Physical Sciences and Mathematics Commons^™

Dances And Escape Of The Vortex Quartet, Brandon Behring

Dissertations

This dissertation considers the linear stability of a one-parameter family of periodic solutions of the four-vortex problem known as 'leapfrogging' orbits. These solutions, which consist of two pairs of identical yet oppositely-signed vortices, were known to W. Gröbli (1877) and A. E. H. Love (1883) and can be parameterized by a dimensionless parameter related to the geometry of the initial configuration. Simulations by Acheson and numerical Floquet analysis by Tophøj and Aref both indicate, to many digits, that the bifurcation occurs at a value related to the inverse square of the golen ratio. Acheson observed that, after an initial period …

Resonant Triad Interactions In One And Two-Layer Systems, Malik Chabane

Dissertations

This dissertation is a study of the weakly nonlinear resonant interactions of a triad of gravity-capillary waves in systems of one and two fluid layers of arbitrary depth, in one and two-dimentions. For one-layer systems, resonant triad interactions of gravity-capillary waves are considered and a region where resonant triads can be always found is identified, in the two-dimensional wavevector angles-space. Then a description of the variations of resonant wavenumbers and wave frequencies over the resonance region is given. The amplitude equations correct to second order in wave slope are used to investigate special resonant triads that, providing their initial amplitude …

Studies Of Two-Phase Flow With Soluble Surfactant, Ryan Peter Atwater

Dissertations

Numerical methods are developed for accurate solution of two-phase flow in the zero Reynolds number limit of Stokes flow, when surfactant is present on a drop interface and in its bulk phase interior. The methods are designed to achieve high accuracy when the bulk Péclet number is large, or equivalently when the bulk phase surfactant has small diffusivity

In the limit of infinite bulk Péclet number the advection-diffusion equation that governs evolution of surfactant concentration in the bulk is singularly perturbed, indicating a separation of spatial scales. A hybrid numerical method based on a leading order asymptotic reduction in this …

Accumulation Of Polar Vorticity On Giant Planets: Towards A Three-Dimensional Theory, Shawn R. Brueshaber

Dissertations

My research investigates the polar atmospheric dynamics of the giant planets: Jupiter and Saturn (gas giants), and Uranus and Neptune (ice giants). I conduct my research modifying and applying the Explicit Planetary Isentropic Coordinate global circulation code to model the polar regions of the four giant planets.

The motivation behind my research is to uncover the reason why giant planet polar atmospheric dynamics differ. Jupiter features multiple circumpolar cyclones arranged in geometrical configurations, whereas Saturn features a single pole-centered cyclone. Uranus and Neptune also appear to have single pole-centered cyclones, albeit, larger than those on Saturn. …