Geodesic
Process of establishing a plane-wave system on ice cover over a dipole moving uniformly in an ideal fluid column
Teoretičeskaâ i matematičeskaâ fizika, Tome 193 (2017) no. 3, pp. 455-465 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

We consider a planar evolution problem for perturbations of the ice cover by a dipole starting its uniform rectilinear horizontal motion in a column of an initially stationary fluid. Using asymptotic Fourier analysis, we show that at supercritical velocities, waves of two types form on the water–ice interface. We describe the process of establishing these waves during the dipole motion. We assume that the fluid is ideal and incompressible and its motion is potential. The ice cover is modeled by the Kirchhoff–Love plate.
Keywords: fluid under ice cover, establishing wave.
Mots-clés : dipole 
@article{TMF_2017_193_3_a5,
     author = {A. T. Il'ichev and A. S. Savin},
     title = {Process of establishing a~plane-wave system on ice cover over a~dipole moving uniformly in an~ideal fluid column},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {455--465},
     year = {2017},
     volume = {193},
     number = {3},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2017_193_3_a5/}
}
TY  - JOUR
AU  - A. T. Il'ichev
AU  - A. S. Savin
TI  - Process of establishing a plane-wave system on ice cover over a dipole moving uniformly in an ideal fluid column
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 2017
SP  - 455
EP  - 465
VL  - 193
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/TMF_2017_193_3_a5/
LA  - ru
ID  - TMF_2017_193_3_a5
ER  - 
%0 Journal Article
%A A. T. Il'ichev
%A A. S. Savin
%T Process of establishing a plane-wave system on ice cover over a dipole moving uniformly in an ideal fluid column
%J Teoretičeskaâ i matematičeskaâ fizika
%D 2017
%P 455-465
%V 193
%N 3
%U http://geodesic.mathdoc.fr/item/TMF_2017_193_3_a5/
%G ru
%F TMF_2017_193_3_a5
A. T. Il'ichev; A. S. Savin. Process of establishing a plane-wave system on ice cover over a dipole moving uniformly in an ideal fluid column. Teoretičeskaâ i matematičeskaâ fizika, Tome 193 (2017) no. 3, pp. 455-465. http://geodesic.mathdoc.fr/item/TMF_2017_193_3_a5/

[1] A. T. Ilichev, “Solitonopodobnye struktury na poverkhnosti razdela voda–led”, UMN, 70:6(426) (2015), 85–138 | DOI | DOI | MR | Zbl

[2] N. E. Kochin, I. A. Kibel, N. V. Roze, Teoreticheskaya gidromekhanika, v. 1, Fizmatgiz, L.–M., 1963 | MR | Zbl

[3] N. E. Kochin, “O volnovom soprotivlenii i pod'emnoi sile pogruzhennykh v zhidkost tel”: N. E. Kochin, Sobranie sochinenii, v. 2, Izd. AN SSSR, M.–L., 1949, 105–182

[4] M. V. Keldysh, M. A. Lavrentev, “O dvizhenii kryla pod poverkhnostyu tyazheloi zhidkosti”: M. V. Keldysh, Izbrannye trudy. Mekhanika, Nauka, M., 1985, 120–151 | MR

[5] M. V. Keldysh, “Zamechaniya o nekotorykh dvizheniyakh tyazheloi zhidkosti”: M. V. Keldysh, Izbrannye trudy. Mekhanika, Nauka, M., 1985, 100–103 | MR

[6] L. N. Sretenskii, Teoriya volnovykh dvizhenii zhidkosti, Nauka, M., 1977

[7] L. M. Miln-Tompson, Teoreticheskaya gidrodinamika, Mir, M., 1964; | MR

[8] J. W. Davys, R. J. Hosking, A. D. Sneyd, “Waves due to a steadily moving source on a floating ice plate”, J. Fluid Mech., 158 (1985), 269–287 | DOI | Zbl

[9] R. M. S. M. Schulkes, A. D. Sneyd, “Time-dependent response of floating ice to a steadily moving load”, J. Fluid Mech., 186 (1988), 25–46 | DOI | Zbl

[10] L. A. Tkacheva, “Vozdeistvie periodicheskoi nagruzki na plavayuschuyu upruguyu plastinu”, Izv. RAN. MZhG, 40:2 (2005), 132–146 | DOI | MR | Zbl

[11] A. V. Pogorelova, V. M. Kozin, A. A. Matyushina, “Issledovaie napryazhenno-deformirovannogo sostoyaniya ledyanogo pokrova pri vzlete i posadke na nego samoleta”, PMTF, 56:5 (2015), 66–74; | DOI

[12] R. G. Chowdhury, B. N. Mandal, “Motion due to fundamental singularities in finite depth water with an elastic solid cover”, Fluid Dynam. Res., 38:4 (2006), 224–240 | DOI | MR | Zbl

[13] A. A. Savin, A. S. Savin, “Generatsiya voln na ledyanom pokrove pulsiruyuschim v zhidkosti istochnikom”, Izv. RAN. MZhG, 2013, no. 3, 24–30 | DOI | MR | Zbl

[14] D. Q. Lu, S. Q. Dai, “Generation of transient waves by impulsive disturbances in an inviscid fluid with an ice-cover”, Arch. Appl. Mech., 76:1–2 (2006), 49–63 | DOI | Zbl

[15] D. Q. Lu, S. Q. Dai, “Flexural- and capillary-gravity waves due to fundamental singularities in an inviscid fluid of finite depth”, Internat. J. Eng. Sci., 46:11 (2008), 1183–1193 | DOI | MR | Zbl

[16] A. S. Savin, “Ustanovlenie poverkhnostnykh voln, vyzyvaemykh gidrodinamicheskimi osobennostyami v ploskom potoke”, Izv. RAN. MZhG, 37:3 (2002), 78–81 | DOI | MR | Zbl

[17] A. A. Savin, A. S. Savin, “Vozmuschenie ledyanogo pokrova dvizhuschimsya v zhidkosti dipolem”, Izv. RAN. MZhG, 47:2 (2012), 3–10 | DOI | MR | Zbl

[18] A. V. Pogorelova, V. M. Kozin, V. L. Zemlyak, “Dvizhenie tonkogo tela v zhidkosti pod plavayuschei plastinoi”, PMTF, 53:1 (2012), 32–44 | DOI | Zbl

[19] I. V. Sturova, “Dvizhenie pogruzhennoi sfery v zhidkosti pod ledyanym pokrovom”, PMM, 3 (2012), 406–417 | DOI | Zbl

[20] I. V. Sturova, “Radiation of waves by a cylinder submerged in water with ice floe or polynya”, J. Fluid Mech., 784 (2015), 373–395 | DOI | MR | Zbl

[21] A. T. Ilichev, A. S. Savin, “O kharaktere protsessa ustanovleniya poverkhnostnykh voln v ploskom potoke”, Izv. RAN. MZhG, 2004, no. 4, 75–83 | DOI | MR | Zbl

[22] A. T. Ilichev, A. A. Savin, A. S. Savin, “Ustanovlenie volny na ledyanom pokrove nad dvizhuschimsya v zhidkosti dipolem”, Dokl. RAN, 444:2 (2012), 156–159 | DOI

[23] A. T. Ilichev, “Uedinennye volnovye pakety pod szhatym ledovym pokrovom”, Izv. RAN. MZhG, 2016, no. 3, 32–42 | DOI | MR | Zbl

[24] V. S. Vladimirov, Obobschennye funktsii v matematicheskoi fizike, Nauka, M., 1976 | MR

[25] A. V. Pogorelova, “Nestatsionarnoe dvizhenie istochnika v zhidkosti pod plavayuschei plastinoi”, PMTF, 52:5 (2011), 49–59 | Zbl

[26] A. A. Savin, A. S. Savin, “Prostranstvennaya zadacha o vozmuschenii ledyanogo pokrova dvizhuschimsya v zhidkosti dipolem”, Izv. RAN. MZhG, 50:5 (2015), 16–23 | DOI | MR | Zbl