Geodesic
Nonlinear amplification of ocean waves in straits
Teoretičeskaâ i matematičeskaâ fizika, Tome 203 (2020) no. 1, pp. 119-133 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

Using the exact Hasselmann equation, we study wind-driven deep-water ocean waves in a strait with the wind directed orthogonally to the shore. The strait has “dissipative” shores with no reflection from the shorelines. We show that the evolution of wave turbulence can be divided into two different regimes in time. During the first regime, waves propagate with the wind, and the wind-driven sea can be described by self-similar solutions of the Hasselmann equation. The second regime starts after a sufficiently significant accumulation of wave energy at the downwind boundary. From this instant, an ensemble of waves propagating against the wind starts to form. Moreover, waves orthogonal to the wind arise and propagate along the strait. The wave system eventually reaches an asymptotic stationary state in which two types of wave motion coexist: an ensemble of self-similar waves propagating with the wind and quasimonochromatic waves propagating almost orthogonally to the wind direction and tending to slant against the wind at the angle of $15^{\circ}$ with respect to the shore of turbulence origination. These “secondary waves" arise only as a result of an intensive nonlinear wave interaction. The total wave energy exceeds its expected value approximately by a factor of two compared with the energy calculated in the absence of shores. We expect that this amplification increases substantially in the presence of reflective shores. We propose calling this "secondary” laser-like mechanism “nonlinear ocean wave amplification” abbreviated NOWA.
Keywords: nonlinear wave, weak turbulence, ocean surface wave, kinetic wave equation. 
@article{TMF_2020_203_1_a8,
     author = {A. N. Pushkarev and V. E. Zakharov},
     title = {Nonlinear amplification of ocean waves in straits},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {119--133},
     year = {2020},
     volume = {203},
     number = {1},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2020_203_1_a8/}
}
TY  - JOUR
AU  - A. N. Pushkarev
AU  - V. E. Zakharov
TI  - Nonlinear amplification of ocean waves in straits
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 2020
SP  - 119
EP  - 133
VL  - 203
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/TMF_2020_203_1_a8/
LA  - ru
ID  - TMF_2020_203_1_a8
ER  - 
%0 Journal Article
%A A. N. Pushkarev
%A V. E. Zakharov
%T Nonlinear amplification of ocean waves in straits
%J Teoretičeskaâ i matematičeskaâ fizika
%D 2020
%P 119-133
%V 203
%N 1
%U http://geodesic.mathdoc.fr/item/TMF_2020_203_1_a8/
%G ru
%F TMF_2020_203_1_a8
A. N. Pushkarev; V. E. Zakharov. Nonlinear amplification of ocean waves in straits. Teoretičeskaâ i matematičeskaâ fizika, Tome 203 (2020) no. 1, pp. 119-133. http://geodesic.mathdoc.fr/item/TMF_2020_203_1_a8/

[1] K. Hasselmann, “On the non-linear energy transfer in a gravity-wave spectrum. Part 1. General theory”, J. Fluid Mech., 12:4 (1962), 481–500 ; “On the non-linear energy transfer in a gravity wave spectrum. Part 2. Conservation theorems; wave-particle analogy; irrevesibility”, 15:2 (1963), 273–281 | DOI | MR | DOI | MR

[2] S. I. Badulin, A. N. Pushkarev, D. T. Resio, V. E. Zakharov, “Self-similarity of wind-driven seas”, Nonlin. Processes Geophys., 12:6 (2005), 891–945 | DOI

[3] A. Pushkarev, V. Zakharov, “Limited fetch revisited: comparison of wind input terms, in surface wave modeling”, Ocean Model., 103 (2016), 18–37 | DOI

[4] V. E. Zakharov, D. Resio, A. Pushkarev, New wind input term consistent with experimental, theoretical and numerical considerations, arXiv: 1212.1069

[5] V. Zakharov, D. Resio, A. Pushkarev, “Balanced source terms for wave generation within the Hasselmann equation”, Nonlinear Processes Geophys., 24:4 (2017), 581–597 | DOI

[6] C. E. Long, D. T. Resio, “Wind wave spectral observations in Currituck Sound, North Carolina”, J. Geophys. Res., 112:C5 (2007), C05001, 21 pp. | DOI

[7] S. I. Badulin, A. V. Babanin, V. E. Zakharov, D. T. Resio, “Weakly turbulent laws of wind-wave growth”, J. Fluid Mech., 591 (2007), 339–378 | DOI

[8] A. Pushkarev, “Nonlinear generation of surface waves against the wind in a limited fetch growth model”, J. Phys.: Conf. Ser., 510:1 (2014), 012048, 10 pp. | DOI

[9] V. E. Zakharov, A. N. Pushkarev, 2013,\par https://pdfs.semanticscholar.org/d807/9d94d6df29d1e74882a0e2c2593b2d196fbb.pdf

[10] A. N. Pushkarev, V. E. Zakharov, “Nonlinear generation of surface waves against the wind in a limited fetch growth model”, Proceedings of the 20th meeting WISE (College Park, MD, USA, April 21–25, 2013), ECMWF, College Park, MD, 2013

[11] R. P. Fedorenko, Vvedenie v vychislitelnuyu fiziku, Izd-vo Mosk. fiz.-tekhn. in-ta, M., 1994

[12] N. N. Kalitkin, Chislennye metody, Nauka, M., 1978 | MR

[13] D. J. Webb, “Non-linear transfers between sea waves”, Deep-Sea Res., 25:3 (1978), 279–298 | DOI

[14] B.A. Tracy, D. T. Resio, Theory and Calculation of the Nonlinear Energy Transfer Between Sea Waves in Deep Water, U. S. Army Engineer Waterways Experiment Station, Vicksburg, MS, 1982