Two fluid numerical model for coastal applications

Wave breaking is an important coastal process, influencing hydro-morphodynamic processes such as turbulence generation and wave energy dissipation, run-up on the beach and overtopping of coastal defence structures. During breaking, waves are complex mixtures of air and water (“white water”) whose properties affect velocity and pressure fields in the vicinity of the free surface and, depending on the breaker characteristics, different mechanisms for air entrainment are usually observed. Several laboratory experiments have been performed to investigate the role of air bubbles in the wave breaking process (Chanson & Cummings, 1994, among others) and in wave loading on vertical wall (Oumeraci et al., 2001; Peregrine et al., 2006, among others), showing that the air phase is not negligible since the turbulent energy dissipation involves air-water mixture. The recent advancement of numerical models has given valuable insights in the knowledge of wave transformation and interaction with coastal structures. Among these models, some solve the RANS equations coupled with a free-surface tracking algorithm and describe velocity, pressure, turbulence and vorticity fields (Lara et al. 2006 a-b, Clementi et al., 2007). The single-phase numerical model, in which the constitutive equations are solved only for the liquid phase, neglects effects induced by air movement and trapped air bubbles in water. Numerical approximations at the free surface may induce errors in predicting breaking point and wave height and moreover, entrapped air bubbles and water splash in air are not properly represented. The aim of the present thesis is to develop a new two-phase model called COBRAS2 (stands for Cornell Breaking waves And Structures 2 phases), that is the enhancement of the single-phase code COBRAS0, originally developed at Cornell University (Lin & Liu, 1998). In the first part of the work, both fluids are considered as incompressible, while the second part will treat air compressibility modelling. The mathematical formulation and the numerical resolution of the governing equations of COBRAS2 are derived and some model-experiment comparisons are shown. In particular, validation tests are performed in order to prove model stability and accuracy. The simulation of the rising of a large air bubble in an otherwise quiescent water pool reveals the model capability to reproduce the process physics in a realistic way. Analytical solutions for stationary and internal waves are compared with corresponding numerical results, in order to test processes involving wide range of density difference. Waves induced by dam-break in different scenarios (on dry and wet beds, as well as on a ramp) are studied, focusing on the role of air as the medium in which the water wave propagates and on the numerical representation of bubble dynamics. Simulations of solitary and regular waves, characterized by both spilling and plunging breakers, are analyzed with comparisons with experimental data and other numerical model in order to investigate air influence on wave breaking mechanisms and underline model capability and accuracy. Finally, modelling of air compressibility is included in the new developed model and is validated, revealing an accurate reproduction of processes. Some preliminary tests on wave impact on vertical walls are performed: since air flow modelling allows to have a more realistic reproduction of breaking wave propagation, the dependence of wave breaker shapes and aeration characteristics on impact pressure values is studied and, on the basis of a qualitative comparison with experimental observations, the numerical simulations achieve good results.

Evaluation of the power production performance of the wavepiston, wave energy converter

In the early 1970 the community has started to realize that have as a main principle the industry one, with the oblivion of the people and health conditions and of the world in general, it could not be a guideline principle. The sea, as an energy source, has the characteristic of offering different types of exploitation, in this project the focus is on the wave energy. Over the last 15 years the Countries interested in the renewable energies grew. Therefore many devices have came out, first in the world of research, then in the commercial one; these converters are able to achieve an energy transformation into electrical energy. The purpose of this work is to analyze the efficiency of a new wave energy converter, called WavePiston, with the aim of determine the feasibility of its actual application in different wave conditions: from the energy sea state of the North Sea, to the more quiet of the Mediterranean Sea. The evaluation of the WavePiston is based on the experimental investigation conducted at the University of Aalborg, in Denmark; and on a numerical modelling of the device in question, to ascertain its efficiency regardless the laboratory results. The numerical model is able to predict the laboratory condition, but it is not yet a model which can be used for any installation, in fact no mooring or economical aspect are included yet. È dai primi anni del 1970 che si è iniziato a capire che il solo principio dell’industria con l’incuranza delle condizioni salutari delle persone e del mondo in generale non poteva essere un principio guida. Il mare, come fonte energetica, ha la caratteristica di offrire diverse tipologie di sfruttamento, in questo progetto è stata analizzata l’energia da onda. Negli ultimi 15 anni sono stati sempre più in aumento i Paesi interessati in questo ambito e di conseguenza, si sono affacciati, prima nel mondo della ricerca, poi in quello commerciale, sempre più dispositivi atti a realizzare questa trasformazione energetica. Di tali convertitori di energia ondosa ne esistono diverse classificazioni. Scopo di tale lavoro è analizzare l’efficienza di un nuovo convertitore di energia ondosa, chiamato WavePiston, al fine si stabilire la fattibilità di una sua reale applicazione in diverse condizioni ondose: dalle più energetiche del Mare del Nord, alle più quiete del Mar Mediterraneo. La valutazione sul WavePiston è basata sullo studio sperimentale condotto nell’Università di Aalborg, in Danimarca; e su di una modellazione numerica del dispositivo stesso, al fine di conoscerne l’efficienza a prescindere dalla possibilità di avere risultati di laboratorio. Il modello numerico è in grado di predirre le condizioni di laboratorio, ma non considera ancora elementi come gli ancoraggi o valutazione dei costi.

Analisi sperimentale delle forze agenti sul dispositivo di conversione di energia da onda "Wave Dragon" in condizioni ondose estreme del Mare del Nord

Per natura, i dispositivi di conversione di energia da onda (WECs) vengono collocati in aree caratterizzate da onde ad elevato potenziale e in queste condizioni i carichi che agiscono su tali dispositivi sono, sfortunatamente, molto alti e, allo stesso tempo, molto difficili da valutare a priori. Allo stato attuale, nessuna delle tecnologie proposte ha raggiunto uno stadio di sviluppo tale da consentire la produzione dei WECs a scala reale e, quindi, il lancio nel mercato principalmente perchè nessuna di esse può contare su un numero suciente di dati operativi da permettere un'analisi sistematica delle condizioni di lavoro. L'applicazione dei modelli disponibili sembra essere accurata per la maggior parte dei WECs in condizioni operative, ma non abbastanza per prevedere le forze agenti e il loro comportamento quando sono esposti all'azione di onde importanti. Sebbene vi è una generale necessità di indagine su diversi aspetti dei WECs, sembra che il punto critico sia lo sviluppo di un adeguato sistema di ormeggio il cui costo può incidere no al 200

Statistical analysis and simulation techniques in wall-bounded turbulence

The present work is devoted to the assessment of the energy fluxes physics in the space of scales and physical space of wall-turbulent flows. The generalized Kolmogorov equation will be applied to DNS data of a turbulent channel flow in order to describe the energy fluxes paths from production to dissipation in the augmented space of wall-turbulent flows. This multidimensional description will be shown to be crucial to understand the formation and sustainment of the turbulent fluctuations fed by the energy fluxes coming from the near-wall production region. An unexpected behavior of the energy fluxes comes out from this analysis consisting of spiral-like paths in the combined physical/scale space where the controversial reverse energy cascade plays a central role. The observed behavior conflicts with the classical notion of the Richardson/Kolmogorov energy cascade and may have strong repercussions on both theoretical and modeling approaches to wall-turbulence. To this aim a new relation stating the leading physical processes governing the energy transfer in wall-turbulence is suggested and shown able to capture most of the rich dynamics of the shear dominated region of the flow. Two dynamical processes are identified as driving mechanisms for the fluxes, one in the near wall region and a second one further away from the wall. The former, stronger one is related to the dynamics involved in the near-wall turbulence regeneration cycle. The second suggests an outer self-sustaining mechanism which is asymptotically expected to take place in the log-layer and could explain the debated mixed inner/outer scaling of the near-wall statistics. The same approach is applied for the first time to a filtered velocity field. A generalized Kolmogorov equation specialized for filtered velocity field is derived and discussed. The results will show what effects the subgrid scales have on the resolved motion in both physical and scale space, singling out the prominent role of the filter length compared to the cross-over scale between production dominated scales and inertial range, lc, and the reverse energy cascade region lb. The systematic characterization of the resolved and subgrid physics as function of the filter scale and of the wall-distance will be shown instrumental for a correct use of LES models in the simulation of wall turbulent flows. Taking inspiration from the new relation for the energy transfer in wall turbulence, a new class of LES models will be also proposed. Finally, the generalized Kolmogorov equation specialized for filtered velocity fields will be shown to be an helpful statistical tool for the assessment of LES models and for the development of new ones. As example, some classical purely dissipative eddy viscosity models are analyzed via an a priori procedure.

Spectral-Element and Adjoint 3D Full-Wave Tomography for the Lithosphere of Central Italy

The primary objective of this thesis is to obtain a better understanding of the 3D velocity structure of the lithosphere in central Italy. To this end, I adopted the Spectral-Element Method to perform accurate numerical simulations of the complex wavefields generated by the 2009 Mw 6.3 L’Aquila event and by its foreshocks and aftershocks together with some additional events within our target region. For the mainshock, the source was represented by a finite fault and different models for central Italy, both 1D and 3D, were tested. Surface topography, attenuation and Moho discontinuity were also accounted for. Three-component synthetic waveforms were compared to the corresponding recorded data. The results of these analyses show that 3D models, including all the known structural heterogeneities in the region, are essential to accurately reproduce waveform propagation. They allow to capture features of the seismograms, mainly related to topography or to low wavespeed areas, and, combined with a finite fault model, result into a favorable match between data and synthetics for frequencies up to ~0.5 Hz. We also obtained peak ground velocity maps, that provide valuable information for seismic hazard assessment. The remaining differences between data and synthetics led us to take advantage of SEM combined with an adjoint method to iteratively improve the available 3D structure model for central Italy. A total of 63 events and 52 stations in the region were considered. We performed five iterations of the tomographic inversion, by calculating the misfit function gradient - necessary for the model update - from adjoint sensitivity kernels, constructed using only two simulations for each event. Our last updated model features a reduced traveltime misfit function and improved agreement between data and synthetics, although further iterations, as well as refined source solutions, are necessary to obtain a new reference 3D model for central Italy tomography.

Modelling the stable, nocturnal boundary layer: different approaches to turbulence closure problem

Il lavoro è dedicato all'analisi fisica e alla modellizzazione dello strato limite atmosferico in condizioni stabili. L'obiettivo principale è quello di migliorare i modelli di parametrizzazione della turbulenza attualmente utilizzati dai modelli meteorologici a grande scala. Questi modelli di parametrizzazione della turbolenza consistono nell' esprimere gli stress di Reynolds come funzioni dei campi medi (componenti orizzontali della velocità e temperatura potenziale) usando delle chiusure. La maggior parte delle chiusure sono state sviluppate per i casi quasi-neutrali, e la difficoltà è trattare l'effetto della stabilità in modo rigoroso. Studieremo in dettaglio due differenti modelli di chiusura della turbolenza per lo strato limite stabile basati su assunzioni diverse: uno schema TKE-l (Mellor-Yamada,1982), che è usato nel modello di previsione BOLAM (Bologna Limited Area Model), e uno schema sviluppato recentemente da Mauritsen et al. (2007). Le assunzioni delle chiusure dei due schemi sono analizzate con dati sperimentali provenienti dalla torre di Cabauw in Olanda e dal sito CIBA in Spagna. Questi schemi di parametrizzazione della turbolenza sono quindi inseriti all'interno di un modello colonnare dello strato limite atmosferico, per testare le loro predizioni senza influenze esterne. Il confronto tra i differenti schemi è effettuato su un caso ben documentato in letteratura, il "GABLS1". Per confermare la validità delle predizioni, un dataset tridimensionale è creato simulando lo stesso caso GABLS1 con una Large Eddy Simulation. ARPS (Advanced Regional Prediction System) è stato usato per questo scopo. La stratificazione stabile vincola il passo di griglia, poichè la LES deve essere ad una risoluzione abbastanza elevata affinchè le tipiche scale verticali di moto siano correttamente risolte. Il confronto di questo dataset tridimensionale con le predizioni degli schemi turbolenti permettono di proporre un insieme di nuove chiusure atte a migliorare il modello di turbolenza di BOLAM. Il lavoro è stato compiuto all' ISAC-CNR di Bologna e al LEGI di Grenoble.

Dispersive wave solutions of the klein-gordon equation in cosmology

L'equazione di Klein-Gordon descrive una ampia varietà di fenomeni fisici come la propagazione delle onde in Meccanica dei Continui ed il comportamento delle particelle spinless in Meccanica Quantistica Relativistica. Recentemente, la forma dissipativa di questa equazione si è rivelata essere una legge di evoluzione fondamentale in alcuni modelli cosmologici, in particolare nell'ambito dei cosiddetti modelli di k-inflazione in presenza di campi tachionici. L'obiettivo di questo lavoro consiste nell'analizzare gli effetti del parametro dissipativo sulla dispersione nelle soluzioni dell'equazione d'onda. Saranno inoltre studiati alcuni tipici problemi al contorno di particolare interesse cosmologico per mezzo di grafici corrispondenti alle soluzioni fondamentali (Funzioni di Green).

Turbulence models in the atmospheric boundary layer under convective conditions

In this work a modelization of the turbulence in the atmospheric boundary layer, under convective condition, is made. For this aim, the equations that describe the atmospheric motion are expressed through Reynolds averages and, then, they need closures. This work consists in modifying the TKE-l closure used in the BOLAM (Bologna Limited Area Model) forecast model. In particular, the single column model extracted from BOLAM is used, which is modified to obtain other three different closure schemes: a non-local term is added to the flux- gradient relations used to close the second order moments present in the evolution equation of the turbulent kinetic energy, so that the flux-gradient relations become more suitable for simulating an unstable boundary layer. Furthermore, a comparison among the results obtained from the single column model, the ones obtained from the three new schemes and the observations provided by the known case in literature ”GABLS2” is made.

Study of a wind-wave numerical model and its integration with ocean and oil-spill numerical models

The ability to represent the transport and fate of an oil slick at the sea surface is a formidable task. By using an accurate numerical representation of oil evolution and movement in seawater, the possibility to asses and reduce the oil-spill pollution risk can be greatly improved. The blowing of the wind on the sea surface generates ocean waves, which give rise to transport of pollutants by wave-induced velocities that are known as Stokes’ Drift velocities. The Stokes’ Drift transport associated to a random gravity wave field is a function of the wave Energy Spectra that statistically fully describe it and that can be provided by a wave numerical model. Therefore, in order to perform an accurate numerical simulation of the oil motion in seawater, a coupling of the oil-spill model with a wave forecasting model is needed. In this Thesis work, the coupling of the MEDSLIK-II oil-spill numerical model with the SWAN wind-wave numerical model has been performed and tested. In order to improve the knowledge of the wind-wave model and its numerical performances, a preliminary sensitivity study to different SWAN model configuration has been carried out. The SWAN model results have been compared with the ISPRA directional buoys located at Venezia, Ancona and Monopoli and the best model settings have been detected. Then, high resolution currents provided by a relocatable model (SURF) have been used to force both the wave and the oil-spill models and its coupling with the SWAN model has been tested. The trajectories of four drifters have been simulated by using JONSWAP parametric spectra or SWAN directional-frequency energy output spectra and results have been compared with the real paths traveled by the drifters.