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Erschienen in: Experiments in Fluids 12/2013

01.12.2013 | Research Article

Wave patterns generated by an axisymmetric obstacle in a two-layer flow

verfasst von: L. Lacaze, A. Paci, E. Cid, S. Cazin, O. Eiff, J. G. Esler, E. R. Johnson

Erschienen in: Experiments in Fluids | Ausgabe 12/2013

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Abstract

Gravity waves generated by a moving obstacle in a two-layer stratified fluid are investigated. The experimental configuration is three-dimensional with an axisymmetric obstacle which is towed in one of the two layers. The experimental method used in the present study is based on a stereoscopic technique allowing the 3D reconstruction of the interface between the two layers. Investigation into the wave pattern as a function of the Froude number, Fr, based on the relative density of the fluid layers and the velocity of the towed obstacle is presented. Specific attention is paid to the transcritical regime for which Fr is close to one. Potential energy trapped in the wave field patterns is also extracted from the experimental results and is analyzed as a function of both the Froude number, Fr, and the transcritical similarity parameter \(\varGamma\). In particular, a remarkable increase in the potential energy around Fr = 1 is observed and a scaling allowing to assemble data resulting from different experimental parameters is proposed.

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Fußnoten
1
As obstacles are towed upside down, they cannot be fully immersed, so effective h m 0 is slightly smaller than the values given above and is 7.5 cm (resp. 11.5 cm) for obstacle A (resp. obstacle B).
 
2
t = 0 is defined here for the frame in which the obstacle center coincides with the center of the field of view.
 
3
It is verified that the obtained value of x m is always smaller than the distance at which reflective waves invade the domain.
 
Literatur
Zurück zum Zitat Apel J, Holbrook J, Liu A, Tsai J (1985) The Sulu sea internal soliton experiment. J Phys Oceanogr 15(12):1625–1651CrossRef Apel J, Holbrook J, Liu A, Tsai J (1985) The Sulu sea internal soliton experiment. J Phys Oceanogr 15(12):1625–1651CrossRef
Zurück zum Zitat Astruc D, Cazin S, Cid E, Eiff O, Lacaze L, Robin P, Toublanc F, Cáceres I (2012) A stereoscopic method for rapid monitoring of the spatio-temporal evolution of the sand-bed elevation in the swash zone. Coast Eng 60:1–20CrossRef Astruc D, Cazin S, Cid E, Eiff O, Lacaze L, Robin P, Toublanc F, Cáceres I (2012) A stereoscopic method for rapid monitoring of the spatio-temporal evolution of the sand-bed elevation in the swash zone. Coast Eng 60:1–20CrossRef
Zurück zum Zitat Benetazzo A (2006) Measurements of short water waves using stereo matched image sequences. Coast Eng 53:1013CrossRef Benetazzo A (2006) Measurements of short water waves using stereo matched image sequences. Coast Eng 53:1013CrossRef
Zurück zum Zitat Cech J, Sara R (2007) Efficient sampling of disparity space for fast and accurate matching. In: Proceedings of BenCOS Workshop CVPR Cech J, Sara R (2007) Efficient sampling of disparity space for fast and accurate matching. In: Proceedings of BenCOS Workshop CVPR
Zurück zum Zitat Chatellier L, Jarny S, Gibouin F, David L (2010) Stereoscopic measurement of free surface flows. In: 14th international conference on experimental mechanics, Poitiers, France Chatellier L, Jarny S, Gibouin F, David L (2010) Stereoscopic measurement of free surface flows. In: 14th international conference on experimental mechanics, Poitiers, France
Zurück zum Zitat Crapper GD (1967) Ship waves in a stratified ocean. J Fluid Mech 29:667CrossRef Crapper GD (1967) Ship waves in a stratified ocean. J Fluid Mech 29:667CrossRef
Zurück zum Zitat de Vries S, Hill DF, de Schipper MA, Stive MJF (2011) Remote sensing of surf zone waves using stereo imaging. Coast Eng 58:239CrossRef de Vries S, Hill DF, de Schipper MA, Stive MJF (2011) Remote sensing of surf zone waves using stereo imaging. Coast Eng 58:239CrossRef
Zurück zum Zitat Douxchamps D, Devriendt D, Capart H, Craeye C, Macq B, Zech Y (2005) Stereoscopic and velocimetric reconstructions of the free surface topography of antidune flows. Exp Fluids 39:533CrossRef Douxchamps D, Devriendt D, Capart H, Craeye C, Macq B, Zech Y (2005) Stereoscopic and velocimetric reconstructions of the free surface topography of antidune flows. Exp Fluids 39:533CrossRef
Zurück zum Zitat Esler JG, Rump OJ, Johnson ER (2007) Non-dispersive and weakly dispersive single-layer flow over an axisymmetric obstacle: the equivalent aerofoil formulation. J Fluid Mech 574:209MathSciNetCrossRefMATH Esler JG, Rump OJ, Johnson ER (2007) Non-dispersive and weakly dispersive single-layer flow over an axisymmetric obstacle: the equivalent aerofoil formulation. J Fluid Mech 574:209MathSciNetCrossRefMATH
Zurück zum Zitat Goler RA, Reeder MJ (2004) The generation of the morning glory. J Atmos Sci 61:1360–1376CrossRef Goler RA, Reeder MJ (2004) The generation of the morning glory. J Atmos Sci 61:1360–1376CrossRef
Zurück zum Zitat Hartley RI, Zisserman A (2004) Multiple view geometry in computer vision. Cambridge University Press, CambridgeCrossRefMATH Hartley RI, Zisserman A (2004) Multiple view geometry in computer vision. Cambridge University Press, CambridgeCrossRefMATH
Zurück zum Zitat Jehle M, Jarny S, David L (2008) Différentes approches pour la mesure d’interfaces et de surface libre. In: 11ème Congrès Francophone de Techniques Lasers, Poitiers, France. p 225. (in French) Jehle M, Jarny S, David L (2008) Différentes approches pour la mesure d’interfaces et de surface libre. In: 11ème Congrès Francophone de Techniques Lasers, Poitiers, France. p 225. (in French)
Zurück zum Zitat Johnson ER, Vilenski GG (2005) Two-dimensional leaps in near-critical flow over isolated orography. Proc R Soc Lond A 61(2064):3747–3763MathSciNetCrossRef Johnson ER, Vilenski GG (2005) Two-dimensional leaps in near-critical flow over isolated orography. Proc R Soc Lond A 61(2064):3747–3763MathSciNetCrossRef
Zurück zum Zitat Johnson ER, Esler JG, Rump OJ, Sommeria J, Vilenski GG (2006) Orographically generated nonlinear waves in rotating and non-rotating two-layer flow . Proc R Soc Lond A 462(2065):3–20MathSciNetCrossRefMATH Johnson ER, Esler JG, Rump OJ, Sommeria J, Vilenski GG (2006) Orographically generated nonlinear waves in rotating and non-rotating two-layer flow . Proc R Soc Lond A 462(2065):3–20MathSciNetCrossRefMATH
Zurück zum Zitat Knigge C, Etling D, Paci A, Eiff O (2010) Laboratory experiments on mountain induced rotors. Q J R Meteorol Soc 136:442–450CrossRef Knigge C, Etling D, Paci A, Eiff O (2010) Laboratory experiments on mountain induced rotors. Q J R Meteorol Soc 136:442–450CrossRef
Zurück zum Zitat Li X, Dong C, Clemente-Colón P, Pichel WG, Friedman KS (2004) Synthetic aperture radar observation of the sea surface imprints of upstream atmospheric solitons generated by flow impeded by an island. J Geophys Res 109. doi:10.1029/2003JC002168 Li X, Dong C, Clemente-Colón P, Pichel WG, Friedman KS (2004) Synthetic aperture radar observation of the sea surface imprints of upstream atmospheric solitons generated by flow impeded by an island. J Geophys Res 109. doi:10.​1029/​2003JC002168
Zurück zum Zitat Lighthill G (1978) Waves in fluids. Cambridge university press, CambridgeMATH Lighthill G (1978) Waves in fluids. Cambridge university press, CambridgeMATH
Zurück zum Zitat Maxworthy T, Chabert d’Hieres H, Didelle H (1984) The generation and propagation of internal gravity waves in a rotating fluid. J Geophys Res 89: doi:10.1029/JC089iC04p06383 Maxworthy T, Chabert d’Hieres H, Didelle H (1984) The generation and propagation of internal gravity waves in a rotating fluid. J Geophys Res 89: doi:10.​1029/​JC089iC04p06383
Zurück zum Zitat Mercier MJ, Garnier NB, Dauxois T (2008) Reflexion and diffraction of internal waves analyzed with the Hilbert transform. Phys Fluids 20:086601CrossRef Mercier MJ, Garnier NB, Dauxois T (2008) Reflexion and diffraction of internal waves analyzed with the Hilbert transform. Phys Fluids 20:086601CrossRef
Zurück zum Zitat Mercier MJ, Mathur M, Gostiaux L, Gerkema T, Magalhes JM, Da Silva JCB, Dauxois T (2012) Soliton generation by internal tidal beams impinging on a pycnocline: laboratory experiments. J Fluid Mech 704:37–60CrossRefMATH Mercier MJ, Mathur M, Gostiaux L, Gerkema T, Magalhes JM, Da Silva JCB, Dauxois T (2012) Soliton generation by internal tidal beams impinging on a pycnocline: laboratory experiments. J Fluid Mech 704:37–60CrossRefMATH
Zurück zum Zitat Munk W, Wunsch C (1998) Abyssal recipes II : energetics of tidal and wind mixing. Deep Sea Res Part I Oceanogr Res Pap 45(12):1977–2010CrossRef Munk W, Wunsch C (1998) Abyssal recipes II : energetics of tidal and wind mixing. Deep Sea Res Part I Oceanogr Res Pap 45(12):1977–2010CrossRef
Zurück zum Zitat New A L, Pingree RD (1992) Local generation of internal soliton packets in the central Bay of Biscay. Deep Sea Res Part A Oceanogr Res Pap 39(9):1521–1534CrossRef New A L, Pingree RD (1992) Local generation of internal soliton packets in the central Bay of Biscay. Deep Sea Res Part A Oceanogr Res Pap 39(9):1521–1534CrossRef
Zurück zum Zitat Porter A, Smyth NF (2002) Modelling the morning glory of the Gulf of Carpentaria. J Fluid Mech 454:1–20CrossRefMATH Porter A, Smyth NF (2002) Modelling the morning glory of the Gulf of Carpentaria. J Fluid Mech 454:1–20CrossRefMATH
Zurück zum Zitat Rabaud M, Moisy F (2013) Ship wakes: Kelvin or Mach angle. Phys Rev Lett 110:214503CrossRef Rabaud M, Moisy F (2013) Ship wakes: Kelvin or Mach angle. Phys Rev Lett 110:214503CrossRef
Zurück zum Zitat Smith RB (1979) The influence of mountains on the atmosphere. Adv Geophys 33:87–230CrossRef Smith RB (1979) The influence of mountains on the atmosphere. Adv Geophys 33:87–230CrossRef
Zurück zum Zitat Tailleux R (2009) On the energetics of stratified turbulent mixing, irreversible thermodynamics, boussinesq models and the ocean heat engine controversy. J Fluid Mech 638:339–382CrossRefMATH Tailleux R (2009) On the energetics of stratified turbulent mixing, irreversible thermodynamics, boussinesq models and the ocean heat engine controversy. J Fluid Mech 638:339–382CrossRefMATH
Zurück zum Zitat Schar C, Smith RB (1993) Shallow-water flow past an isolated topography. Part I: Vorticity production and wake formation. J Atmos Sci 50:1373–1400MathSciNetCrossRef Schar C, Smith RB (1993) Shallow-water flow past an isolated topography. Part I: Vorticity production and wake formation. J Atmos Sci 50:1373–1400MathSciNetCrossRef
Zurück zum Zitat Wehausen JV (1973) The wave resistance of ships. Adv Appl Mech 13:93–245CrossRef Wehausen JV (1973) The wave resistance of ships. Adv Appl Mech 13:93–245CrossRef
Zurück zum Zitat Wells H, Vosper SB (2010) The accuracy of linear theory for predicting mountain-wave drag: implications for parametrization schemes. Q J R Meteorol Soc 136:429–441 Wells H, Vosper SB (2010) The accuracy of linear theory for predicting mountain-wave drag: implications for parametrization schemes. Q J R Meteorol Soc 136:429–441
Metadaten
Titel
Wave patterns generated by an axisymmetric obstacle in a two-layer flow
verfasst von
L. Lacaze
A. Paci
E. Cid
S. Cazin
O. Eiff
J. G. Esler
E. R. Johnson
Publikationsdatum
01.12.2013
Verlag
Springer Berlin Heidelberg
Erschienen in
Experiments in Fluids / Ausgabe 12/2013
Print ISSN: 0723-4864
Elektronische ISSN: 1432-1114
DOI
https://doi.org/10.1007/s00348-013-1618-z

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