Date of Award

Spring 2026

Abstract

Geophysical flows are central to important climatological processes, yet their strong turbulence and additional complexities -- density stratification, wave-current interaction, and phase change -- make analytical prediction and direct numerical simulation infeasible in many regimes. This dissertation adopts a reductionist approach in which simplified representations -- often inspired by observed scale disparities -- are utilized to isolate and investigate the organizing mechanisms of these complex flows. Within this framework, three distinct but thematically connected problems are studied.

We first study Langmuir turbulence in the open ocean, in which surface gravity waves interact with wind-driven currents to organize the mixed layer into wind-aligned, counter-rotating vortex pairs. The emphasis is on evaluating a reduced model, derived for the extreme wave-dominated limit, through head-to-head comparisons with the full governing equations, and on delineating the asymptotic regime of `pure' Langmuir turbulence. Simulations of the reduced model reveal a tendency to produce unphysical cross-wind-invariant bands, traced to a gauge freedom absent from the full equations and removed by imposing an additional constraint. With this correction, the reduced model reproduces the key statistical and structural signatures of Langmuir turbulence -- mean profiles, variability, and spectral organization -- in the wave-dominated regime, enabling the identification and characterization of a persistent, downwind-propagating travelling wave component that organizes the dynamics.

Next, we investigate the dynamics of shelf-water polynyas (SWPs) -- climatologically vital regions of open water next to ice shelves maintained by strong katabatic winds. Characterized by a rich interplay of turbulent dynamics and phase change, SWPs exhibit distinct surface signatures indicative of Langmuir circulation. To further explore these dynamics, we formulate a continuum model coupling 2D equations for Langmuir circulation to thermodynamic evolution equations for heat, salt, and ice concentration. We then derive a simplified system that isolates the coupling between LC and ice-induced buoyancy, and obtain three distinct families of exact solutions: an ice-free state, one with surface-confined ice, and another with deep-reaching ice. Linear stability analysis reveals that while deep-reaching ice completely suppresses instability, surface-confined states with positively buoyant frazil ice robustly reshape -- rather than extinguish -- Langmuir circulation, altering its growth rates and vertical structure.

Finally, we attempt to derive insight into the dynamics of the Layered Anisotropic Stratified Turbulence (LAST) regime through the (highly idealized) lens of a two-dimensional, strongly stratified flow with applied sinusoidal body forcing. Motivated by exploratory simulations in long domains which exhibit long-wave modulation of turbulent activity, we perform a secondary stability analysis of the system's exact coherent states. We find that these are linearly unstable to long-wavelength oscillatory instabilities. Direct numerical simulations initialized with unstable modes demonstrate that their nonlinear evolution leads to a streamwise compression of the billow train and a non-uniform breakdown of coherence. This process ultimately yields temporally and spatially localized patches of turbulence, reminiscent of the spatiotemporal intermittency characteristic of the LAST regime.

Document Type

Dissertation

First Advisor

Gregory P Chini

Second Advisor

Christopher M White

Third Advisor

Nathan Laxague

Department or Program

Mechanical Engineering

Degree Name

Doctor of Philosophy

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