Geodesic
Spectral Analysis of the Efficiency of Vertical Mixing in the Deep Ocean due to Interaction of Tidal Currents with a Ridge Running down a Continental Slope
R. N. Ibragimov1, 2 ; A. Tartakovsky1, 3
1 Pacific Northwest National Laboratory, Richland, WA 99352, USA
2 Lead Mathematician, Applied Statistics Lab, GE Global Research 1 Research Circle Niskayuna, NY 12309
3 School of Geosciences, Department of Mathematics and Statistics University of South Florida, Tampa, FL
Mathematical modelling of natural phenomena, Tome 9 (2014) no. 5, pp. 119-137.

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Efficiency of mixing, resulting from the reflection of an internal wave field imposed on the oscillatory background flow with a three-dimensional bottom topography, is investigated using a linear approximation. The radiating wave field is associated with the spectrum of the linear model, which consists of those mode numbers n and slope values α, for which the solution represents the internal waves of frequencies ω = nω0 radiating upwrad of the topography, where ω0 is the fundamental frequency at which internal waves are generated at the topography. The effects of the bottom topography and the earth’s rotation on the spectrum is analyzed analytically and numerically in the vicinity of the critical slopeαn,θc = arcsin (n 2ω02-f 2 / N 2-f 2) 1/2 which is a slope with the same angle to the horizontal as the internal wave characteristic. In this notation, θ is latitude, f is the Coriolis parameter and N is the buoyancy frequency, which is assumed to be a constant, which corresponds to the uniform stratification.
DOI : 10.1051/mmnp/20149508

R. N. Ibragimov 1, 2 ; A. Tartakovsky 1, 3

1 Pacific Northwest National Laboratory, Richland, WA 99352, USA
2 Lead Mathematician, Applied Statistics Lab, GE Global Research 1 Research Circle Niskayuna, NY 12309
3 School of Geosciences, Department of Mathematics and Statistics University of South Florida, Tampa, FL 
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R. N. Ibragimov; A. Tartakovsky. Spectral Analysis of the Efficiency of Vertical Mixing in the Deep Ocean due to Interaction of Tidal Currents with a Ridge Running down a Continental Slope. Mathematical modelling of natural phenomena, Tome 9 (2014) no. 5, pp. 119-137. doi : 10.1051/mmnp/20149508. http://geodesic.mathdoc.fr/articles/10.1051/mmnp/20149508/

[1] C.H. Appenzeller, C.H. Davies, W.A. Norton J. Geophys. Res. 1996 1435 1456

[2] L. Armi J. Mar. Res. 1997 515 530

[3] P.G. Baines. Topographic Effects in Stratified Flows. CambridgeUniversity Press. 1971.

[4] P.G. Baines Deep Sea Res. 1982 307 338

[5] N.J. Balmforth, G.R. Ierley, W.R. Young J. Phys. Oceanogr. 2002 2900 2914

[6] T.H. Bell J. Fluid Mech. 1975 705 722

[7] R. Bedard, M. Previsic, G. Hagerman. North American Ocean Energy Status March 2007.Electric Power Research Institute (EPRI) Tidal Power (TP), Volume 8, G. 2007.

[8] G.D. Egbert, R. Ray. Signi cant dissipation of tidal energy in the deep ocean inferred from satellite altimeter data. Nature, 2000.

[9] N. Fraser. Surfing an oil rig. Energy Rev., (1999), 20–4 February/March.

[10] C. Garrett Nature 2003 477 478

[11] C. Garrett, P. Maccready, P.B. Rhines Annu. Rev. Fluid Mech. 1993 291 323

[12] R. Grimshaw, N. Smyth J. Fluid Mech. 1986 429 464

[13] A. Gill. Atmosphere-Ocean Dynamics. New York, etc., Academic Press., A., 1983.

[14] R.N. Ibragimov Physica Scripta 2008 065801

[15] R. Ibragimov, N. Yilmaz, A. Bakhtiyarov Mech. Res. Comm. 2011 261 266

[16] R.N. Ibragimov Phys. Fluids 2011 123102

[17] R.N. Ibragimov, V. Vatchev Phys. Let. A 2011 94 101

[18] R.N. Ibragimov, G. Jefferson, J. Carminati Int. J. Non-Linear Mech. 2013 28 44

[19] J.C. Kaimal, J.J. Finnigan. Atmospheric Boundary Layer Flows. Their Structure and Measurement. Oxford University Press, 1994 London.

[20] L.H. Kantha, C.A. Clayson. Small Scale Processes in Geophysical Fluid Flows. New York, etc., Academic Press, International Geophysics Series, V. 67, 2000.

[21] S. Khatiwala. Generation of internal tides in an ocean of finite depth: analytical and numerical calculations. Deep See Res., I, 50 2003, 3-21.

[22] P.K. Kundu. Fluid Mechanics. Academic Press, Inc. 1990.

[23] E. Kunze, C. Garrett nnu. Rev. Fluid Mech 2007 57 87

[24] F. Lam, L. Mass, T. Gerkema Deep-See Res., I 2004 10751096

[25] S. Legg, A. Adcroft J. Phys. Oceanogr. 2003 2224 2247

[26] S. Legg J. Phys. Oceanogr. 2004 1824 1838

[27] S.G. Llewellyn Smith, W.R. Young J. Phys.Oceanogr. 2002 1554 1566

[28] R.R. Long Annu. Rev. Fluid Mech. 1972 69 92

[29] P. Maccready, G. Pawlak J. Phys. Oceanogr. 2001 2824 2838

[30] J.W. Miles.Waves and wave drag in stratified flows. Applied Mechanics: Proc. 12th Int.Cong. Appl. Mech., Springer, 1969.

[31] P. Muller, A. Naratov. The internal wave action model (IWAM). Proceedings, Aha Huliko’a Hawaiian Winter Workshop, School of Ocean and Earth Science and Technology, Special Publication, 2003.

[32] W. Munk, C. Wunsch Deep Sea Res. 1998 1977 2010

[33] J.C. Nappo. An introduction to atmospheric gravity waves. Academic Press, San Diego, 2002.

[34] J.D. Nash, J.M. Moum Geophys. Res. 2001 4593 4612

[35] G.T. Needler Phil. Trans. R. Soc. London A 1986 177 187

[36] K.L. Polzin, J.M. Toole, J.R. Ledwell Science 1997 93 96

[37] P. Queney Bull. Am. Meteorol. Soc. 1948

[38] R.S. Scorer. Environmental Aerodynamics, Halsted Press, N.-Y., 1978.

[39] S.A. Thorpe J. Phys. Oceanogr. 1996 191 204

[40] S.A. Thorpe Proc. Roy. Soc. London A 1992 115 130

[41] J.H. Trowbridge, S.J. Lentz J. Pjys. Oceanogr. 1991 1171 1185

[42] U.S. Department of Energy, 2009: Wind Hydropower Technologies Program. http://www1.eere.energy.gov/windandhydro/hydrokinetic/. Accessed April 2009.

[43] G.N. Watson. A Treatise on the Theory of Bessel Functions. 2nd ed., Cambridge University Press, 1966.

[44] C. Wunsch, R. Ferrari Annu. Rev. Fluid Mech. 2004 281 314

[45] M.G. Wurtele, R.D. Sharman, A. Datta Annu. Rev. Fluid Mech. 1996 429 476

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