Volcanic eruption columns inject high concentrations of ash into the atmosphere. Some of this ash is carried downwind forming ash clouds in the atmosphere that are hazardous for private and commercial aviation. Current models rely on inputs such as plume height, duration, eruption rate, and meteorological wind fields. Eruption rate is estimated from plume height using relations that depend on the rate of air entrainment into the plume, which is not well quantified. A wind tunnel experiment has been designed to investigate these models by injecting a vertical air jet into a cross-flow. The ratio of the cross-flow and jet velocities is varied to simulate a weak plume, and flow response is measured using particle image velocimetry. The plumes are characterized and flow data relative to the centerline is examined to measure the growth of weak plumes and the entrainment velocity along its trajectory. It was found that cross-flow recirculates behind the jet and entrainment occurs both up and downstream of the jet. Analysis of the generation of turbulence enhanced results by identifying the transition point to bending plume and the growth of the shear layer in a bending plume. This provides information that can be used to improve models of volcanic ash concentration changes in the atmosphere. The author would like to thank Dr. Raúl Cal for guidance through the Masters program, Portland State University's Department of Mechanical and Materials Engineering for funding and support, the members of the Wind Energy and Turbulence Lab including Dr. Nicholas Hamilton and Elizabeth Camp for training and guidance through experiments, Dr. Steven Solovitz from Washington State University and Dr. Larry Mastin of USGS for guidance through this project, Joshua McCraney for coding and mathematical theory support, as well as Dr. Mark Glauser and Dr. Jacques Lewalle from Syracuse University for guidance during my early research experiences as an undergraduate at Syracuse University. iii Contents List of Tables v List of Figures vi Nomenclature viii 1 Chapter 1 Introduction and Motivation Chapter 2 Turbulence and Volcanic Theory 5 2.1 Reynolds-Averaged Navier-Stokes Equation for Turbulent Flow .

During volcanic eruptions, model predictions of plume height are limited by the accuracy of entrainment coefficients used in many plume models. Typically, two parameters are used, and , which relate the entrained air speed to the jet speed in the axial and cross-flow directions, respectively. To improve estimates of these parameters, wind tunnel experiments have been conducted for a range of cross-wind velocities and turbulence conditions. Measurements are compared directly to computations from the 1-D plume model, Plumeria, in the near-field, bending region of the jet. Entrainment coefficients are determined through regression analysis, demonstrating optimal combinations of effective and values. For turbulent conditions, all wind speeds overlapped at a single combination, = 0.06 and = 0.46, each of which are slightly reduced from standard values. Refined coefficients were used to model plume heights for 20 historical eruptions. Model accuracy improves modestly in most cases, agreeing to within 3 km with observed plume heights. For weak eruptions, uncertainty in field measurements can outweigh the effects of these refinements, illustrating the challenge of applying plume models in practice.Ash transport models (ATMs) forecast the path and concentrations of volcanic ash clouds and are used to assign areas to avoid by aircraft. A critical source parameter for all ATMs is mass eruption rate (MER) as MER affects ATM estimations of airborne particle concentrations and fallout. MER is estimated either through field observations or mathematical plume models. One-dimensional steady-state numerical plume models, for example, Plumeria, are commonly used to estimate MER through inversion of observed plume height (H obs ). In practice, forecasters input weather conditions and H obs that allow for real-time MER estimates used in ATM models for hazard assessments. These models can be used in real time, making them possible tools for operations. There are several models available , all of which operate along the same physical principles of mass, momentum, and energy conservation. Despite their utility and flexibility, 1-D plume model accuracy is limited by model parameters and field data uncertainty.Although based on fundamental concepts, 1-D plume models require the use of empirical parameters related to entrainment. Hence, their accuracy is limited by the understanding of entrainment Woodhouse et al., 2015), which this research aims to address. For plumes in cross flow, two parameters are used to describe entrainment: and . The former parameter quantifies entrainment associated with shear due to differential flow velocities parallel to the axis of the plume, while the latter is associated with entrainment due to shear perpendicular to the axis of the plume (i.e., cross flow). The entrainment coefficients are

This work would not be possible without the incredible support I have received over the last six years. I would first like to acknowledge my advisor, Dr. Raúl Bayoán Cal, who I am indebted to for his incredible support − both in taking a chance in giving me this opportunity and nurturing my curiosity throughout my graduate education. Special thanks to Dr. Stephen Solovitz, and Dr. Larry Mastin for their encouragement and discussions that helped shape the interdisciplinary research in this dissertation. This work would also not be possible without the support of the graduate students of the Wind Energy and Turbulence Lab. Their assistance in the laboratory, discussions on theory and fundamentals and moral support at conferences helped guide my research. Special thanks to the former students who taught me how to devise and run experiments, and my committee, who tirelessly reviewed my research for my benefit and treated me as a colleague at the conclusion of my defense.

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