2009 Lecture Series Schedule


"Nonlinear Waves" - June 15 - August 21

Monday, June 15

Lecture 1 - 10:00 AM

Water waves

Harvey Segur, University of Colorado
Derivation of the standard equations for irrotational water waves due to gravity and/or surface tension for an inviscid, incompressable, homogeneous fluid.

Lecture 2 - 11:00 AM

Canonical nonlinear wave equations
Roger Grimshaw, Loughborough University
Introduction to the Korteweg-de Vries (KdV) equation as a model for weakly nonlinear long waves, and to the Nonlinear Schrodinger equation (NLS) as a model for weakly nonlinear wave packets.

Tuesday, June 16

Lecture 3 - 10:00 AM

Zakharov formulation of water waves

Harvey Segur, University of Colorado
Introduction to the Hamiltonian formulation, and issues such as integrability.

Lecture 4 - 11:00 AM

Waves in shallow water, part 1
Harvey Segur, University of Colorado
Derivation of KdV for water waves by multiple scales; integrability and inverse scattering, comparison with experiments.

Wednesday, June 17

Lecture 5 - 10:00 AM

Internal Waves
Roger Grimshaw, Loughborough University
Derivation of KdV for weakly nonlinear long internal waves in the ocean.

Lecture 6 - 11:00 AM

Nonlinear waves in a variable medium
Roger Grimshaw, Loughborough University
The variable-coefficient KdV equation, and slowly-varying solitary waves.

Afternoon lecture - 2:00 PM

Friedrich Busse, University of Bayreuth
What can thermal convection teach us about the nature of turbulence?

Thursday, June 18

Lecture 7 - 10:00 AM

Oceanographic applications
Harvey Segur, University of Colorado
The 2004 tsunami, hurricane Katrina (2006), experiments etc.; the periodic solutions of the Kadomtsev-Petviashvili (KP) equation (spatial extension of the KdV equation).

Lecture 8 - 11:00 AM

The shallow water equations
Harvey Segur, University of Colorado
The nonlinear shallow water equations, method of characteristics, wave breaking, dissipative or dispersive regularization; wave shoaling.

Afternoon lecture - 2:00 PM

The extra invariant for Rossby wave dynamics
Alexander Balk, University of Utah

Friday, June 19

Lecture 9 - 10:00 AM

Internal solitary waves in the ocean
Roger Grimshaw, Loughborough University
Application of the variable-coefficient KdV equation, and related model equations, to the description of large-amplitude internal waves in the coastal ocean.

Lecture 10 - 11:00 AM

Modulated periodic waves
Roger Grimshaw, Loughborough, University
Introduction to the Whitham modulation theory, undular bores, using the context of the KdV equation.

Monday, June 22

Lecture 11 - 10:00 AM

Transcritical flow over an obstacle
Roger Grimshaw, Loughborough, University
Description of flow interaction of an obstacle, based on the forced KdV equation.

Lecture 12 - 11:00 AM

Triad interactions
Harvey Segur, University of Colorado
Three-wave resonant triad equations, applications to gravity-capillary waves and internal waves.

Tuesday, June 23

Lecture 13 - 10:00 AM

Waves in deep water, part 1
Harvey Segur, University of Colorado
Modulation (Benjamin-Feir) instability, the NLS model, integrability of NLS in one spatial dimension, envelope solitons.

Lecture 14 - 11:00 AM

Waves in deep water, part 2
Harvey Segur, University of Colorado
NLS model in one and two spatial dimensions, recurrence of initial states, downshifting, two-dimensional wave patterns, the role of damping.

Wednesday, June 24

Lecture 15 - 10:00 AM

Solitary waves
Roger Grimshaw, Loughborough University
Existence of solitary waves, as homoclinic orbits in a spatial dynamical system.

Lecture 16 - 11:00 AM

Generalized solitary waves
Roger Grimshaw, Loughborough University
Resonance between long and short waves, exponential asymptotics

Thursday, June 25

Lecture 17 - 10:00 AM

Wave-mean flow interaction, part1
Roger Grimshaw, Loughborough University
Application of the Whitham modulation theory to the interaction of nonlinear water waves with currents.

Lecture 18 - 11:00 AM

Wave-mean flow interaction, part 2
Roger Grimshaw, Loughborough University
The generalized Lagrangian mean theory, applied to internal waves.

Friday, June 26

Lecture 19 - 10:00 AM

Explosive Instability
Harvey Segur, University of Colorado
Explosive instability due to 3-wave or 4-wave mixing.

Lecture 20 - 11:00 AM

Harvey Segur, University of Colorado
Topics left over from previous lectures.  If time permits:  rip currents (in shallow water), rogue waves (in deep water).

Monday, June 29

10:30 AM

Waves and vortices in fluids and superfluids
Oliver Buhler, Courant Institute

Tuesday, June 30

10:30 AM

Resonant forcing of gravity-capillary lumps in deep water
Triantaphyllos Akylas, MIT

Wednesday, July 1

10:30 AM

Internal wave representation in OGCMs
Eric Chassignet, Florida State University

Thursday, July 2

10:30 AM

Near-resonant internal wave triads
Kevin Lamb, University of Waterloo
A resonant-triad is a set of three weakly non-linearly interacting waves whose wave vectors and frequencies sum to zero.  They occur in many physical systems and have played an important role in our understanding of the nonlinear evolution of the internal wave field in the deep ocean.  Near-resonant triads are sets of three waves which are detuned:  the sum of the wave vectors and/or wave frequencies is no longer exactly zero.  In this talk I will discuss numerical simulations of tidally generated internal waves in a linearly stratified fluid for which near-resonant interactions are the dominant form of weakly-nonlinear interactions in the internal wave field.

2:00 PM

Hydraulics miscellany:  Rossby waves and 2D internal waves
Ted Johnson, University College London

Friday, July 3


Monday, July 6

10:30 AM

Mixing in the southern ocean
Raffaele Ferrari, MIT

Tuesday, July 7

10:30 AM

Fluid dynamics in the solar interior
Pascale Garaud, University of California, Santa Cruz

Wednesday, July 8

10:30 AM

Internal solitary waves with trapped cores
Karl Helfrich, WHOI

Thursday, July 9

10:30 AM

Dynamics of inertial particles in fluid flows
Themis Sapsis, MIT

Friday, July 10

10:30 AM

Dynamics and stability of interacting buoyant currents
Claudia Cenedese, WHOI

Monday, July 13

10:30 AM

Large amplitude non-linear internal waves in the South China Sea
Lou St. Laurent, WHOI

Tuesday, July 14

10:30 AM

The influence of horizontal current shear on salt fingers
Melvin Stern, Florida State University

Wednesday, July 15

10:30 AM

Extreme waves - should one expect the unexpected?
Johannes Gemmrich, University of Victoria

2:00 PM

Trapped waves in a baroclinic ocean in mid-latitudes
Nathan Paldor, Hebrew University of Jerusalem

Thursday, July 16

10:30 AM

Aspects of stratified shear instability
Neil Balmforth, University of British Columbia

Friday, July 17

Nonlinear Excursions

10:00 AM

Rather more can be said:  the science of Lou Howard
Oliver Buhler, Courant Institute

11:00 AM

Rip current as an instability
Jie Yu, North Carolina State University

2:00 PM

Lou, me and science
Nancy Kopell, Boston University

3:00 PM

Heat transport by turbulent convection
Charlie Doering, University of Michigan

Monday, July 20

10:30 AM

A tale of two jets:  one liquid, the other granular
Patrick Weidman, University of Colorado

Tuesday, July 21

10:30 AM

Rigorous bounds revisited:  A prediction for the optimal stratification for turbulent mixing
Colm Caulfield, University of Cambridge

Wednesday, July 22


Thursday, July 23

10:30 AM

Propulsion through diffusion
Tom Peacock, MIT

Friday, July 24

10:30 AM

A discontinuous Galerkin method for the Vlasov-Poisson equation
Phil Morrison, University of Texas at Austin

Monday, July 27

10:30 AM

Modeling of "genuinely strong" internal waves
Lev Ostrovsky, NOAA

2:00 PM

Stability of relative equilibria of three vortices
Hassan Aref, Technical University of Denmark and Virginia Tech

Tuesday, July 28

10:30 AM

Turbulent convection in the presence of density fronts
John Taylor, MIT

Wednesday, July 29

10:30 AM

Generation of internal waves by gravity currents in two-layer and continuous stratification
Brian White, University of North Carolina, Chapel Hill

Thursday, July 30

10:30 AM

Beyond Ray Theory for Internal Waves:  Nonlinear Effects
Bruce Sutherland, University of Alberta

2:00 PM

Diffusion of swimming cells, flagella as coupled oscillators, and advective micro-mixing
Jerry Gollub, Haverford College

Friday, July 31

10:30 AM

Stability of the Atlantic meridional overturning circulation in a zonally-averaged ocean model
Alexey Federov, Yale University

Monday, August 3


Tuesday, August 4


Wednesday, August 5

10:30 AM

Internal waves and wave turbulence
Yuri Lvov, Rensselaer Polytechnic Institute

Thursday, August 6

PUBLIC LECTURE, Reception to follow - Clark 507, Quissett Campus

3:00 PM

Flight at small scales
Geoff Spedding, Dept. of Aerospace and Mechanical Engineering, University of Southern California

Friday, August 7

10:30 AM

Sinking amid bubbles
Andrew Belmonte, Penn State University

August 10-14


August 17-21 - Fellows' Presentations

Tuesday, August 18

10:00 AM

Destabilizing a seiche with a movable dam
Hélène Scolan, Ecole Normale Supérieure de Lyon

11:00 AM

Nonlinear peristaltic waves
Daisuke Takagi, University of Cambridge

2:00 PM

Degradation of the internal tide over long bumpy topography
Erinna Chen, University of California, Santa Cruz

3:00 PM

Resonant triad interactions on an extended equatorial β-plane
Michael Bates, University of South Wales

Wednesday, August 19

10:00 AM

Quantum vortices in a glass of Bose-Einstein condensate
Nicholas Grisouard, Université Joseph Fourier, Grenoble

11:00 AM

Variation of the eddy diffusivity across jets in the southern ocean due to discontinuities
Alireza Mashayekhi, University of Toronto

2:00 PM

Laboratory experiment on two coalescing axisymmetric turbulent plumes in a rotating fluid
Hiroki Yamamoto, Kyoto University

3:00 PM

Nonlinear Rossby shelf waves in a rotating annulus
Andrew Stewart, University of Oxford

Thursday, August 20

10:00 AM

Some geometrical aspects of nonlinear waves
Andong He, Penn State Universiy

11:00 AM

Transverse stability of Su-Gardner solutions
Adrienne Traxler, University of California, Santa Cruz

1:00 PM

The derivation and application of convective pattern equations
Yiping Ma, University of California, Berkeley