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.

Concentrations of organic carbon, nitrogen and phosphorus on vertical profiles in waters of the tropical North Atlantic in March 2002

In the literature, an inconsistency exists between estimates of biotically-effected carbon export inferred from large-scale geochemical studies (Jenkins 1982; 47 gC m-2 a-1) and local measurements of turbulent nutrient supply (Lewis et al. 1986; 4 gC m-2 a-1) in the eastern subtropical North Atlantic. Nutrient supply to the upper ocean by turbulent mixing is reexamined using local standard oceanographic measurements and high-resolution vertical profiles of nutrients averaged over a large region directly comparable to that investigated by Jenkins (1982). Turbulent fluxes induced by internal waves and salt fingering, respectively, are separated according to Gregg (1989) and Zhang et al. (1998). Nutrient transport into the nutrient-consuming surface layer by salt fingering is more than fivefold higher than transport due to internal-wave induced turbulence. Still, this cannot resolve the above- mentioned apparent inconsistency, even if additional physical transport mechanisms such as eddy pumping, advection and horizontal diffusion are accounted for. Estimated nitrate fluxes due to vertical turbulent diffusion are 0.05-0.15 mol m-2 a-1, corresponding to 4-11 gC m-2 a-1. Observed NO3/PO4 turbulent flux ratios of up to 23 are interpreted as the imprint of N2 fixation.