The aim of the course TRANSPORT PHENOMENA IN FLUIDS (9 CFU) is to provide advanced knowledge on the dynamics of transport-diffusion-dispersion phenomena in surface waters, with particular reference to the coastal and estuarine environment. The course is aimed at giving the competencies needed for the the development of mathematical models of main relevant phenomena and for their application to the simulation and the investigation of realistic cases. The main skills acquired by the students are: to understand and model the dynamics of transport-diffusion-dispersion phenomena in surface waters, to apply suitable mathematical models to realistic cases, to get and manage numerical data.
scheda docente
materiale didattico
.Concepts and definitions
.Dimensional analysis and Pi-theorem
.Fickian diffusion
.Formal derivation of the pure diffusion equation
.Self-similar solution of the 1d pure diffusion equation.
2) Advection diffusion equation (ADE)
.Concepts and definitions
.Heuristic derivation of the ADE
.Formal derivation of the ADE
.Analytical solutions for the advection diffusion equation
.Definition and physical meaning of the main non-dimensional governing parameters
3) Turbulent diffusion and advection dispersion equation
.Turbulence: main concepts
.Derivation of the turbulent ADE
. Turbulent diffusion coefficients: longitudinal, vertical e transversal
.Derivation of the advection dispersion equation (Taylor approach)
4) Advection diffusion equation with reactions
.Concepts and definitions
.Chemical kinetics: concepts
. First order reactions
.Second and higher order reactions
.Derivation of the advection diffusion reaction equation (homogeneous and heterogeneous reactions)
5) Atmospheric mixing
.Concepts and definitions
.Turbulence in the atmospheric boundary layer
. Turbulent ADE in 3D
. Derivation of the solution for the steady Gaussian plume
6) Mixing in estuaries
.Concepts and definitions
.Taylor-Aris dispersion: Asymptotic analysis derivation
.Turbulent flows in estuaries
.The turbulent kinetic energy equation for estuarine flows
.Stratification: Brunt-Vaisala frequency and Richardson number
7) Sediment transport
.Concepts and definitions
. Sediment properties in coastal areas
. Falling velocity
.Shield Theory
.Bed load transport: Einstein theory and Bagnold correction
.Vertical distribution of sediments in a steady current
.Vertical distribution of sediments in a pure oscillatory flow
8) Numerical solution to the ADE with applications
.Concepts and definitions
.Finite difference method
. Accuracy of a numerical scheme with the modified wavenumber approach
. Taylor table method
.Stability, accuracy and consistency
. FTCS scheme for ADE
.Von Neumann analysis
.Upwind schemes
2) Chemical fate and transport in the environment, HF Hemond, EJ Fechner
3) Mechanics of coastal sediment transport, J. Fredsoe and R. Deigaard
Programma
1) Pure diffusion equation.Concepts and definitions
.Dimensional analysis and Pi-theorem
.Fickian diffusion
.Formal derivation of the pure diffusion equation
.Self-similar solution of the 1d pure diffusion equation.
2) Advection diffusion equation (ADE)
.Concepts and definitions
.Heuristic derivation of the ADE
.Formal derivation of the ADE
.Analytical solutions for the advection diffusion equation
.Definition and physical meaning of the main non-dimensional governing parameters
3) Turbulent diffusion and advection dispersion equation
.Turbulence: main concepts
.Derivation of the turbulent ADE
. Turbulent diffusion coefficients: longitudinal, vertical e transversal
.Derivation of the advection dispersion equation (Taylor approach)
4) Advection diffusion equation with reactions
.Concepts and definitions
.Chemical kinetics: concepts
. First order reactions
.Second and higher order reactions
.Derivation of the advection diffusion reaction equation (homogeneous and heterogeneous reactions)
5) Atmospheric mixing
.Concepts and definitions
.Turbulence in the atmospheric boundary layer
. Turbulent ADE in 3D
. Derivation of the solution for the steady Gaussian plume
6) Mixing in estuaries
.Concepts and definitions
.Taylor-Aris dispersion: Asymptotic analysis derivation
.Turbulent flows in estuaries
.The turbulent kinetic energy equation for estuarine flows
.Stratification: Brunt-Vaisala frequency and Richardson number
7) Sediment transport
.Concepts and definitions
. Sediment properties in coastal areas
. Falling velocity
.Shield Theory
.Bed load transport: Einstein theory and Bagnold correction
.Vertical distribution of sediments in a steady current
.Vertical distribution of sediments in a pure oscillatory flow
8) Numerical solution to the ADE with applications
.Concepts and definitions
.Finite difference method
. Accuracy of a numerical scheme with the modified wavenumber approach
. Taylor table method
.Stability, accuracy and consistency
. FTCS scheme for ADE
.Von Neumann analysis
.Upwind schemes
Testi Adottati
1) Special topics in Mixing and Transport Processes in the Environment, S. Socolofsky and G. Jirka2) Chemical fate and transport in the environment, HF Hemond, EJ Fechner
3) Mechanics of coastal sediment transport, J. Fredsoe and R. Deigaard
Bibliografia Di Riferimento
1) Special topics in Mixing and Transport Processes in the Environment, S. Socolofsky and G. Jirka 2) Chemical fate and transport in the environment, HF Hemond, EJ Fechner 3) Mechanics of coastal sediment transport, J. Fredsoe and R. DeigaardModalità Erogazione
the lessons are held in the classroomModalità Frequenza
attendance is optionalModalità Valutazione
The exam is oral