Skip to main content Accessibility help
×
Home
Hostname: page-component-559fc8cf4f-dxfhg Total loading time: 0.665 Render date: 2021-02-26T05:43:53.267Z Has data issue: true Feature Flags: { "shouldUseShareProductTool": true, "shouldUseHypothesis": true, "isUnsiloEnabled": true, "metricsAbstractViews": false, "figures": false, "newCiteModal": false, "newCitedByModal": true }

Quasi-two-dimensional properties of a single shallow-water vortex with high initial Reynolds numbers

Published online by Cambridge University Press:  19 October 2010

D.-G. SEOL
Affiliation:
Institute for Hydromechanics, Karlsruhe Institute of Technology, Kaiserstr. 12, Karlsruhe 76131, Germany
G. H. JIRKA
Affiliation:
Institute for Hydromechanics, Karlsruhe Institute of Technology, Kaiserstr. 12, Karlsruhe 76131, Germany
Corresponding
E-mail address:

Abstract

The evolution and dynamics of a shallow-water vortex system with high initial Reynolds numbers are investigated experimentally without background rotation. A single vortex is generated by rotating a water mass at the centre of an experimental tank using a bottomless cylinder with internal sectors. The surface velocity field is observed via particle image velocimetry. The experimentally observed vorticity fields indicate that strong shallowness (the ratio of the cylinder diameter to the water depth) and high Reynolds number contribute to the formation of large-scale coherent structures in the form of a tripolar vortex system. The shallow-water vortices with high initial Reynolds numbers experience the transition from turbulent to laminar regimes in their decay process. The proposed first-order vortex decay model predicts that a shallow-water vortex decays as t−1 in the initial turbulent stage and as e−t in the later laminar stage due to horizontal diffusion and bottom friction. The estimated transition time scale from the turbulent to laminar stage increases with initial vortex Reynolds number and with shallowness. By taking the vortex expansion into consideration, the second-order vortex decay model is also presented. The azimuthally ensemble-averaged data elucidate effects of the vortex instabilities and of turbulent energy transfer on the formation of large-scale coherent flow structures. Normal mode analysis of the vortex systems is conducted to study the effect of shallowness and Reynolds number on the generation of two-dimensional large-scale coherent structures. The results show that the perturbation wavenumber of mode 2 is the fastest-growing instability in shallow-water conditions, and its effect depends on initial Reynolds number and shallowness.

Type
Papers
Copyright
Copyright © Cambridge University Press 2010

Access options

Get access to the full version of this content by using one of the access options below.

Footnotes

Deceased on 14 February 2010

References

Akkermans, R. A. D., Cieslik, A. R., Kamp, L. P. J., Trieling, R. R., Clercx, H. J. H. & van Heijst, G. J. F. 2008 The three-dimensional structure of an electromagnetically generated dipolar vortex in a shallow fluid layer. Phys. Fluids 20 (11), 116601116615.CrossRefGoogle Scholar
Batchelor, G. K. 1967 An Introduction to Fluid Dynamics. Cambridge University Press.Google Scholar
Beckers, M. & van Heijst, G. J. F. 1998 The observation of a triangular vortex in a rotating fluid. Fluid Dyn. Res. 22 (5), 265279.CrossRefGoogle Scholar
Carmer, C. F. v., Rummel, A. C. & Jirka, G. H. 2004 Influx of secondary motion in large-scale coherent vortical structures on the mass transport in a shallow turbulent wake flow. In Shallow Flows. Balkema.Google Scholar
Carnevale, G. F. & Kloosterziel, R. C. 1994 Emergence and evolution of triangular vortices. J. Fluid Mech. 259, 305331.CrossRefGoogle Scholar
Carton, X. J. 2001 Hydrodynamical modeling of oceanic vortices. Surv. Geophys. 22 (3), 179263.CrossRefGoogle Scholar
Carton, X. J., Flierl, G. R. & Polvani, L. M. 1989 The generation of tripoles from unstable axisymmetric isolated vortex structures. Europhys. Lett. 9 (4), 339344.CrossRefGoogle Scholar
Carton, X. & Legras, B. 1994 The life-cycle of tripoles in two-dimensional incompressible flows. J. Fluid Mech. 267, 5382.CrossRefGoogle Scholar
Cenedese, C., Adduce, C. & Fratantoni, D. M. 2005 Laboratory experiments on mesoscale vortices interacting with two islands. J. Geophys. Res. 110, C09023.CrossRefGoogle Scholar
Chen, D. & Jirka, G. H. 1995 Experimental study of plane turbulent wakes in a shallow water layer. Fluid Dyn. Res. 16 (1), 1141.CrossRefGoogle Scholar
Clercx, H. J. H., van Heijst, G. J. F. & Zoeteweij, M. L. 2003 Quasi-two-dimensional turbulence in shallow fluid layers: the role of bottom friction and fluid layer depth. Phys. Rev. E 67 (6), 066303.CrossRefGoogle Scholar
Creutin, J. D., Muste, M., Bradley, A. A., Kim, S. C. & Kruger, A. 2003 River gauging using PIV techniques: a proof of concept experiment on the Iowa river. J. Hydrol. 277 (3–4), 182194.CrossRefGoogle Scholar
Dolzhanskii, F. V., Krymov, V. A. & Manin, D. Yu. 1992 An advanced experimental investigation of quasi-two-dimensional shear flow. J. Fluid Mech. 241, 705722.CrossRefGoogle Scholar
Fischer, H. B., List, E. G., Koh, R. C. Y., Imberger, J. & Brooks, N. H. 1979 Mixing in Inland and Coastal Waters. Academic.Google Scholar
Flierl, G. R. 1988 On the instability of geostrophic vortices. J. Fluid Mech. 197, 349388.CrossRefGoogle Scholar
Flór, J. B. & van Heijst, G. J. F. 1996 Stable and unstable monopolar vortices in a stratified fluid. J. Fluid Mech. 311, 257287.CrossRefGoogle Scholar
Fujita, I., Muste, M. & Kruger, A. 1998 Large-scale particle image velocimetry for flow analysis in hydraulic engineering applications. J. Hydraul. Res. 36 (3), 397414.CrossRefGoogle Scholar
van Heijst, G. J. F. & Clercx, H. J. H. 2009 Laboratory modeling of geophysical vortices. Annu. Rev. Fluid Mech. 41 (1), 143164.CrossRefGoogle Scholar
van Heijst, G. J. F. & Flór, J. B. 1989 Dipole formation and collisions in a stratified fluid. Nature 340 (20), 212215.CrossRefGoogle Scholar
van Heijst, G. J. F. & Kloosterziel, R. C. 1991 Laboratory experiments on the tripolar vortex in a rotating fluid. J. Fluid Mech. 225, 301331.CrossRefGoogle Scholar
Jirka, G. H. 2001 Large scale flow structures and mixing processes in shallow flows. J. Hydraul. Res. 39 (6), 567573.CrossRefGoogle Scholar
Jirka, G. H. & Seol, D.-G. 2010 Dynamics of isolated vortices in shallow flows. J. Hydro-Environ. Res. 4 (2), 6573.CrossRefGoogle Scholar
Jirka, G. H. & Uijttewaal, W. S. J. 2004 Shallow Flows. Balkema.Google Scholar
Jüttner, B., Marteau, D., Tabeling, P. & Thess, A. 1997 Numerical simulations of experiments on quasi-two-dimensional turbulence. Phys. Rev. E 55 (5), 54795488.CrossRefGoogle Scholar
Kloosterziel, R. C. & Carnevale, G. F. 1999 On the evolution and saturation of instabilities of two-dimensional isolated circular vortices. J. Fluid Mech. 388, 217257.CrossRefGoogle Scholar
Kloosterziel, R. C. & van Heijst, G. J. F. 1991 An experimental study of unstable barotropic vortices in a rotating fluid. J. Fluid Mech. 223, 124.CrossRefGoogle Scholar
Kloosterziel, R. C. & van Heijst, G. J. F. 1992 The evolution of stable barotropic vortices in a rotating free-surface fluid. J. Fluid Mech. 239, 607629.CrossRefGoogle Scholar
Legras, B., Santangelo, P. & Benzi, R. 1988 High-resolution numerical experiments for forced two-dimensional turbulence. Europhys. Lett. 5, 3742.CrossRefGoogle Scholar
Lin, J.-C., Ozgoren, M. & Rockwell, D. 2003 Space–time development of the onset of a shallow-water vortex. J. Fluid Mech. 485, 3366.CrossRefGoogle Scholar
Lodewijks, B. B. F. M. 2008 Experiments on barotropic vortex instabilities in a rotating fluid. Tech. Rep. R-1737-A. Eindhoven University of Technology.Google Scholar
McWilliams, J. C. 1984 The emergence of isolated coherent vortices in turbulent flow. J. Fluid Mech. 146, 2143.CrossRefGoogle Scholar
Meinhart, C. D., Wereley, S. T. & Santiago, J. G. 2000 A PIV algorithm for estimating time-averaged velocity fields. J. Fluids Engng 122 (2), 285289.CrossRefGoogle Scholar
Meselhe, E. A., Peeva, T. & Muste, M. 2004 Large scale particle image velocimetry for low velocity and shallow water flows. J. Hydraul. Engng 130 (9), 937940.CrossRefGoogle Scholar
Nguyen Duc, J.-M. & Sommeria, J. 1988 Experimental characterization of steady two-dimensional vortex couples. J. Fluid Mech. 192, 175192.Google Scholar
Nicolau del Roure, F., Socolofsky, S. A. & Chang, K.-A. 2009 Structure and evolution of tidal starting jet vortices at idealized barotropic inlets. J. Geophys. Res. 114, C05024.CrossRefGoogle Scholar
Orlandi, P. & Carnevale, G. F. 1999 Evolution of isolated vortices in a rotating fluid of finite depth. J. Fluid Mech. 381, 239269.CrossRefGoogle Scholar
Orlandi, P. & van Heijst, G. J. F. 1992 Numerical simulation of tripolar vortices in 2D flow. Fluid Dyn. Res. 9, 179206.CrossRefGoogle Scholar
Paireau, O., Tabeling, P. & Legras, B. 1997 A vortex subjected to a shear: an experimental study. J. Fluid Mech. 351, 116.CrossRefGoogle Scholar
Paret, J., Marteau, D., Paireau, O. & Tabeling, P. 1997 Are flows electromagnetically forced in thin stratified layers two dimensional? Phys. Fluids 9 (10), 3102.CrossRefGoogle Scholar
Pingree, R. D. & Le Cann, B. 1992 Three anticyclonic slope water oceanic eddies (SWODDIES) in the southern bay of Biscay in 1990. Deep Sea Res. I 39 (7–8), 11471175.CrossRefGoogle Scholar
Raffel, M., Willert, C. & Kompenhans, J. 1998 Particle Image Velocimetry: A Practical Guide. Springer.CrossRefGoogle Scholar
Satijn, M. P., Cense, A. W., Verzicco, R., Clercx, H. J. H. & van Heijst, G. J. F. 2001 Three-dimensional structure and decay properties of vortices in shallow fluid layers. Phys. Fluids 13 (7), 19321945.CrossRefGoogle Scholar
Sous, D., Bonneton, N. & Sommeria, J. 2005 Transition from deep to shallow water layer: formation of vortex dipoles. Eur. J. Mech. B Fluids 24 (1), 1932.CrossRefGoogle Scholar
Streeter, V. L. & Wylie, E. B. 1985 Fluid Mechanics, 8th edn. McGraw-Hill.Google Scholar
Sukhodolov, A., Uijttewaal, W. S. J. & Engelhardt, C. 2002 On the correspondence between morphological and hydrodynamical patterns of groyne fields. Earth Surf. Process. Landf. 27 (3), 289305.CrossRefGoogle Scholar
Trieling, R. R. & van Heijst, G. J. F. 1998 Decay of monopolar vortices in a stratified fluid. Fluid Dyn. Res. 23 (1), 2743.CrossRefGoogle Scholar
Uijttewaal, W. S. J. & Booij, R. 2000 Effects of shallowness on the development of free-surface mixing layers. Phys. Fluids 12, 392402.CrossRefGoogle Scholar
Voropayev, S. I., McEachern, G. B., Boyer, D. L. & Fernando, H. J. S. 1999 Experiment on the self-propagating quasi-monopolar vortex. J. Phys. Oceanogr. 29, 27412751.2.0.CO;2>CrossRefGoogle Scholar
Wells, M. G. & van Heijst, G. J. F. 2003 A model of tidal flushing of an estuary by dipole formation. Dyn. Atmos. Oceans 37, 223244.CrossRefGoogle Scholar
Zavala Sansón, L. & van Heijst, G. J. F. 2002 Ekman effects in a rotating flow over bottom topography. J. Fluid Mech. 471, 239255.Google Scholar

Full text views

Full text views reflects PDF downloads, PDFs sent to Google Drive, Dropbox and Kindle and HTML full text views.

Total number of HTML views: 0
Total number of PDF views: 69 *
View data table for this chart

* Views captured on Cambridge Core between September 2016 - 26th February 2021. This data will be updated every 24 hours.

Send article to Kindle

To send this article to your Kindle, first ensure no-reply@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about sending to your Kindle. Find out more about sending to your Kindle.

Note you can select to send to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be sent to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

Find out more about the Kindle Personal Document Service.

Quasi-two-dimensional properties of a single shallow-water vortex with high initial Reynolds numbers
Available formats
×

Send article to Dropbox

To send this article to your Dropbox account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Dropbox.

Quasi-two-dimensional properties of a single shallow-water vortex with high initial Reynolds numbers
Available formats
×

Send article to Google Drive

To send this article to your Google Drive account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Google Drive.

Quasi-two-dimensional properties of a single shallow-water vortex with high initial Reynolds numbers
Available formats
×
×

Reply to: Submit a response


Your details


Conflicting interests

Do you have any conflicting interests? *