Date of Award

Spring 2026

Abstract

Turbulent entrainment (TE) in buoyant jets plays a key role in dispersing environmental contaminants, carrying significant socio-economic implications. For example, the transport of heat and solutes through submarine volcanoes and the discharge of subglacial meltwater crucially affect the marine ecosphere. This, in turn, impacts coastal communities, the supply chains they support, and the broader socio-economic landscape. Therefore, advancing our understanding of how submerged buoyant jets mix and developing remote sensing tools to help monitor their changing status is crucial for devising strategies to mitigate marine-related challenges quickly, economically, and effectively. Therefore, this dissertation has three primary objectives: (I) examine the effects of buoyancy on TE in plumes; (II) identify a dynamically important length scale for TE and ascertain the effects of buoyancy on this length scale; and (III) leverage free surface interface dynamics to identify key flow metrics for developing remote sensing tools that link the surface features of a submerged plume to its source conditions and TE properties. The dissertation is structured with a dedicated chapter for each objective. \par

The first objective examines the mechanics of buoyancy-enhanced TE in plumes. A mean-flow-based integral analysis for a far-field plume shows that buoyancy enhances TE by reducing the length scale over which the mean-momentum flux doubles. The scaling laws derived from this analysis also show that buoyancy strengthens the vorticity in plumes primarily through a leading-order effect of enhancing the mean flow (and hence the mean shear) rather than through lower-order contributions to the baroclinic torque. The analysis also investigates how buoyancy-invigorated large-scale turbulence affects smaller scales through the turbulent cascade. By energizing the mean flow, buoyancy expands the range of scales comprising the spectrum of turbulent motions. This expansion causes smaller scales of motion to intensify and further shrink in size, thereby enhancing TE while preserving the scale invariance of its flux. \par

The second objective requires analyzing the structure of the turbulent/non-turbulent interface (TNTI), which facilitates the multi-scale TE of a non-turbulent ambient fluid into a turbulent flow. Using a kinematic scaling argument, a scale of dynamic importance is identified for the turbulent sublayer of the TNTI by matching the time scales between the relevant scales of motion. This yields the mixed length-scale parameter $\eta^{2/3}\lambda^{1/3}$ (where $\eta$ is the Kolmogorov scale and $\lambda$ is the Taylor scale), matching the physical thickness of the turbulent sublayer across a wide range of flow conditions ($60 \leq Re_\lambda = u'\lambda/\nu \leq 400$) and types (wall-bounded, shear-free, and free-shear turbulent flows). Physically, the scale $\eta^{2/3}\lambda^{1/3}$: (i) describes the turbulent sublayer thickness over a distance along the TNTI corresponding to $\lambda$, such that the coherent strain along the axial length of scales within the sublayer scales with $\lambda$ instead of $\eta$; and (ii) mediates the transition between inertial effects (due to $\lambda$) and dissipative effects (due to $\eta$) within the turbulent sublayer. Given the outcomes from Objective (I), the influence of buoyancy is to shrink this length scale while intensifying the motions associated with it. Practically, this length scale is important for reduced-order models of TNTI dynamics and falls within the resolution limits of several past high-$Re_\lambda$ TNTI experiments, offering critical guidance for the design of future investigations. \par

The third objective involves experimentally investigating the response of free surface features to sub-surface and source conditions using thermal imagery. High-fidelity free-surface thermal fields were obtained covering a range of source-based Reynolds numbers ($600 \leq Re_D = U_0 D/\nu \leq 10200$), and free-surface locations ($35 \leq h/D \leq 65$) (where $\nu$ is the kinematic viscosity of water with bulk velocity $U_0$ at a jet orifice of fixed diameter $D$, separated from the free surface by distance $h$). To filter measurement noise, raw images were reconstructed using orthogonally decomposed modes corresponding to the noise-free part of the signal estimated via power spectra. These de-noised thermal fields were systematically processed for thermal pattern tracking using a particle image velocimetry algorithm to access the mean and turbulent velocity fields. A bi-directional correlation analysis of the thermal scales (radial and angular) revealed their sensitivity to source momentum flux (parametrized by $Re_D$) and source-surface separation $h$; while the former decreased the angular thermal scales by amplifying free surface-induced shear, the latter increased the radial scales by allowing more room for the jet to spread laterally. For velocity fields, increasing $Re_D$ at a fixed $h$ amplified the mean and turbulent motions, while increasing $h$ at a fixed $Re_D$ weakened these motions and spread them over larger radial distances. Additionally, the mean flow profiles, when rescaled using appropriate velocity and length scales, collapsed onto a self-similar curve. Consistent with the obtained self-similar profile, asymptotic analysis predicts motion increasing linearly near the center of the flow field and decaying inversely far from it. While the linear behavior originates from a geometry-enforced balance between angular and radial turbulent velocity fluctuations, the inverse decay originates from the turbulent redistribution of the radial advection of mean radial momentum. Self-similar profiles imply that free surface interfacial processes are passive; they do not impose any additional characteristic scales and represent the adjusted continuation of the self-similar impinging flow as it is redirected along the free surface plane. Therefore, the scales yielding self-similar profiles act as surrogates for estimating sub-surface flow and its TE properties, facilitating the development of remotely observable flow metrics for geophysical and engineering applications.

Document Type

Dissertation

First Advisor

Tracy L. Mandel

Second Advisor

Christopher M. White

Third Advisor

Nathan Laxague

Department or Program

Mechanical Engineering

Degree Name

Doctor of Philosophy

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