99076 - Planetary Boundary Layer and Turbulent Diffusion

Learning outcomes

At the end of the course, the student knows the fundamentals of the theory of turbulent flows in the atmosphere and the theory of turbulent dispersion. In particular, the student:

- will be able to analyze and interpret qualitative and quantitative observations relating to the structure of the atmospheric boundary layer and the dispersion;

- will be able to produce reports and documents at a basic level on problems relating to the atmospheric boundary layer and air quality problems;

- will be able to use simple models relating to dynamics and dispersion in the atmospheric boundary layer;

- will be able to critically evaluate the characterizing aspects of complex models.

Course contents

Module 1 focuses on theoretical aspects and theory of the atmospheric boundary layer and dispersion. Module 2 will put in practice the learnt concept by using computational fluid dynamics.

Module 1 course content

1) Introduction: Definition of atmospheric boundary layer (ABL) - the diurnal cycle of ABL on land - ABL on the sea - measuring the ABL

2) Variables defining the ABL: stochastic variables - probability density function (pdf) - moments, mean value, fluctuations; correlation functions and spectra; from wave numbers to frequency (frozen turbulence hypothesis)

3) Equations (1): the equations for the velocity components and for the passive scalar; scale analysis; hydrostatic pressure; potential temperature; geostrophic wind

4) Equations (2): the equations for prime moments; the equations for fluctuations; the equations for the second moments; the equation for turbulent kinetic energy (TKE); the equation for the variance of a scalar; turbulent flows and the mixing length model; horizontal and vertical heat flows

5) Introduction to turbulence: Eulerian and Lagrangian description; universal characteristics of turbulent flows; a fundamental paradigm: Kolmogorov (1941); spectra and structure functions; the pdf of the velocity

6) Horizontally homogeneous ABL on flat ground: observations; equations for mean velocity and mean temperature; internal and external 'scaling'; definition of surface layer (SL)

7) Near neutral ABL (QNBL): Richardson number of flow and Obukhov length; neutral conditions in SL; mean velocity variance profile and TKE dissipation rate; integral scales; the neutral Ekman layer; weakly stratified conditions; average velocity and average temperature profiles; variances; turbulent diffusion coefficients for momentum and heat;

8) The convective boundary layer (CBL): observations; the pdf of the speed; scales for speed and temperature; average velocity and average temperature profiles; second and third order moments; TKE dissipation rate; a model for horizontal heat flows; potential temperature balance and height of the CBL; the encroachment model; more complex models

9) The residual layer (RL): observations; numerical simulations; a simplified model

10) The stable boundary layer (SBL): observations; extension of the definition of ABL under stable conditions; Long-lasting SBL; other types of SBL; transfer of TKE from top to bottom; local similarity theory: the Nieuwstadt model (1984); average quantity profiles in SL; critical Richardson number

11) Similarity functions in SL: nondimensional gradients of average quantities; nondimensional profiles; Richardson numbers of gradient and bulk

12) The flow in a vegetable 'canopy' and in an urban 'canopy'       observations of average velocity and second moments; flow above the 'canopy'; flow within the 'canopy layer'; friction due to obstacles, urban canyons

13) Introduction to turbulent dispersion

Fundamental equations and analysis of solutions for different types of sources

14) Large-scale atmospheric dispersion

dispersion in a neutral laboratory boundary layer

dispersion in the CBL

Mikkelsen et al. (1987): horizontal 'meandering' in SL

flow dispersion on topography

15) Simple fluid dynamic models for plumes:

case of point source without buoyancy

case of point source with buoyancy

16) Dispersion in an urban environment

Analysis of models and approaches for the analysis of dispersion in urban areas

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Module 2

1. Introduction: discussion of the main numerical methods for computational fluid dynamics, Raynolds-Averaged Navier-Stokes (RANS), Large-Eddy Simulation (LES), Direct-Numerical Simulation (DNS) approaches.

2. Turbulence models: presentation and derivation of some of the most used turbulence models.

3. Numerical methods: brief overview of numerical techniques for solving fluid dynamics equations. Algorithms, solution schemes, computational grid.

4. Practical case studies: presentation of case studies for the reproduction of a planetary boundary layer, dispersion of pollutants in an urban environment, ventilation of urban areas. Data analysis and postprocessing techniques. 5. OpenFOAM simulator: computer tools for numerical simulations, C ++ programming languages, OpenFOAM open-source software, customized scripts.

6. Simulation and analysis: simulation case setting, data and statistics

Readings/Bibliography

Module 1

Lecture notes

Books:

• Stull: Introduction to Boundary-Layer Meteorology, 1988;
• Wyngaard, J. C., 2010. Turbulence in the atmosphere, Cambridge University Press;
• Csanady, G. T., 1973. Turbulent diffusion in the environment, Reidel Pu. Co., Dordrecht;
• Seinfeld, J. H. and Pandis, Spyros N., 1998. Atmospheric chemistry and physics, John Wiley and Sons.
• Kaimal and Finnigan, 1994: “Atmospheric Boundary-Layer Flows”

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Module 2

Lecture notes.

S.B. Pope. Turbulent Flows. Cambridge University Press (2000).

Teaching methods

Module 1: Frontal teaching

Module 2: Frontal teaching and practice in the computer science laboratory where guided excercises will be carried out by the students.

Assessment methods

A single oral examination for the two modules with 3 questions. The first topoc is chosend by the student. During the exams the student will discuss and respond to questions related to the laboratory final report (module 2).

Teaching tools

PC, Blackboard

Computer science laboratory with computers having UNIX/LINUX operative system

Office hours

See the website of Silvana Di Sabatino

See the website of Carlo Cintolesi