Development of a relationship between physical parameters of tsunami waves and tsunami intensity based on macroscopic effects and its application to the Italian tsunami database

Tsunamis are rare events. However, their impact can be devastating and it may extend to large geographical areas. For low-probability high-impact events like tsunamis, it is crucial to implement all possible actions to mitigate the risk. The tsunami hazard assessment is the result of a scientific process that integrates traditional geological methods, numerical modelling and the analysis of tsunami sources and historical records. For this reason, analysing past events and understanding how they interacted with the land is the only way to inform tsunami source and propagation models, and quantitatively test forecast models like hazard analyses. The primary objective of this thesis is to establish an explicit relationship between the macroscopic intensity, derived from historical descriptions, and the quantitative physical parameters measuring tsunami waves. This is done first by defining an approximate estimation method based on a simplified 1D physical onshore propagation model to convert the available observations into one reference physical metric. Wave height at the coast was chosen as the reference due to its stability and independence of inland effects. This method was then implemented for a set of well-known past events to build a homogeneous dataset with both macroseismic intensity and wave height. By performing an orthogonal regression, a direct and invertible empirical relationship could be established between the two parameters, accounting for their relevant uncertainties. The target relationship is extensively tested and finally applied to the Italian Tsunami Effect Database (ITED), providing a homogeneous estimation of the wave height for all existing tsunami observations in Italy. This provides the opportunity for meaningful comparison for models and simulations, as well as quantitatively testing tsunami hazard models for the Italian coasts and informing tsunami risk management initiatives.

Comparative study of the different models for the calculation of BLEVEs overpressure effects

The BLEVE, acronym for Boiling Liquid Expanding Vapour Explosion, is one of the most dangerous accidents that can occur in pressure vessels. It can be defined as an explosion resulting from the failure of a vessel containing a pressure liquefied gas stored at a temperature significantly above its boiling point at atmospheric pressure. This phenomenon frequently appears when a vessel is engulfed by a fire: the heat causes the internal pressure to raise and the mechanical proprieties of the wall to decrease, with the consequent rupture of the tank and the instantaneous release of its whole content. After the breakage, the vapour outflows and expands and the liquid phase starts boiling due to the pressure drop. The formation and propagation of a distructive schock wave may occur, together with the ejection of fragments, the generation of a fireball if the stored fluid is flammable and immediately ignited or the atmospheric dispersion of a toxic cloud if the fluid contained inside the vessel is toxic. Despite the presence of many studies on the BLEVE mechanism, the exact causes and conditions of its occurrence are still elusive. In order to better understand this phenomenon, in the present study first of all the concept and definition of BLEVE are investigated. A historical analysis of the major events that have occurred over the past 60 years is described. A research of the principal causes of this event, including the analysis of the substances most frequently involved, is presented too. Afterwards a description of the main effects of BLEVEs is reported, focusing especially on the overpressure. Though the major aim of the present thesis is to contribute, with a comparative analysis, to the validation of the main models present in the literature for the calculation and prediction of the overpressure caused by BLEVEs. In line with this purpose, after a short overview of the available approaches, their ability to reproduce the trend of the overpressure is investigated. The overpressure calculated with the different models is compared with values deriving from events happened in the past and ad-hoc experiments, focusing the attention especially on medium and large scale phenomena. The ability of the models to consider different filling levels of the reservoir and different substances is analyzed too. The results of these calculations are extensively discussed. Finally some conclusive remarks are reported.

Mathematical models for cellular aggregation: the chemotactic instability and clustering formation

In this thesis we present a mathematical formulation of the interaction between microorganisms such as bacteria or amoebae and chemicals, often produced by the organisms themselves. This interaction is called chemotaxis and leads to cellular aggregation. We derive some models to describe chemotaxis. The first is the pioneristic Keller-Segel parabolic-parabolic model and it is derived by two different frameworks: a macroscopic perspective and a microscopic perspective, in which we start with a stochastic differential equation and we perform a mean-field approximation. This parabolic model may be generalized by the introduction of a degenerate diffusion parameter, which depends on the density itself via a power law. Then we derive a model for chemotaxis based on Cattaneo's law of heat propagation with finite speed, which is a hyperbolic model. The last model proposed here is a hydrodynamic model, which takes into account the inertia of the system by a friction force. In the limit of strong friction, the model reduces to the parabolic model, whereas in the limit of weak friction, we recover a hyperbolic model. Finally, we analyze the instability condition, which is the condition that leads to aggregation, and we describe the different kinds of aggregates we may obtain: the parabolic models lead to clusters or peaks whereas the hyperbolic models lead to the formation of network patterns or filaments. Moreover, we discuss the analogy between bacterial colonies and self gravitating systems by comparing the chemotactic collapse and the gravitational collapse (Jeans instability).