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03/01/02 Colloquium
DR. ALAN NEWELL
DEPARTMENT OF MATHEMATICS
University of Arizona
DEPARTMENT OF MATHEMATICS
University of Arizona
WAVE TURBULENCE AND WHITECAPS
Abstract: Wave Turbulence, the turbulence of a sea of weakly coupled, dispersive wavetrains has a natural asymptotic closure. The result is a kinetic equation and a frequency renormalization. The kinetic equation has a rich family of solutions which include the well known thermodynamic equilibria (Rayleigh-Jeans, Fermi-Dirac, Bose-Einstein) but also contain the less well known but more important finite flux Kolmogorov-Zakharov solutions which describe how the conserved densities such as energy and particle number flow from sources to sinks. We will discuss how these solutions are set up and their breakdown at very small or very large scales. Illustrations will include the behavior of ocean waves and the onset of whitecapping and optical waves and condensate formation and the resulting intermittency.About The Speaker:
Dr. Newell is Professor of Mathematics at the University of Arizona. He is an applied mathematician who is an expert on solitons, nonlinear waves, and pattern formation. He was the Chair of the Mathematics Department at the University of Arizona during the 80s and early 90s. During this time, his efforts were responsible for the applied mathematics group at the University of Arizona becoming one of the world's leaders in pattern formation and nonlinear waves.
