Oceanic Vortices

Total Page:16

File Type:pdf, Size:1020Kb

Oceanic Vortices Lecture Notes in Physics Founding Editors: W. Beiglbock,¨ J. Ehlers, K. Hepp, H. Weidenmuller¨ Editorial Board R. Beig, Vienna, Austria W. Beiglbock,¨ Heidelberg, Germany W. Domcke, Garching, Germany B.-G. Englert, Singapore U. Frisch, Nice, France F. Guinea, Madrid, Spain P. Hanggi,¨ Augsburg, Germany W. Hillebrandt, Garching, Germany R. L. Jaffe, Cambridge, MA, USA W. Janke, Leipzig, Germany H. v. Lohneysen,¨ Karlsruhe, Germany M. Mangano, Geneva, Switzerland J.-M. Raimond, Paris, France M. Salmhofer, Heidelberg, Germany D. Sornette, Zurich, Switzerland S. Theisen, Potsdam, Germany D. Vollhardt, Augsburg, Germany W. Weise, Garching, Germany J. Zittartz, Koln,¨ Germany The Lecture Notes in Physics The series Lecture Notes in Physics (LNP), founded in 1969, reports new developments in physics research and teaching – quickly and informally, but with a high quality and the explicit aim to summarize and communicate current knowledge in an accessible way. Books published in this series are conceived as bridging material between advanced grad- uate textbooks and the forefront of research and to serve three purposes: • to be a compact and modern up-to-date source of reference on a well-defined topic • to serve as an accessible introduction to the field to postgraduate students and nonspecialist researchers from related areas • to be a source of advanced teaching material for specialized seminars, courses and schools Both monographs and multi-author volumes will be considered for publication. Edited volumes should, however, consist of a very limited number of contributions only. Pro- ceedings will not be considered for LNP. Volumes published in LNP are disseminated both in print and in electronic formats, the electronic archive being available at springerlink.com. The series content is indexed, ab- stracted and referenced by many abstracting and information services, bibliographic net- works, subscription agencies, library networks, and consortia. Proposals should be sent to a member of the Editorial Board, or directly to the managing editor at Springer: Christian Caron Springer Heidelberg Physics Editorial Department I Tiergartenstrasse 17 69121 Heidelberg / Germany [email protected] Jan-Bert Flor´ (Ed.) Fronts, Waves and Vortices in Geophysical Flows ABC Jan-Bert Flor´ LEGI (Laboratoire des Ecoulements Geophysiques´ et Industriels) Universite´ de Grenoble B.P.53X, 38041 Grenoble Cedex 09 France Jan-Bert Flor´ (Ed.): Fronts, Waves and Vortices in Geophysical Flows, Lect. Notes Phys. 805 (Springer, Berlin Heidelberg 2010), DOI 10.1007/978-3-642-11587-5 Lecture Notes in Physics ISSN 0075-8450 e-ISSN 1616-6361 ISBN 978-3-642-11586-8 e-ISBN 978-3-642-11587-5 DOI 10.1007/978-3-642-11587-5 Springer Heidelberg Dordrecht London New York Library of Congress Control Number: 2010922993 c Springer-Verlag Berlin Heidelberg 2010 This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilm or in any other way, and storage in data banks. Duplication of this publication or parts thereof is permitted only under the provisions of the German Copyright Law of September 9, 1965, in its current version, and permission for use must always be obtained from Springer. Violations are liable to prosecution under the German Copyright Law. The use of general descriptive names, registered names, trademarks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. Cover design: Integra Software Services Pvt. Ltd., Pondicherry Printed on acid-free paper Springer is part of Springer Science+Business Media (www.springer.com) Foreword Without coherent structures atmospheres and oceans would be chaotic and unpre- dictable on all scales of time. Most well-known structures in planetary atmospheres and the Earth oceans are jets or fronts and vortices that are interacting with each other on a range of scales. The transition from one state to another such as in unbalanced or adjustment flows involves the generation of waves, as well as the interaction of coherent structures with these waves. This book presents from a fluid mechanics perspective the dynamics of fronts, vortices, and their interaction with waves in geophysical flows. It provides a basic physical background for modeling coherent structures in a geophysical context and gives essential information on advanced topics such as spontaneous wave emission and wave-momentum transfer in geophysical flows. The book is targeted at graduate students, researchers, and engineers in geophysics and environmental fluid mechanics who are interested or working in these domains of research and is based on lectures given at the Alpine summer school entitled ‘Fronts, Waves and Vortices.’ Each chapter is self-consistent and gives an extensive list of relevant literature for further reading. Below the contents of the five chapters are briefly outlined. Chapter comprises basic theory on the dynamics of vortices in rotating and strati- fied fluids, illustrated with illuminating laboratory experiments. The different vortex structures and their properties, the effects of Ekman spin-down, and topography on vortex motion are considered. Also, the breakup of monopolar vortices into multiple vortices as well as vortex advection properties will be discussed in conjunction with laboratory visualizations. In Chap. 2, the understanding of the different vortex instabilities in rotating, stratified, and – in the limit – homogenous fluids are considered in conjunction with laboratory visualizations. These include the shear, centrifugal, elliptical, hyperbolic, and zigzag instabilities. For each instability the responsible physical mechanisms are considered. In Chap. 3, oceanic vortices as known from various in situ observations and measurements introduce the reader to applications as well as outstanding ques- tions and their relevance to geophysical flows. Modeling results on vortices high- light physical aspects of these geophysical structures. The dynamics of ocean deep sea vortex lenses and surface vortices are considered in relation to their genera- v vi Foreword tion mechanism. Further, vortex decay and propagation, interactions as well as the relevance of these processes to ocean processes are discussed. Different types of model equations and the related quasi-geostrophic and shallow water modeling are presented. In Chap. 4 geostrophic adjustment in geophysical flows and related problems are considered. In a hierarchy of shallow water models the problem of separation of fast and slow variables is addressed. It is shown how the separation appears at small Rossby numbers and how various instabilities and Lighthill radiation break the separation at increasing Rossby numbers. Topics such as trapped modes and symmetric instability, ‘catastrophic’ geostrophic adjustment, and frontogenesis are presented. In Chap. 5, nonlinear wave–vortex interactions are presented, with an empha- sis on the two-way interactions between coherent wave trains and large-scale vor- tices. Both dissipative and non-dissipative interactions are described from a unified perspective based on a conservation law for wave pseudo-momentum and vortex impulse. Examples include the generation of vortices by breaking waves on a beach and the refraction of dispersive internal waves by three-dimensional mean flows in the atmosphere. Grenoble, France Jan-Bert Flór Contents 1 Dynamics of Vortices in Rotating and Stratified Fluids .............. 1 G.J.F. van Heijst 1.1 VorticesinRotatingFluids.................................... 1 1.1.1 Basic Equations and Balances . ........................ 2 1.1.2 HowtoCreateVorticesintheLab ....................... 9 1.1.3 The Ekman Layer . ................................... 12 1.1.4 Vortex Instability. ................................... 14 1.1.5 EvolutionofStableBarotropicVortices................... 15 1.1.6 Topography Effects . ................................... 18 1.2 VorticesinStratifiedFluids.................................... 20 1.2.1 Basic Properties of Stratified Fluids . .................... 20 1.2.2 Generation of Vortices . ............................... 22 1.2.3 Decay of Vortices . ................................... 24 1.2.4 Instability and Interactions. ........................ 30 1.3 Concluding Remarks . ................................... 33 References . ..................................................... 33 2 Stability of Quasi Two-Dimensional Vortices ....................... 35 J.-M. Chomaz, S. Ortiz, F. Gallaire, and P. Billant 2.1 Instabilities of an Isolated Vortex . ........................ 36 2.1.1 The Shear Instability . ............................... 37 2.1.2 The Centrifugal Instability . ........................ 37 2.1.3 Competition Between Centrifugal and Shear Instability . 40 2.2 Influence of an Axial Velocity Component . .................... 41 2.3 Instabilities of a Strained Vortex ............................... 43 2.3.1 The Elliptic Instability . ............................... 44 2.3.2 The Hyperbolic Instability.............................. 46 2.4 The Zigzag Instability . ................................... 47 2.4.1 The Zigzag Instability in Strongly Stratified Flow Without Rotation . ........................... 47 2.4.2 The Zigzag Instability in Strongly Stratified FlowwithRotation..................................
Recommended publications
  • Abstract Turbulent Shear Flow in a Rapidly Rotating
    ABSTRACT Title of dissertation: TURBULENT SHEAR FLOW IN A RAPIDLY ROTATING SPHERICAL ANNULUS Daniel S. Zimmerman, Doctor of Philosophy, 2010 Dissertation directed by: Professor Daniel P. Lathrop Department of Physics This dissertation presents experimental measurements of torque, wall shear stress, pressure, and velocity in the boundary-driven turbulent flow of water between concentric, independently rotating spheres, commonly known as spherical Couette flow. The spheres' radius ratio is 0.35, geometrically similar to that of Earth's core. The measurements are performed at unprecedented Reynolds number for this geometry, as high as fifty-six million. The role of rapid overall rotation on the turbulence is investigated. A number of different turbulent flow states are possible, selected by the Rossby number, a dimensionless measure of the differential rotation. In certain ranges of the Rossby number near state borders, bistable co-existence of states is possible. In these ranges the flow undergoes intermittent transitions between neighboring states. At fixed Rossby number, the flow properties vary with Reynolds number in a way similar to that of other turbulent flows. At most parameters investigated, the large scales of the turbulent flow are characterized by system-wide spatial and temporal correlations that co-exist with intense broadband velocity fluctuations. Some of these wave-like motions are iden- tifiable as inertial modes. All waves are consistent with slowly drifting large scale patterns of vorticity, which include Rossby waves and inertial modes as a subset. The observed waves are generally very energetic, and imply significant inhomogene- ity in the turbulent flow. Increasing rapidity of rotation as the Ekman number is lowered intensifies those waves identified as inertial modes with respect to other velocity fluctuations.
    [Show full text]
  • A Laboratory Model of Exchange and Mixing Between Western Boundary Layers and Subbasin Recirculation Gyres*
    1870 JOURNAL OF PHYSICAL OCEANOGRAPHY VOLUME 32 A Laboratory Model of Exchange and Mixing between Western Boundary Layers and Subbasin Recirculation Gyres* HEATHER E. DEESE,LARRY J. PRATT, AND KARL R. HELFRICH Woods Hole Oceanographic Institution, Woods Hole, Massachusetts (Manuscript received 25 January 2001, in ®nal form 8 November 2001) ABSTRACT Chaotic advection is suggested as a possible mechanism for ¯uid exchange and mixing among a western boundary current and subbasin recirculation gyres. Applications include the North Atlantic Deep Western Bound- ary Current and its adjacent mesoscale recirculation gyres. Visualization and quanti®cation of certain aspects of chaotic advection in a laboratory analog are described. Depending on the strength of the forcing, recirculating ¯uid offshore of the western boundary layer may be contained in a single gyre (not favorable for chaotic advection) or twin gyre with a ``®gure-eight'' geometry (favorable for chaotic advection). When time dependence is imposed on these steady ¯ows by varying the forcing periodically, the resulting ¯uid exchange, stirring, and mixing is most dramatic in the case of the twin gyre. A template for these processes can be formed by highlighting certain material contours (invariant manifolds) using dye and other techniques. These objects can be used to identify blobs of ¯uid (turnstile lobes) that are carried into and out of the gyres. The associated transports and ¯ushing times can be estimated. The preferential stirring and mixing in the twin-gyre case is quanti®ed by calculating the effective diffusivity of the ¯ow ®eld based on snapshots of the dye ®elds at longer times. The experiment suggests how tracers in a western boundary current might be transported into and out of neighboring recirculations and where regions of strong zonal or meridional transport might occur.
    [Show full text]
  • Downloaded 09/25/21 03:30 PM UTC
    2250 JOURNAL OF PHYSICAL OCEANOGRAPHY VOLUME 35 Relationships between Tracer Ages and Potential Vorticity in Unsteady Wind-Driven Circulations HONG ZHANG,THOMAS W. N. HAINE, AND DARRYN W. WAUGH Department of Earth and Planetary Sciences, The Johns Hopkins University, Baltimore, Maryland (Manuscript received 4 June 2004, in final form 17 May 2005) ABSTRACT The relationships between different tracer ages and between tracer age and potential vorticity are ex- amined by simulating barotropic double-gyre circulations. The unsteady model flow crudely represents aspects of the midlatitude, middepth ocean circulation including inhomogeneous and anisotropic variability. Temporal variations range in scale from weeks to years, although the statistics are stationary. These variations have a large impact on the time-averaged tracer age fields. Transport properties of the tracer age fields that have been proved for steady flow are shown to also apply to unsteady flow and are illustrated in this circulation. Variability of tracer ages from ideal age tracer, linear, and exponential transient tracers is highly coordinated in phase and amplitude and is explained using simple theory. These relationships between different tracer ages are of practical benefit to the problem of interpreting tracer ages from the real ocean or from general circulation models. There is also a close link between temporal anomalies of tracer age and potential vorticity throughout a significant fraction of the domain. There are highly significant anticorrelations between ideal age and potential vorticity in the subtropical gyre and midbasin jet region, but correlation in the central subpolar gyre and eastern part of the domain is not significant. The existence of the relationship is insensitive to the character of the flow, the tracer sources, and the potential vorticity dynamics.
    [Show full text]
  • A Steady-State Analysis of the Atlantic Ocean
    REPORT UDC 551.464:551.465 CM-71 August 1987 ON INVERSE METHODS FOR COMBINING CHEMICAL AND PHYSICAL OCEANOGRAPHIC DATA: A STEADY-STATE ANALYSIS OF THE ATLANTIC OCEAN Bert Bolin, Anders Björkström, Kim Holmen and Berrien Moore Institute for the Study of Earth, Oceans and Space, University of New Hampshire, Durham, New Hampshire 03824 USA, and Laboratoire de Physique et Chimie Marines, Université Pierre et Marie Curie, Paris VI. DEPARTMENT OF METEOROLOGY <5 Ä'J> UNIVERSITY OF STOCKHOLM g ^f$f £ INTERNATIONAL METEOROLOGICAL -7, *f S> INSTITUTE IN STOCKHOLM ISSN 0280-445X DEPARTMENT OF METEOROLOGY REPORT CM-71 1 (220) UNIVERSITY OF STOCKHOLM (MISU) 1987-08-01 UDC 551.464:551.465 INTERNATIONAL METEOROLOGICAL INSTITUTE IN STOCKHOLM (IMI) Arrhenius Laboratory S-106 91 STOCKHOLM, Sweden Tel 08/16 2406 ON INVERSE METHODS FOR COMBINING CHEMICAL AND PHYSICAL OCEANOGRAPHIC DATA: A STEADY-STATE ANALYSIS OF THE ATLANTIC OCEAN by Bert Bolin, Anders Björksträn, Kim Holmen and Berrien Moore *) Abstract An attempt has been made to increase the spatial resolution in the vise of inverse methods to deduce rates of water circulation and detritus formation by the simultaneous use of tracer data and the condition of quasi-geostrophic flow. It is shown that an cverdetermined system of equations is desirable to permit analysis of the sensitivity of a solution to errors in the data fields. The method has been tested for the Atlantic Ocean, in which case we employ an 84-box model (eight layers in the vertical and 12 regions in the horizontal define the box configuration). As quasi-steady tracers we consider dissolved inorganic carbon (DIC), radiocarbon, alkalinity, phosphorus, oxygen, salinity and enthalpy.
    [Show full text]