Beneath the Surface: Mathematical Perspectives on Flows Generated by Submarine Volcanic Eruption in Stratified Oceans.

Abstract

This thesis addresses critical gaps in understanding the fluid dynamics generated by submarine volcanic eruptions in both shallow and deep ocean environments. The research utilizes a combination of analytical and numerical models in two and three dimensions, integrating heat and mass flux associated with volcanic activity within stratified ocean systems. For deep-sea eruptions, the primary focus is on developing a comprehensive three-dimensional framework to analyze flow dynamics, with particular attention to the generation of convective flows. The influence of oceanic stratification, specifically temperature and salinity gradients, is systematically investigated to elu- cidate their role in modulating convective flow patterns and shaping complex marine processes. The research further investigates how different stratification intensities ranging from strong to weak affect the behavior of volcanic plumes, as well as the rotational dynamics that develop during sustained or gradual eruptions. A significant component of the study involves examining how variations in ocean stratification, which are increasingly affected by climate change and rising sea surface temperatures, alter the generation and propagation of tsunamis triggered by sub- marine eruptions. This aspect is explored using a two-dimensional potential theory model to analytically evaluate the impact of stratification on tsunami wave dynam- ics. Also, a 3-dimensional computational model is used to generate gravity waves by applying a high heat flux at the seabed in a shallow environment. In addition, the study presents a detailed analysis of the influence of submarine volcanic activity on equatorial oceanic flows. This is accomplished by applying an established model for equatorial ocean dynamics, deriving analytical solutions for flow velocities, and exam- ining the interaction between volcanic-induced perturbations and ambient currents. To simulate complex three-dimensional processes, the Process Study Ocean Model (PSOM) is employed, incorporating the effects of thermal and salinity stratification and heat flux in both deep and shallow oceanic settings. These simulations provide insight into the interplay between submarine volcanic activity and broader ocean cir- culation, contributing to a more refined understanding of how such eruptions influence oceanic flows and potentially impact global marine systems. This thesis contributes to a deeper understanding of submarine volcanic phenom- ena, providing new insights into how stratification modifies flow dynamics and surface wave formation, with implications for predicting the impacts of volcanic eruptions in changing oceanic conditions.