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Who 1-86-45 1986 WHO 1-86-45 1986 COURSE LECTURES ABSTRACTS OF SEMINARS LECTURES OF THE FELLOWS MOI-86-45 SUMMER STUDY PROGRAM IN GEOPHYSICAL FLUID DYNAMICS WOODS HOLE OCEANOGRAPHIC INSTITUTION ORDER AND DISORDER IN TURBULENT SHEAR FPOOW BY MELVIN E, STERN WOODS HOLE OCEANOGRAPHIC INSTITUTION WOODS HOLE, MSSACHUSETTS DECEMBER, 1986 TECHNICAL REPORT rrepared for the Office of Naval Research under contract N00014-82-G-0079 and the National Science Foundation under Grant DMS-85-04166. Reproduction in whole or in part is permitted for any purpose of the United States Government. This report should be cited as Woods Hole Oceanographic Institution Technical Report WHO1 86-45. Approval for Distribution: 9. Charles D. Hollister Dean of Graduate Studies 1986 SWRSTUDY PROGRAM IN GEOPHYSICAL FLUID DYNAMICS AT TIE WOODS HOLE OCEANOGRAPHIC INSTITUTION ORDER AND DISORDER IN TURBULENT SHEAR FLOW GEOPHYSICAL FLUID DYNAMICS PROGRAM STAFF AND VISITORS Altman, Donald B. University of British Columbia Emmanual, Kerry Massachusetts Institute of Technology Flament, Pierre Scripps Institution of Oceanography Flierl, Glenn Massachusetts Institute of Technology Herring, Jackson, R. National Center for Atmospheric Research Johansson, Arne Royal Institute of Technology Keller, Joseph B. Stanford University Kelley, David E. Dalhousie University Kunze, Eric Woods Hole Oceanographic Institution Landahl, Martin Massachusetts Institute of Technology Malkus, W.V.R. Massachusetts Institute of Technology Melander, Mogens V. University of Pittsburgh Newell, Alan C University of Arizona Nof, Doran Florida State University Patera, Anthony T. Massachusetts Institute of Technology Pearson, C. Frederick Massachusetts Institute of Technology Pierrehumbert, Raymond T. Geophysical Fluid Dynamics Laboratories/NOAA Rhines, Peter University of Washington Rizzoli, Paola Malanotte Massachusetts Institute of Technology Rossby, Thomas University of Rhode Island Russell, John M. University of Oklahoma Salmon, Rick Scripps Institution of Oceanography Samelson, Roger Oregon State University Spence, Thomas W. Office of Naval Research Spiegel, E. A. Columbia University Stern, Melvin University of Rhode Island Tryggvason, Gretar Brown University Veronis, George Yale University Wygnanski, Israel University of Arizona Young, William R. Massachusetts Institute of Technology Zabusky, Norman J. University of Pittsburgh FELLOWS Agnon, Yehuda Massachusetts Institute of Technology Barsugli, Joseph University of Washington Biebuyck, Gavin University of Texas at Austin Brummel, Nicholas H. Imperial College Henningson, Dan Royal Institute of Technology Hedstrom, Katherine Scripps Institution of Oceanography Lu, Ya Yan Massachusetts Institute of Technology Quin, Zhongshan Columbia University Send, Uwe Scripps Institution of Oceanography Van Buskirk, Robert Harvard University I-'- I-' . I ROW 1: spiegel, pieg gel, Biebuyck, Henningson, Stern, Landahl, Veronis, Flament, Agnon, Nof, Lu, Hedstrom, Keller Row 2: Lippert, Malkus, Johansson, Van Buskirk, Send, Quin, Berthel, Morrell, Brummel, FlierlFlier1 EDITOR' S PREFACE Our thanks go to Martin Landahl for his stimulating expository lectures on recent development in "lab scale" turbulent flow. This subject was covered by him and other staff members from the experimental, analytic, and numerical point of view. The seminars on two-dimensional coherent structures provided a nice connecting link for subsequent lectures on large scale ocean eddy dynamics (e.g. warm core rings detaching from the Gulf Stream). The purpose of these notes is to indicate the range of the topics covered, and the degree of beneficial comunication. It is something of a wonder, with all these lectures going on, that our GFD Fellows are still able to come up with a (sometimes) admirable research project! For this our thanks go to those staff members who have given so generously of their time and spirit. We acknowledge with sincere appreciation the financial support provided by the Office of Naval Research and the National Science Foundation. Melvin E. Stern -v- TABLE OF CONTENTS ORDER AND DISORDER IN TURBULENT SHEAR FLOW Page Martin E. Landahl . ORDERED AND DISORDERED STRUCTURES IN SHEAR FLOW Lecture 1. What is Coherent Structure ................2 Lecture 2. Statistical Measures of Turbulence. ...........12 Lecture 3. Review of Experiments ..................24 Lecture 4. Coherent Structures in the Laboratory and inNature .........................29 Lecture 5. Equations of Motion .......... .........39 Lecture 6. Shear Flow Instability.................. 44 Lecture 7. Turbulence and Flow Instability ..............51 Lecture 8. Euler Description of Fluctuating Field ..........57 Lecture 9. Coherent Structure Modeling ................62 Lecture 10. Modeling. Numerical Simulation. Final Questions ......65 - vi - ABSTRACTS OF SEMINARS Page Merger, Binding, Axisymmetrization and Other Basic Processes in 2D Incompressible Flows. (Applications of Pseudospectral and Contour Dynamical DC Algorithms) NormanZabusky ............................76 Horizontal Entrainment and Detrainment In Large Scale Eddies MelvinE. Stern. ...........................77 Isolated Eddy Models for Geophysical Flows GlenFlierl..............................78 Experiments on Internal Wave Critical Layers Donald A1 tman. ........................... .8 7 Simple Models of the General Circulation of the Ocean Rick Salmon .............................89 Chaos and Turbulence AlanC.Newell......... ...................90 Instabilities in Channel Flows: Three-dimensionality, Geometry, and Resonance Anthony T. Patera ......................... .I04 Stability Bounds on Turbulent Poiseuills Flow Willem V. R. Malkus (in collaboration with Glenn R. Ierly) .....I05 Formation and Destruction of Inviscid Large Eddies Raymond T. Pierrehumbert. ..................... ,106 Vortex Dynamics - Computer Simulations and Mathematical Models Mogens V. Melander. .........................I07 Normal Forms for Partial Differential Equations Near to the Onset of Instabilities E.A.Spiege1 ............................108 Weir Flows, Pouring Flows, and Sink Flows Joseph Keller and Jean-Marc Vanden-Broeck ..............I14 Numerical Experiments in Forced Stably Stratified Turbulence Jackson R. Herring. ........................ .I15 Review of Baroclinic Lenses in the Ocean Thomas Rossby ........................... .I16 Page Amplitude Propagation in Trains of Orr-Somerfield Waves JohnM.Russel1.. .........................I1 8 Movements and Interactions of Isolated Eddies Doran Nof ............................. .I20 Instabilities of Salt Fingers George Veronis. .......................... .I23 Vortex Methods for Stratified Flows Gretar Tryggvason ......................... .I24 Deep-Ocean Circulation and Topography PeterRhines...... ......................125 On Large Scale Structures in Free Shear Layers Israel Wygnaski .......................... ,129 Negative Energy Waves WilliamYoung. .......................... .I31 Coherent Structures in a Baroclinic Atmosphere: Theory for Atmospheric Blocking and Comparison with Data Paola Malanotte Rizzoli ...................... .I32 A Model for Fastest-Growing Fingers in a Gradient Eric Kunze. ............................ .I32 Shear-Layer Structures in Near-Wall Turbulence, Their Evolution and Connection to Wall-Pressure Peaks Arne Johansson. .......................... .I33 Optical Microstructure During C-Salt .................. .I33 Eric Kunze Stability of Streamwise Vortices C. Frederick Pearson. ....................... .I34 Flow Structures in the California Current Pierre Flament. .......................... .I35 Chaos off the Shelf: Topographically Generated Mean Flow on the Continental Slope Roger Samelson. .......................... .I37 Simple Models f the General Circulation of the Ocean RickSalmon....... ......................138 Effects of Condensation and Wind-Induced Surface Heat Fluxes on Baroclinic Instability Kerry Emanuel ........................... .I39 - viii - LECTURES OF FELLOWS Page Interactions Between a Point Vortex and a Shear-Flow Katherine Hedstrom. ....................... .I42 Stability of Parallel Shear Flows with Mean Spanwise Variation Dan Henningson. ......................... .I53 Convection with Spatial Forcing and Mean Flow Generation Ya Yan Lu ............................ .I68 The Lives of an Eddy-Experimental Study of Planetary Eddies YehudaAgnon. .......................... .I80 Self-Propagation of a Barotropic Circular Eddy Gavin L. Bievuyck ........................ .I93 Stability of Stationary-Enstrophy Beta-Channel Flow Joseph Barsugli ......................... .202 Non-hysteretic Non-intermittent Transitions Directly Related to Chaos R.VanBuskirk........ .................. .212 Instability Waves in Galatic Slab Zhongshan Qian. ......................... .232 Barotropic Shear Flow Instability Over the Continental Shelf Uwe Send ............................ .241 Hexagons, Harmonics and Helmoltz Nicholas H. Brwell. ...................... .251 GFD PROGRAM SUMMER 1986 ORDERED AND DISORDERED STRUCTURES IN SHEAR FLOW Introductory lectures by Martin T. Landahl Massachusetts Institute of Technology & The Royal Institute of Technology, Stockholm Part I: THE FACTS - OBSERVATIONAL AND EXPERIMENTAL DATA Lecture 1 WHAT IS A COHERENT STRUCTURE 1.1 Some early findings We wish to examine the physical nature of so called coherent structures and what they imply regarding turbulence. There is a great deal of information but not much is known in the sense well understood. This is because a great deal of the 'knowledge'
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