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Laser-like wave amplification in straits

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Abstract

We present research on the excitation of ocean surface wind waves in non-homogeneous situations, for the case of a deep water strait in the presence of a constant wind, blowing perpendicular to the coast line. The statistical wave model used is based on the Hasselmann equation with high-wavenumbers wave-breaking dissipation, exact non-linear four-wave interaction, and ZRP (Zakharov-Resio-Pushkarev (Zakharov et al. Nonlin Process Geophys 24:581–597 2017) wind input term. At the first stage, the waves propagate in the wind direction in a step-like moving front manner, which is the combination of self-similar fetch-limited and duration-limited solutions of the Hasselmann equation. The second stage begins after intermediate self-similar linear asymptotics for wave energy is built along the fetch. Beginning with that time, the wave groups, propagating across and against the wind due to nonlinear interaction, are observed. Despite the absence of long-wave dissipation, the system asymptotically evolves into a complex quasi-stationary state, comprised of the self-similar “wind sea” in the wind direction, and quasi-monochromatic waves, radiating close to orthogonally with respect to the wind, while slightly tilting from perfectly orthogonal to the wind direction, with the angle slant increasing toward the wave turbulence origination shore line, and reaching 15∘ close to it. The total wave energy in the asymptotic state exceeds the wave sea energy propagating along the wind by a factor of two due to the presence of quasi-orthogonal and counter the wind wave fields. Very similar turbulence structure was previously observed experimentally; this paper presents a theoretical explanation of these results.

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References

  • Ardag D, Resio D (2019) Inconsistent spectral evolution in operational wave models due to inaccurate specification of nonlinear interactions. J Phys Oceanogr 49(3):705–722. https://doi.org/10.1175/JPO-D-17-0162.1

    Article  Google Scholar 

  • Badulin SI, Babanin AV, Resio DT, Zakharov VE (2007) Weakly turbulent laws of wind-wave growth. J Fluid Mech 591:339–378

    Article  Google Scholar 

  • Badulin SI, Zakharov VE (2012) The generalized Phillips’ spectra and new dissipation function for wind-driven seas. arXiv:1212.0963 [physics.ao-ph], pp 1–16

  • Cavaleri L, Abdalla S, Benetazzo A, Bertottia L, Bidlot JR, Breivik O, Carniela S, Jensen RE, Portilla-Yandune J, Rogers WE, Roland A, Sanchez-Arcilla A, Smith JM, Staneva J, Toledo Y, van Vledder GP, van der Westhuysen AJ (2018) Wave modelling in coastal and inner seas. Prog Oceanogr 167:164–233. https://doi.org/10.1016/j.pocean.2018.03.010

    Article  Google Scholar 

  • Chalikov D (1995) The parameterization of the wave boundary layer. JPO 25:1333–1349

    Article  Google Scholar 

  • Dommermuth DG, Yue KP (1987) A high-order spectral method for the study of nonlinear gravity waves. J Fluid Mech 184:267–288. https://doi.org/10.1017/S002211208700288X

    Article  Google Scholar 

  • Donelan MA, Curcic M, Chen SS, Magnusson AK (2012) Modeling waves and wind stress. J Geophys Res 117:C00J23. https://doi.org/10.1029/2011JC007787

    Google Scholar 

  • Ardhuin F, Herbers T, Watts K, Vledder GV, Jensen R, Graber H (2007) Swell and slanting-fetch effects on wind wave growth. J Phys Oceanogr 37(4):908–931. https://doi.org/10.1175/JPO3039.1

    Article  Google Scholar 

  • Fedorenko RP (1994) Introduction into computational physics. Nauka, Moscow. in Russian

    Google Scholar 

  • Hasselmann K (1962) On the non-linear energy transfer in a gravity-wave spectrum. Part 1. General theory. J Fluid Mech 12:481–500

    Article  Google Scholar 

  • Hasselmann K (1963) On the non-linear energy transfer in a gravity wave spectrum. Part 2. Conservation theorems; wave-particle analogy; irreversibility. J Fluid Mech 15:273–281

    Article  Google Scholar 

  • Hsiao SV, Shemdin OH (1983) Measurements of wind velocity and pressure with a wave follower during MARSEN. JGR 88:9841–9849

    Article  Google Scholar 

  • Hwang PA, Wang DW, Rogers WE, Kaihatu JM (2000) A discussion on the directional distribution of wind-generated ocean waves. In: Resio D T (ed) 6th International workshop on wave hindcasting and forecasting, Monterey. Meteorological Service of Canada Environment Canada, Enviroment Canada, 4905 Dufferin Street M3H 5T4. http://resolver.tudelft.nl/uuid:ed727b97-db13-432c-854d-09a547c3654e, pp 273–279

  • Hwang PA, Wang DW, Rogers WE, Swift RN, Yungel J, Krabill WB (2001a) Bimodal directional propagation of wind-generated ocean surface waves. https://doi.org/10.13140/RG.2.1.4591.5689

  • Hwang PW, Wang WD, Rogers WE, Kaihatu J, Yungel J, Swift R, Krabill W (2001b) Bimodal directional distribution of the second kind: resonant propagation of wind-generated ocean waves. NRL Review, pp 160–162. https://www7320.nrlssc.navy.mil/pubs/2001/rogers-2001.pdf

  • Hwang P (2002) Retondo080102bimodal. https://doi.org/10.13140/RG.2.1.2101.2001

  • Hwang PA, Wang DW, Yungel J, Swift RN, Krabill WB (2019) Do wind-generated waves under steady forcing propagate primarily in the downwind direction? arXiv:1907.01532v1

  • Kalitkin NN (1978) Chislennye metody. Nauka, Moscow. in Russian

    Google Scholar 

  • Komen GJ, Hasselmann S, Hasselmann K (1984) On the existence of a fully developed wind-sea spectrum. J Phys Oceanogr 14:1271–1285

    Article  Google Scholar 

  • Korotkevich AO, Pushkarev AN, Resio D, Zakharov VE (2008) Numerical verification of the weak turbulent model for swell evolution. Eur J Mech B - Fluids 27:361–387

    Article  Google Scholar 

  • Long C, Resio D (2007) Wind wave spectral observations in Currituck Sound, North Carolina. JGR 112:C05001

    Article  Google Scholar 

  • Perrie W, Zakharov VE (1999) The equilibrium range cascades of wind-generated waves. Eur J Mech B/Fluids 18:365–371

    Article  Google Scholar 

  • Pushkarev AN, Zakharov VE (1996) Turbulence of capillary waves. Phys Rev Lett 76:3320

    Article  Google Scholar 

  • Pushkarev AN, Zakharov VE (2013) Nonlinear generation of surface waves against the wind in a limited fetch growth model. In: 20th meeting WISE. ECMWF, ECMWF, College Park

  • Pushkarev A (2014) Nonlinear generation of surface waves against the wind in limited fetch growth model. J Phys Conf Ser 510:012048

    Article  Google Scholar 

  • Pushkarev A (2018) Comparison of different models for wave generation of the Hasselmann equation. Procedia IUTAM 26:132–144. https://doi.org/10.1029/2011JC007787

    Article  Google Scholar 

  • Pushkarev A, Resio D, Zakharov V (2003) Weak turbulent approach to the wind-generated gravity sea waves. Physica D 184:29–63

    Article  Google Scholar 

  • Pushkarev A, Zakharov V (2016) Limited fetch revisited: comparison of wind input terms, in surface wave modeling. Ocean Model 103:18–37. https://doi.org/10.1016/j.ocemod.2016.03.005

    Article  Google Scholar 

  • Pushkarev A, Zakharov V (2020) Nonlinear amplification of ocean waves in straits. Theor Math Phys 203:534–546. https://doi.org/10.1134/S0040577920040091

    Article  Google Scholar 

  • Resio D, Perrie W (1989) Implications of an f− 4 equilibrium range for wind-generated waves. JPO 19:193–204

    Article  Google Scholar 

  • Resio DT, Long CE, Vincent CL (2004) Equilibrium-range constant in wind-generated wave spectra. J Geophys Res 109:CO1018

    Article  Google Scholar 

  • Resio DT, Long CE (2007) Wind wave spectral observations in Currituck Sound, North Carolina. J Geophys Res 112:C05001

    Google Scholar 

  • Rogers W, Vledder GPV (2013) Frequency width in predictions of windsea spectra and the role of the nonlinear solver. Ocean Model 70:52–61. https://doi.org/10.1016/j.ocemod.2012.11.010

    Article  Google Scholar 

  • Simanesew AW, Krogstad HE, Trulsen K, Nieto Borge JC (2018) Bimodality of directional distributions in ocean wave spectra: a comparison of data-adaptive estimation techniques. J Atmos Ocean Technol 35(2):365–384. https://doi.org/10.1175/JTECH-D-17-0007.1

    Article  Google Scholar 

  • Snyder RL, Dobson FW, Elliott JA, Long RB (1981) Array measurements of atmospheric pressure fluctuations above surface gravity waves. J Fluid Mech 102:1–59

    Article  Google Scholar 

  • Tracy B, Resio D (1982) Theory and calculation of the nonlinear energy transfer between sea waves in deep water. WES report 11. U.S. Army Engineer Waterways Experiment Station, Vicksburg

  • Tsagareli KN, Babanin AV, Walker DJ, Young RI (2010) Numerical investigation of spectral evolution of wind waves. part i: Wind-input source function. J Phys Oceanogr 40(4):656–666. https://doi.org/10.1175/2009JPO4345.1

    Article  Google Scholar 

  • Webb DJ (1978) Non-linear transfers between sea waves. Deep-Sea Res 25:279–298

    Article  Google Scholar 

  • Zakharov VE, Filonenko NN (1967) The energy spectrum for stochastic oscillations of a fluid surface. Sov Phys Docl 11:881–884

    Google Scholar 

  • Zakharov VE (1968) Stability of periodic waves of finite amplitude on the surface of deep fluid. Zhurnal Prikladnoi Mekhaniki i Technicheskoi Fiziki 9(2):86–94

    Google Scholar 

  • Zakharov VE, Pushkarev AN, Shvets VF, Yankov VV (1988) Soliton turbulence. Pis’ma Zh Exp Teor Fiz 48(2):79–82

    Google Scholar 

  • Zakharov V, Resio D, Pushkarev A (2017) Balanced source terms for wave generation within the Hasselmann equation. Nonlin Process Geophys 24:581–597. https://doi.org/10.5194/npg-24-581-2017

    Article  Google Scholar 

  • Zakharov VE, Pushkarev AN (2013) Classical and non-classical regimes of the limited-fetch wave growth and localized structures on the surface of water. https://www.onr.navy.mil/reports/FY13/nopushka.pdf

  • Zakharov VE, Resio D, Pushkarev A (2012) New wind input term consistent with experimental, theoretical and numerical considerations. 1212.1069/

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Funding

The presented research has been accomplished due to the support of the grant “Wave turbulence: the theory, mathematical modeling and experiment” of the Russian Scientific Foundation No 19-72-30028.

The author gratefully acknowledges the support of this foundation.

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Authors and Affiliations

  1. Skoltech, Bolshoy Boulevard 30, bld. 1, Moscow, 121205, Russia

    Andrei Pushkarev

  2. Lebedev Physical Institute RAS, Leninsky 53, Moscow, 119991, Russia

    Andrei Pushkarev

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  1. Andrei Pushkarev
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Correspondence to Andrei Pushkarev.

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Responsible Editor: Val Swail

This article is part of the Topical Collection on the 16th International Workshop on Wave Hindcasting and Forecasting in Melbourne, AU, November 10–15, 2019

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Pushkarev, A. Laser-like wave amplification in straits. Ocean Dynamics 71, 195–215 (2021). https://doi.org/10.1007/s10236-020-01425-w

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  • DOI: https://doi.org/10.1007/s10236-020-01425-w

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