## Fluid Mechanics and the Environment: Dynamical Approaches: A Collection of Research Papers Written in Commemoration of the 60th Birthday of Sidney LeibovichThe papers in this volume were written by his students and colleagues to honor Sidney Leibovich, Samuel B. Eckert Professor in the Sibley School of Mechanical and Aerospace Engineering at Cornell University, in commemoration of his 60th birthday, 2 April 1999. They were presented at a symposium held at Cornell, 23 and 24 August 1999. Sid obtained his Bachelor of Science degree with honors from The California Institute of Technology in 1961, graduating first in his class. He came to Cornell to work with Geoffrey Ludford on Magnetohydrodynamics, and obtained his Ph.D. in 1965 in the Department of Theoretical and Applied Mechanics. He spent a year at University College, London as a NATO Postdoctoral Fellow, and returned to Cornell as an Assistant Professor. He has been here ever since, and is currently Director of the Sibley School. Since returning to Cornell, Sid has concentrated on rotating fluids and n- linear waves, in various combinations and applications, producing some 3.2 - pers a year with an applied-mathematical bent. In particular this interest led to both Langmuir circulation and vortex breakdown, two areas in which Sid has had enormous influence, and both, of course, examples of rotating fluids interacting with waves. It was impossible to work in this area without being distracted by the study of the nonlinear dispersive and dissipative waves themselves, and Sid has made substantial contributions in this area. |

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### Contents

Point Vortex Models and the Dynamics of Strong Vortices in the Atmosphere and Oceans | 1 |

SelfSimilarity and Cascading Physics | 19 |

Implicit Multigrid Computation of Unsteady Flows with Applications to Aeroelasticity | 35 |

SecondHarmonic Resonance with Parametric Excitation and Damping | 63 |

Bubble and Temperature Fields in Langmuir Circulation | 91 |

Computing Periodic Orbits | 107 |

Dynamics of Layers in Geophysical Flows | 121 |

Radiative Transport in Anisotropic Media | 151 |

Synchronised Behaviour in Three Coupled Faraday Disk Homopolar Dynamos | 225 |

LargeEddy Simulation Using Projection onto Local Basis Functions | 239 |

Preliminary Results | 267 |

Is High Reynolds Number Turbulence Locally Isotropic? | 285 |

A Story of Mixing | 295 |

a Model Problem and Flow Through a Diffuser with Variable Angle | 315 |

Consequences for Capillary Wave Damping | 337 |

A Spectral Domain Decomposition Method and Its Application to the Simulation of ShearStratified Turbulence | 353 |

A Problem in Fluid Mechanics | 163 |

Turbulent Bursts in CouetteTaylor Flow | 183 |

and Currents in Marine Boundary Layers | 201 |

Wing Wake Vortices and Temporal Vortex Pair Instabilities | 379 |

Laboratory Measurements of the Generation of Langmuir Circulations and Surface Waves | 401 |

### Common terms and phrases

advection algorithm amplitude approximately average basis functions bifurcation boundary conditions boundary layer bubble cloud buoyancy burst cycle capillary wave coefficients computed convergence Coriolis corresponding Crow instability cylinder damping delta wing density developed diffusivity direct numerical simulations dissipation dynamics eddy Ediss effects eigenfunctions energy evolution Figure fixed points Floquet fluctuations Fluid Mech flux frequency gradient grid heteroclinic cycle horizontal initial integration interaction interface laminar phase Langmuir circulation Leibovich LES-PLB limit cycles linear mean flow measured mechanism method mixed layer modes motion multigrid Navier-Stokes equations nonlinear numerical simulations observed ocean oscillation parameter periodic orbits perturbation phase phase synchronisation Phys problem region Reynolds number rotation scalar scale shown in Fig shows solutions spatial stable stratified streamwise structure subiteration surface waves surfactant temperature theory trajectories values variables vector velocity field viscosity vortex core vortex pair vortices wake wave field wavelength wavenumber wind zero