vol. 231, pp. 439–480. https://doi.org/10.1017/s0022112091003464
Voisin, B., Internal wave generation in uniformly stratified fluids. Part 2. Moving point sources, J. Fluid Mech., 1994, vol. 261, pp. 333–374. https://doi.org/10.1017/s0022112094000364
Voisin, B., Limit states of internal wave beams, J. Fluid Mech., 2003, vol. 496, pp. 243–293. https://doi.org/10.1017/s0022112003006414
Bulatov, V.V. and Vladimirov, Yu.V., Far fields of internal gravitywaves generated by a perturbation source in a stratified rotating medium, Fluid Dyn., 2016, vol. 51, no. 5, pp. 633–638. https://doi.org/10.1134/s0015462816050070
Bulatov, V.V. and Vladimirov, I.Yu., Uniform asymptotics of internal gravitational wave fields from an initial radially symmetric perturbation, Fluid Dyn., 2021, vol. 56, no. 8, pp. 1112–1118. https://doi.org/10.1134/s0015462821080103
Abramowitz, M. and Stegun, I.A., Handbook of Mathematical Functions, New York: Dover, 1992.
Watson, G.N., A Treatise on the Theory of Bessel Functions, Cambridge: Cambridge Univ. Press, 1995.
Funding
The work is supported by the Russian Science Foundation, project no. 23-21-00194.
Author information
Authors and Affiliations
Corresponding author
Ethics declarations
The author of this work declares that he has no conflicts of interest.
Additional information
Translated by E. Oborin
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
Bulatov, V.V. Peculiarities of Pulse Dynamics in Stratified Incompressible Media. Fluid Dyn 58 (Suppl 2), S230–S239 (2023). https://doi.org/10.1134/S001546282360311X
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S001546282360311X