31903 - Planetary Boundary Layer and Turbulent Diffusion

Learning outcomes

At the end of the course, the student knows the fundamentals of the theory of turbulent atmospheric flows and turbulent dispersion. In particular, the student is:
- able to analyze and interpret (both qualitatively and quantitatively) observations of the structure of the boundary layer and dispersion properties;
- able to produce reports and documents at a basic level related to issues of the atmospheric boundary layer and air quality;
- able to use simple models of the dynamics and the dispersion of pollutants (including particulate matter) in the atmospheric boundary layer;
- able to critically evaluate the characteristic features of complex models.

Course contents

1) Introduction: Definition of the atmospheric boundary layer (ABL) - the diurnal cycle of ABL on Earth – ABL over the sea – observing the ABL.
2) Variables that define the ABL: stochastic variables - density probability function (pdf) - moments, mean value, fluctuations; correlation functions and spectra; from wave to frequency numbers (hypothesis of frozen turbulence).
3) Equations (1): equations for the components of the velocity and for the passive scalar; scale analysis; hydrostatic pressure; potential temperature; geostrophic wind.
4) Equations (2): equations for the first moments; equations for the fluctuations; equations for the second moments; equation for the turbulent kinetic energy (TKE); equation for the variance of a scalar; turbulent flows and the mixing length model; horizontal and vertical heat fluxes.
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 velocity.
6) ABL horizontally homogeneous on flat terrain: remarks; equations for mean velocity and mean temperature; internal and external scaling; definition of the surface layer (SL)
7) Quasi neutral ABL (QNBL): Richardson number, Obukhov length; neutral conditions in SL; mean velocity profiles, variances and dissipation rate of TKE; integral scales; the neutral Ekman layer; weakly stratified conditions; profiles of mean velocity and mean temperature; variances; coefficients of turbulent diffusion for momentum and heat.
8) The convective boundary layer (CBL): observations; the pdf of velocity; scales for velocity and temperature; profiles of mean velocity and mean temperature; moments of the second and third order, dissipation rate of TKE; a model for the horizontal heat flows; the potential temperature budget and height of 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 in stable conditions; SBL of long duration; other types of SBL; transfer of TKE from the top to down; local similarity theory: the model of Nieuwstadt (1984); profiles of mean variables within the SL; the critical Richardson number.
11) Similarity functions in the SL: non-dimensional gradients of mean variables; non-dimensional profiles; gradient and 'bulk' Richardson numbers.
12) The energy balance at the surface: radiative flux; Bowen ratio; heat flux in the soil; accumulation of heat in complex surfaces ( 'canopies').
13) The internal boundary layer (IBL): change of surface roughness for neutral flows; change of heat flux: the convective model.
14) Vegetative and urban canopies: observations and models for the mean velocity and second moments above the 'canopy', within the canopy and in street canyons.
15) Flow in complex topography: observations and analyses; morning and evening transitions.
16) Introduction to turbulent dispersion: the transport problem; pdf of the position of particles and mean concentration; the concept of absolute dispersion and 'meandering'.
17) The Brownian motion: a diffusion equation solution; absolute dispersion: Taylor (1921); field effects of non-uniform velocity; the problem of the gradient of mean velocity.
18) Ballistic phase in the logarithmic ABL: the ballistic phase in a turbulence field; inhomogeneous, relative dispersion, observations.
19) Atmospheric dispersion at large scale: dispersion in a neutral laboratory boundary layer dispersion in CBL; Mikkelsen et al. (1987): horizontal 'meandering' in the SL; dispersion in presence of topography.      

20) Dispersion models (1) the equivalence between the equations of Fokker-Planck (FP) and Langevin (L) N = 6: formulation of Thomson (1987) for the absolute dispersion; the 'well mixed condition' and the consistency with the inertial interval; derivation of the terms of the L equation; the solution for a Gaussian pdf.    

21) Dispersion Models (2) integration of L equation in case of one-dimensional flow; discussion of the non-Gaussian CASE; a different formulation of the model N = 3: the diffusive model; identification of terms; solutions of the diffusion equation.

22) Simple models for plumes and jets: point source with initial momentum; point source with buoyancy. 

23) Heavy particles: friction law (Stokes solution; Newton model): effects of gravity field;
Brownian diffusion; phoretic effects; turbulent dispersion characteristics; analysis of Csanady (1963); parameterization of the time scales.
24) Models for turbulent flows: closures for RANS equations; k-epsilon model; LES equations; Smagorinsky model (1963) for the closure; behavior in the inertial subrange

Readings/Bibliography

In addition to lecture nores made available at the beginning of the course on ALMA MATER website, the student may consult the following books:

- 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.

Teaching methods

Traditional in the classroom. All lectures are delivered as frontal teaching. The course includes a laboratory of numerical simulations applied to atmosheric boundary-layer processes and dispersion in urban environments.

Assessment methods

The exam is oral and its duration is typically one hour. Usually three main questions are asked one of which may be chosen by the student. During the exam it will also discussed the essay associated to the laboratory exercises.

Teaching tools

PC and slide projector; blackboard.

Office hours

See the website of Silvana Di Sabatino