UNIVERSITA` DEGLI STUDI DI TRIESTE XXVI CICLO DEL DOTTORATO DI RICERCA IN ENVIRONMENTAL AND INDUSTRIAL FLUID MECHANICS Large-Eddy Simulation for wind and tidally driven sea circulation in coastal semi-closed areas Settore scientifico-disciplinare: ICAR/01 Ph.D. Student: Anthony Galea Ph.D. Program Director and Thesis Supervisor: Prof. Vincenzo Armenio ACADEMIC YEAR 2012/2013 Anthony Galea Dipartimento di Ingegneria e Architettura, Universit`adegli Studi di Trieste, P.le Europa 1, 34127, Trieste, Italy [email protected] Day of the defence: 23rd April 2014 Signature from head of Ph.D. committee: ii Abstract A novel high-resolution, eddy-resolving numerical model (LES-COAST) is used to investigate currents, mixing and water renewal in Barcelona harbour and Taranto bay. These environmental sites are of particular importance due to the interplay between touristic and commercial activities, requiring detailed and high-definition studies of water quality within the harbour. We use Large Eddy Simulation (LES) which directly resolves the anisotropic and energetic large scales of motion and parametrizes the small, dissipative, ones. Small-scale turbulence is modelled by the Anisotropic Smagorinsky Model (ASM) which is employed in presence of large cell anisotropy. The complexity of the harbour is modelled using a combination of curvilinear, structured, non-staggered grid and the Immersed Boundary Method (IBM). Both computation grids and harbour structures are purposely constructed for these applications by appropriate programs. Boundary conditions for wind forcing at the free surface and currents at the inlets of the port are obtained from in-situ measurements (for the case of Barcelona harbour) or by nesting this numerical model into a coastal model (Taranto bay). In this dissertation thesis an important modification to LES-COAST is im- plemented and is proposed as a prototype scheme, namely the possibility to consider the effect of surface waves in coastal semi-closed areas. Partic- ularly, a linear formulation of the free surface boundary condition is con- sidered, which would be able to reproduce the presence of seiches and tides on the dynamics of the area under investigation. The methodology is val- idated against analytical solution for a stationary oscillating surface wave in a simple computational grid. In both harbours considered, first- and second-order statistics, such as the mean velocity field, turbulent kinetic energy, and horizontal and vertical eddy viscosities are calculated and their spatial distribution is assessed. Wa- ter residence time is also considered for the two coastal semi-closed areas examined. Finally, the LES solution is validated against available field data. The study shows the presence of sub-surface elongated rolling structures (with a time scale of a few hours), contributing to the vertical water mix- ing. The time-averaged velocity field reveals intense upwelling and down- welling zones along the walls of the harbours. The analysis of second-order statistics in these harbours shows strong inhomogeneity of turbulent kinetic energy and horizontal and vertical eddy viscosities in the horizontal plane, with larger values in the regions characterized by stronger currents. The water renewal within the port is quantified for particular sub-domain re- gions, showing that the complexity of the harbour is such that certain inner basins of Barcelona harbour have a water renewal of over five days, includ- ing its yacht marina area, and over seven days for Taranto bay. For the Barcelona simulation, the LES solution compares favourably with available current-meter data; it is also compared with a RANS solution obtained in literature for the same site under the same forcing conditions, the compari- son demonstrating a large sensitivity of properties to model resolution and frictional parametrization. To my nephew Jacques, who sees the sea as a pretty playground. Acknowledgements This Ph.D. thesis is the work of over three years carried out in Trieste, where memorable moments have been shared with many people. I express my profound gratitude to everyone that contributed directly or indirectly to this work. My first debt of gratitude goes to my supervisor Prof. Vincenzo Armenio for his staunch support and guidance through these years, sharing his intu- itions and providing limitless good suggestions to accomplish my research work. It has been a great privilege for me to work in his Fluid Mechan- ics lab at the University of Trieste and I was lucky to be part of such a group. I am also extremely indebted to Dr. Federico Roman for his valuable ad- vice, constructive criticism and his extensive discussions around my work. Special thanks also goes to Dr. Andrea Petronio for his valuable suggestions and support. I take this opportunity to sincerely acknowledge the board of the Doctoral School in Environmental and Industrial Fluid Mechanics, and the University of Trieste for offering plenty of learning opportunities to grow professionally and financially supporting this research project. The numerical simulations were carried out using computational facilities procured through the European Regional Development Fund, Project ERDF- 080 ‘A Supercomputing Laboratory for the University of Malta. I wish to acknowledge the HPC facility Albert in Malta and its staff for the compu- tational time and support, in particular Dr. Alessio Magro. I kindly acknowledge Prof. J. P. McCreary from the University of Hawaii at Manoa (USA) and Prof. Bernard J. Geurts from the University of Twente (Netherlands) for their very useful discussion and comments. Working with computers and other electronic devices, it was inevitable to encounter software/hardware problems. Therefore, I thank the lab techni- cian Daniele Bellini who was also on my phone speed dial and ready to help. Trieste, characterised by the bracing air of the famous Bora wind and by its splendid views of the Adriatic Sea, hosts many world renowned institu- tions and international organisations. Living in such a city of science has allowed me to meet many celebrated scientists at seminars, workshops, and scientific conferences. My interest in the sea has brought me a long way, not only academically but by experiencing new cultures and indulging my love of kayaking and cycling along the karst coastline. Lastly but not least, I would like to pay high regards to my family and friends, both in Italy and Malta, for their constant support. To my friends in Italy, I am grateful for time spent together, numerous coffee breaks and aperitifs, hospitality and memorable trips in Italy, Slovenia, Croatia, and Austria. Ai compagni d’ufficio, Carlo e Giulia che mi hanno accolto nono- stante il mio fischiettare; alle matematiche Chiara e Sabrina per le pausette e sostegno, e in fine a Rita per il suo appoggio. Particularly to my family in Malta, whom I will thank in Maltese: Nirringrazzja lil ommi u missieri, Lora u Raymond, tas-sapport morali illimitabli li dejjem tawni u tal-pac˙enzja li ~adu biha. Nestendi r-ringrazzjamenti lil o~ti Angele, lil ~aten Arnaud u liz˙-z˙g~ir Jacques, talli dejjem kienu prez˙enti g~alija. Nesprimi l-gratitudni tieg~i lil Manuel ta’ kemm-il darba g˙ie g~alija meta kelli bz˙onn. Grazzi. viii Contents List of Figures xi 1 Introduction 1 2 Numerical Method 5 2.1 Approachestopredictingturbulentflows. 5 2.2 LES-COASTmodel ............................. 8 2.2.1 The governing equations . 9 2.2.2 Discretization............................. 11 2.2.3 Sub-gridscales(SGS)model . 12 2.2.4 Treatment of solid boundaries . 15 2.2.5 Treatment of open boundaries . 17 2.2.6 Treatment of free surface . 18 3 Free Surface 19 3.1 Boundary condition at the free surface . 19 3.2 Fractionalstepmethod............................ 23 3.2.1 Predictor step ............................ 25 3.2.2 Corrector step ............................ 25 3.2.3 Solution of Poisson equation . 26 3.2.4 Overall scheme of the fractional step method . 26 3.3 Implementation of the free surface condition . 28 3.4 Numericaltests................................ 30 3.5 Validation against analytical solution . 33 ix CONTENTS 4 Water mixing in Barcelona Harbour 37 4.1 Introduction.................................. 37 4.2 Numericalset-up ............................... 41 4.2.1 Comupational domain . 41 4.2.2 Boundary conditions . 42 4.3 ResultsandDiscussion............................ 44 4.3.1 The instantaneous field . 45 4.3.2 Turbulencestatistics . 51 4.3.3 Validation against field data . 58 4.4 Conclusions .................................. 60 5 Water Mixing in Taranto bay 63 5.1 Introduction.................................. 63 5.2 Numericalset-up ............................... 64 5.2.1 Computational domain . 64 5.2.2 Boundary conditions . 66 5.3 ResultsandDiscussion............................ 68 5.3.1 The instantaneous field . 68 5.3.2 Turbulencestatistics . 71 5.4 Conclusions .................................. 74 6 Conclusions 77 References 81 x List of Figures 2.1 Visualization of the flow in a mixing layer. [Source: Brown and Rochko (1974)]..................................... 6 2.2 Atypicalenergyspectrumofturbulence.. 7 2.3 A control volume of the non-staggered grid and the mapping in two dimensions. [Source: Zang et al. (1994)]................... 10 2.4 Variation of optimal empirical constants Ch and Cv with the grid anisotropy. [Source: Roman et al. (2010)]......................... 14 2.5 Ray tracing method to find the solid nodes in the computational domain: scheme of the method in two (a) and in three (b) dimensions. [Source: