Date of Award

5-2018

Document Type

Thesis

Degree Name

Master of Science (MS)

College/School

College of Science and Mathematics

Department/Program

Mathematical Sciences

Thesis Sponsor/Dissertation Chair/Project Chair

Eric Forgoston

Committee Member

Lora Billings

Committee Member

Ashuwin Vaidya

Subject(s)

Lagrange equations, Inertia (Mechanics), Fluid dynamics

Abstract

Lagrangian Coherent Structures (LCS) provide a skeleton for the underlying structures in geophysical flows. It is known that LCS govern the movement of fluid particles within a flow, but it is not well understood how these same LCS influence the movement of inertial particles within a fluid flow. In this thesis, we consider two geophysical flows, the double-gyre model, and a single-layer quasi-geostrophic PDE model. In particular, we use finite-time Lyapunov exponents (FTLE) to characterize the attracting and repelling LCS for these models and show how inertial particles aggregate with respect to LCS. We numerically investigate the dynamics of inertial particles for a range of Stokes numbers and density ratios. We also examine the effects of Coriolis force on the preferential aggregation of inertial particles in the double-gyre model. Additionally, we highlight the funneling behavior of inertial particles due to the western boundary effect that arises in the quasi-geostrophic model.

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