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Experiments on barotropic–baroclinic conversion and the applicability of linear n-layer internal wave theories

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Abstract

Interfacial internal waves in a stratified fluid excited by periodic free-surface perturbations in a closed tank are studied experimentally. Barotropic–baroclinic energy conversion is induced by the presence of a bottom obstacle. The connection between horizontal surface velocities and internal wave amplitudes is investigated, the developing flow patterns are described qualitatively, and the wave speeds of internal waves are systematically analyzed and compared to linear two- and three-layer theories. We find that, despite the fact that the observed internal waves can have considerable amplitudes, a linear three-layer approximation still gives fairly good agreement with the experimental results.

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References

  • Adrian RJ (1991) Particle-imaging techniques for experimental fluid mechanics. Annu Rev Fluid Mech 23(1):261–304

    Article  Google Scholar 

  • Apel JR (2003) A new analytical model for internal solitons in the ocean. J Phys Oceanogr 33(11):2247–2269

    Article  MathSciNet  Google Scholar 

  • Balmforth NJ et al (2005) 2004 program of study: tides. Woods Hole Oceanographic Institution, Woods Hole

    Book  Google Scholar 

  • Boschan J, Vincze M, Jánosi IM, Tél T (2012) Nonlinear resonance in barotropic–baroclinic transfer generated by bottom sills. Phys Fluids 24(4):046601

    Article  Google Scholar 

  • Camassa R, Tiron R (2011) Optimal two-layer approximation for continuous density stratification. J Fluid Mech 669:32–54

    Article  MathSciNet  MATH  Google Scholar 

  • Dupont P, Kadri Y, Chomaz J (2001) Internal waves generated by the wake of Gaussian hills. Phys Fluids 13(11):3223–3233

    Article  MATH  Google Scholar 

  • Farmer DM, Smith JD (1980) Tidal interaction of stratified flow with a sill in Knight Inlet. Deep Sea Res Part A 27:239

    Article  Google Scholar 

  • Fructus D, Grue J (2004) Fully nonlinear solitary waves in a layered stratified fluid. J Fluid Mech 505:323–347

    Article  MathSciNet  MATH  Google Scholar 

  • Garrett C, Munk W (1979) Internal waves in the ocean. Annu Rev Fluid Mech 11(1):339–369

    Article  MathSciNet  MATH  Google Scholar 

  • Helfrich KR, Melville WK, Miles JW (1984) On interfacial solitary waves over slowly varying topography. J Fluid Mech 149:305–317

    Article  MathSciNet  MATH  Google Scholar 

  • Hogg AMC, Ivey GN (2003) The Kelvin–Helmholtz to Holmboe instability transition in stratified exchange flows. J Fluid Mech 477:339–362

    Article  MathSciNet  MATH  Google Scholar 

  • Holloway PE, Merrifield MA (1999) Internal tide generation by seamounts, ridges, and islands. J Geophys Res 104(C11):25937–25951

    Article  Google Scholar 

  • Hunt JN (1961) Interfacial waves of finite amplitude. La Houille Blanche 4:515–531

    Article  MathSciNet  Google Scholar 

  • Kakutani T, Jamasaki N (1978) Solitary waves on a two-layer fluid. J Phys Soc Jpn 45(2):674–679

    Article  Google Scholar 

  • Kelly SM, Nash JD, Kunze E (2010) Internal tide energy over topography. J Geophys Res 115(C6):C06014

    Article  Google Scholar 

  • Khabakhpashev GA (1990) Modeling the propagation of internal waves in a two-layer ocean. Izv Atmos Ocean Phys 26:47–54

    Google Scholar 

  • Koop CG, Butler G (1981) An investigation of internal solitary waves in a two-fluid system. J Fluid Mech 112:225–251

    Article  MathSciNet  MATH  Google Scholar 

  • Kundu PK, Cohen IM (2008) Fluid mechanics, 4th edn. Academic, Amsterdam

    Google Scholar 

  • Llewellyn Smith SG, Young WR (2002) Conversion of the barotropic tide. J Phys Oceanogr 32(5):1554–1566

    Article  MathSciNet  Google Scholar 

  • Maas LRM (2011) Topographies lacking tidal conversion. J Fluid Mech 684:5–24

    Article  MathSciNet  MATH  Google Scholar 

  • Martin JP, Rudnick DL, Pinkel R (2006) Spatially broad observations of internal waves in the upper ocean at the Hawaiian Ridge. J Phys Oceanogr 36(6):1085–1103

    Article  Google Scholar 

  • Massel SR (2015) Internal gravity waves in the shallow seas. Springer, Bern

    Book  Google Scholar 

  • Mercier MJ, Vasseur R, Dauxois T (2011) Resurrecting dead-water phenomenon. Nonlinear Process Geophys 18:193

    Article  Google Scholar 

  • Parsmar R, Stigebrandt A (1997) Observed damping of barotropic seiches through baroclinic wave drag in the Gullmar fjord. J Phys Oceanogr 27:380

    Article  Google Scholar 

  • Pedlosky J (2013) Waves in the ocean and atmosphere: introduction to wave dynamics. Springer, New York

    Google Scholar 

  • Piechura J, Beszczynska-Möller A (2004) Inflow waters in the deep regions of the southern Baltic Sea-transport and transformations. Oceanologia 46(1):113

    Google Scholar 

  • Rainville L, Pinkel R (2006) Propagation of low-mode internal waves through the ocean. J Phys Oceanogr 36(6):1220–1236

    Article  MathSciNet  Google Scholar 

  • Rodenborn BE, Kiefer D, Zhang HP, Swinney HL (2011) Harmonic generation by reflecting internal waves. Phys Fluids 23(2):026601

    Article  Google Scholar 

  • Segur H, Hammack JL (1982) Soliton models of long internal waves. J Fluid Mech 118:285–304

    Article  MathSciNet  MATH  Google Scholar 

  • Stigebrandt A (1999) Baroclinic wave drag and barotropic to baroclinic energy transfer at sills as evidenced by tidal retardation, seiche damping and diapycnal mixing in fjords. Dyn Intern Gravity Waves II:73–82

    Google Scholar 

  • Sutherland BR (2010) Internal gravity waves. Cambridge University Press, Cambridge

    Book  MATH  Google Scholar 

  • Vallis GK (2006) Atmospheric and oceanic fluid dynamics: fundamentals and large-scale circulation. Cambridge University Press, Cambridge

    Book  Google Scholar 

  • Vincze M, Kozma P, Gyüre B, Jánosi IM, Szabó KG, Tél T (2007) Amplified internal pulsations on a stratified exchange flow excited by interaction between a thin sill and external seiche. Phys Fluids 19(10):108108

    Article  MATH  Google Scholar 

  • Vlasenko V, Stashchuk N, Hutter K (2005) Baroclinic tides: theoretical modeling and observational evidence. Cambridge University Press, Cambridge

    Book  MATH  Google Scholar 

  • Zhang HP, King B, Swinney HL (2008) Resonant generation of internal waves on a model continental slope. Phys Rev Lett 100(24):244504

    Article  Google Scholar 

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Acknowledgements

The authors are grateful for Anna Kohári, Imre M. Jánosi and Balázs Tóth for the crucial support. The fruitful discussions with Tamás Tél are also highly acknowledged. This work is supported by the Hungarian National Research, Development and Innovation Office (NKFIH) under Grant Number FK125024.

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Correspondence to Miklós Vincze.

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Vincze, M., Bozóki, T. Experiments on barotropic–baroclinic conversion and the applicability of linear n-layer internal wave theories. Exp Fluids 58, 136 (2017). https://doi.org/10.1007/s00348-017-2418-7

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  • DOI: https://doi.org/10.1007/s00348-017-2418-7

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