## 20810164-1 - GENERAL THEORY

Numerical and statistical methods for Civil Engineering aims at providing students with fundamental knowledge on numerical and statistical methods for civil engineering problems, and at developing the competences required for designing and coding simple numerical and statistical models, also to learn how apply high level softwares for engineering analysis. The course aims at providing in depth knowledge of 1) a technical/scientific programming language; 2) main numerical methods for the solution of ordinary and partial differential equations; 3) descriptive and inferential statistics. Students shall be able of: 1) using a technical/scientific programming language to develop numerical models and to carry out statistical analyses; 2) designing, developing, validating and applying algorithms for the integration of ordinary and partial differential equations of interest for the civil engineering field; 3) carrying out statistical analysis on large datasets; 4) designing and carrying out statistical analyses; 5) finding and understanding scientific publications for specific problems of interest, also using scientific search engines/databases (Scopus, Web Of Science)
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Programme

Governing equations for viscous and turbulent flows
Viscous flows and Navier-Stokes equations, turbulent flows and Reynolds equations.

Governing equations for rotating flows
Rotating framework of reference, Unimportance of the centrifugal force, Acceleration on a three-dimensional rotating planet, Equations of Fluid Motion (Mass budget , Momentum budget, Equation of state, Energy budget, Salt and moisture budgets) Boussinesq approximation, Scales of motion, Important dimensionless numbers, Boundary conditions.

Rotation effects
Geostrophic flows and vorticity dynamics, cyclonic and anticyclonic flows, the bottom Ekman layer and the surface Ekman layer.

Ocean
Oceanic General Circulation; What drives the oceanic circulation; Large-scale ocean dynamics (Sverdrup dynamics). Western boundary currents. Thermohaline circulation; Abyssal circulation;

Atmosphere: generalities (structure and physical characteristics), definition of standard atmosphere and standard lapse rate. Atmospheric stability: dry and wet adiabatic lapse rate and atmospheric stability, conditional stability. Planetary Heat Budget.

Large scale Dynamics in atmosphere: Generalities(main sources of global scale circulation, effects of the Coriolis forces, direct and indirect cells, prevailing winds). Governing equations for large scale dynamics in atmosphere. Thermal wind relation, large-scale circulation in Hadley and Ferrel cells (theoretical analysis).

The Atmospheric Boundary Layer (ABL): generalities and definitions. Turbulent phenomena in the ABL: Mechanical and thermal turbulence, the turbulent cascade, statistical approach to turbulence in ABL (turbulence intensity and turbulent fluxes). The Turbulent kinetic equation, analysis of atmospheric stability from the vertical turbulent flux of temperature. Closure relations: local closures and K-theory, zeroth order closures based on similarity theory. Definition of the main length, time and velocity scales in ABL flows. Vertical structure of the boundary layer. Derivation of the potential temperature from the 1st law of thermodynamics. Day-night cycles of ABL in fair weather conditions. Dynamical Evolution of the ABL: entrainment zone, daily variation of the entrainment zone. Cloud-topped boundary layer overland.

Anabatic and katabatic winds. Hydrodynamic phenomena in presence of synoptic scale forcing.

Cloud physics: Generalities and definitions on cloud and rain droplets. Main Mechanisms for rain formation. Effect of curvature on condensation and evaporation (Kelvin theory). Solute effect on rain formation (Raoult's Law). Köhler theory and formation conditions for a rain droplet. Vapor deposition and early-stage growth of cloud condensation nuclei.

Core Documentation

- A. Cenedese, 2006, Meccanica dei fluidi ambientale, Mc Graw-Hill.
- B. Cushman-Roisin, 1994, Introduction to Geophysical Fluid Dynamics, Prentice Hall.

Type of delivery of the course

Lectures

Type of evaluation

Oral examination, with a duration of about one hour, with questions on theory