Lecture-by-lecture log of topics covered (2012)

• Penman's combination equation for potential evapotranspiration (atmospheric demand) & the Penman-Monteith equation "big leaf" model for canopy evapotranspiration. Inverse dispersion using the MO-bLS method. (Thurs 29 Nov.)

• Determining surface-air fluxes within an ideal (undisturbed) surface layer. Symmetry assumption. Definition of flux footprint. Eddy covariance. WPL corrections (imposition of an idealized, height-invariant mean vertical velocity). Flux loss corrections (for sensor separation, pathlength etc.) based on a transfer function T(f) applied to an idealized co-spectral density function, e.g. for a scalar whose concentration is c the co-spectral density is S_wc(f). Example of a flux-gradient method for determining a vertical flux. Bowen ratio method for evapotranspiration. (Tues 27 Nov.)

• Disturbed micrometeorological flows. Shelter flows. (Thurs 22 Nov.)

• Disturbed micrometeorological flows. Local advection. (Tues 20 Nov.)

• Video of particle trajectories computed by LS model to simulate Oklahoma City tracer experiment (lower view)

• Continuation -- LS model for turbulent dispersion. eas572_dispersion_B.pdf, eas572_urbanLS.pdf (Thurs 15 Nov.)

• Thomson's 2-D LS model for horizontally-homogeneous Gaussian turbulence. Flesch-Wilson model for canopy dispersion. Well-mixed 1D LS model for the CBL.(Thurs 8 Nov.)

• Thomson's (1987) well-mixed condition for Lagrangian stochastic (LS) models. The unique 1-D LS model for Gaussian inhomogeneous turbulence; supplying velocity statistics (including TKE dissipation rate epsilon) for its application to surface layer dispersion. The "diffusion limit," and criteria for the Kolmogorov coefficient C₀ in the ASL. (Thurs 8 Nov.)

• Taylor's results for the r.m.s. displacement in the near and far fields of a source. Zeroth-order Lagrangian stochastic (LS) model (position assumed Markovian). Langevin equation (velocity and position jointly Markovian) - example of a first-order LS model. Generalized Langevin equation in 1D and 3D, and the corresponding Fokker-Planck equation for the joint density for (1D) position and velocity, p(z,w,t|release conditions). (Tues 6 Nov.)

• Particle displacement transition density function and the relationship between source density and mean concentration. G.I. Taylor's theory of dispersion in homogeneous turbulence. (Thurs 1 Nov.)

• Go over short answer questions B, C of midterm exam. Some background on Project Prairie Grass. More-realistic K-solutions for surface layer dispersion (height-dependent wind speed and diffusivity). Lagrangian similarity theory. eas572_dispersion.pdf (Tues 30 Oct.)

• Midterm exam (Thurs 25 Oct.)

• Turbulent Dispersion. Relative and absolute dispersion. Eulerian approach. Constant-K solutions. Instantaneous point source in unbounded space (Gaussian puff). Parabolic (t^1/2) growth. Analogy with drunkard's walk in one dimension. Adding or subtracting an image source (diffusion in the half-space). Crosswind-integrated concentration. (Tues 23 Oct.)

• Two further examples of dimensional analysis (highway collision rate; mean wind speed at the top of a canopy). Using an "integrated horizontal flux" method to estimate the rate of injection of dust into the atmosphere by a road. Canopy flow (continued): background on PDFs, standardized varaibles, the Gaussian PDF, skew velocity PDFs in a canopy; wake production of TKE in a canopy; the TKE budget (not in local equilibrium); observed counter-gradient mean vertical fluxes in Urriarra forest. (Thurs 18 Oct.)

• Mid-term exam will be based on material prior to the lectures on canopy flow

• Feedback on assignment 1. Review of the salient characteristics of flow in the inertial sublayer, incl. mean profiles of wind speed and potential temperature, and profiles of heat flux and shear stress. Contrasting characteristics of the flow in plant canopies. Intermittency of flow. Ramps, microfronts. Gusts, ejections, quadrant analysis. (Tues 16 Oct.)

• Conceptions of, and models of, the nocturnal boundary layer (SBL). Flow in plant canopies; qualitative profiles of mean wind speed and shear stress; the U-momentum equation in differential (point) and discrete (layer) form, i.e. balance of shear stress divergence and drag on plant parts; the philosophical requirement to introduce a spatial average; dispersive fluxes/stresses. (Thurs 11 Oct.)

• Rate eqn. for ABL depth. Heirarchy of first order (eddy viscosity) closure models (a section covering this has been added to the course booklet). (Tues 9 Oct.)

• Large -z/L limit of MO scaling (local free convection scaling). Above the surface layer -- the outer ABL. (Thurs 4 Oct.)

• Intro. to turbulence spectra; wavenumber vs. frequency spectrum (transformation of the spectral density); Kolmogorov's proposition that in the "inertial subrange of scales" the spectral density depends only on TKE dissiption rate, leading to the "minus five thirds law"; Kaimal's idealized spectral curves for the convective ABL; the spectral peak at low frequency in the u- and v- spectra signifies the large, slow, quasi-horizontal "inactive eddies"; MO scaling for variance of w. (Tues 2 Oct).

• Monin-Obukhov similarity theory (MOST): interpretation of the Obukhov length; suggested forms for the universal functions for mean wind speed and temperature; mean wind and temperature profiles; eddy diffusivities; relationship between gradient Richardson number and z/L. Images relating to the hh_ASL (horiz. homog. atmospheric surface layer). (Thurs 27 Sept.)

• Budget equations for the sensible heat and for the vertical (sensible) heat flux density, in a "hh_ABL" (horiz. homog. ABL). Three types of terms in the transport equations: storage terms, transport terms, source terms. Concept of constant flux layer justified on basis of estimated rate of change of heat flux with height (for typical rate of temperature change). Order of magnitude of the (summer, fairweather, afternoon) sensible heat flux Q_H (constrained by the surface energy budget). Budgets for the (u,v,w) velocity variances and for the TKE in the hh_ABL. Redistribution of turbulent kinetic energy between the three components. Concept of local equilibrium. Flux Richardson number. Shear stress budget in hh_ABL, and the implications for the generality of the eddy viscosity model. The postulates of Monin-Obukhov similarity theory - which is intended to apply in the inertial sublayer of the hh_ASL (ideal constant flux layer). The Obukhov length. The MO result for the dimensionless mean wind shear function, and the implied mean wind profile in neutral (|L|=infinity) and stable (L>0) stratification. (Tues 25 Sept.)

• Reynolds-averaging the water vapour conservation equation. Mechanism of the humidity/vert. veloc covariance. Vertical profiles of the humidity flux across a horiz. homog. ABL. Relationship between the vapour flux and the latent heat flux (QE). The surface energy budget, Q*=QH+QE+QG. The Reynolds equations for mean velocity. The Reynolds stress tensor. Mechanism explaining the u'-w' covariance. The streamwise momentum budget in a horiz. homog. ABL -- role of the Reynolds stress divergence ("friction"), and the Geostophic momentum budget in the free troposphere. Vertical profile of the Reynolds stress across the ABL. The concept of a "constant stress layer." Heuristic derivation of the log profile for mean wind in the constant stress layer. Definition and importance of the friction velocity. (Thurs 20 Sept.)

• Conservation equation for mass of "air" -- the continuity equation (in flux form and in advection form). Non-divergent/incompressible flow. Cauchy's equation of motion. Stress-strain relationship for a Newtonian fluid. The Navier-Stokes equations. Boussinesq (or "shallow water") approximation. Salient qualitative characteristics of "turbulence". Committment to a "statistical" approach. Reynolds averaging. The (vertical, convective) eddy flux of (sensible) heat.(Tues 18 Sept.)

• Molecular flux-gradient laws (Newton, Fourier, Fick). Tensor notation. Surface and body forces. Continuum approximation. Relationship of the molecular stress tensor to the velocity gradient tensor (generalization -- or symmetrization -- of Newton's law). Lagrangian derivative. Advection. Derivation of a generalized conservation equation. Conservation equation for water vapour. (Thurs 13 Sept.)

• Illustrate method of indices. Meaning of "complete similarity" of systems; example, flow about a cylinder. (Tues 11 Sept.)

• Sublayers of the ABL. Potential temperature. Buckingham Pi theorem. Dimensional analysis of pendulum. (Thurs 6 Sept.)

Last Modified: 30 Nov., 2012