Lefschetz Center for Dynamical Systems Seminar
Abstract: From the dynamical systems point of view, the behavior of the Earth's atmosphere is extremely high dimensional (e.g., a realistic atmospheric model based on a modal expansion would necessarily include many modes). In spite of the atmosphere's high dimensionality, in this talk I will demonstrate that, in a suitable sense, the local finite-time atmospheric dynamics is often low dimensional. Furthermore, I will show how this finding has important implications for weather forecasting. More generally, this behavior may be common to other physical spatio-temporally chaotic systems, and these systems may also be amenable to the type of analysis that is introduced for the atmosphere.
Brown Analysis Seminar
Center for Fluid Mechanics Seminar
Abstract: A phenomenological model for in-plane transverse vortex-induced vibrations of slender structures in crosswise stationary uniform flow is proposed. Its properties are evaluated analytically and verified by numerical simulations. The fluctuating nature of the near wake vortex street is modeled by diffusive interacting van der Pol oscillators, continuously distributed along the structure extent. The structure, e.g. a cable, is forced by a fluctuating lift model and reacts on the fluid through linear inertial effects. The coupled system is shown to support traveling waves, the main features of which are the following: the fluid selects the frequency, according to Strouhal's law; the structure then responds by fixing the wavelength, as dictated by its dispersion relation; finally, vibration amplitudes are set by the diffusive interaction in the fluid model, scaled by the wavelength. These results are discussed in relation with some experimental and numerical data.
PDE Seminar
Department of Mathematics Colloquium
<--- 2001 Index