ENV 356 - Environmental Fluid Mechanics

General Information

• Instructor: Gabriel Katul
• Number of Credits: 3 Units
• Prerequisites: Working knowledge of partial differential equations, statistics, hydrology or some elementary fluid mechanics class.
• Workload: 5 Homework, 1 project, an inclass midterm and a final.

Topics

1. Introduction to fluid mechanics: fluid properties and the Continuum Theory (CT), introduction to turbulent flow.
2. Mathematical and conceptual tools: Statistical fluid mechanics, stationarity, homogeneity, isotropy, and the concept of ergodicity. Generalization to atmospheric flows are considered. Tensor notation and tensor algebra will be reviewed.
3. Application of mass and momentum conservation equations to turbulent flows: Brief development of the Navier-Stokes equations for incompressible fluids. Discussion on Eulerian and Lagrangian frame of references in fluid flow.
4. Eulerian prognostic equations for turbulent fluxes, variances, turbulent kinetic energy, and other flow statistics.
5. Statistical Tools: Introduction to autocorrelation, cross-correlation, structure function, spectra, co-spectra, and coherency and their applications to analyze turbulence measurements.
6. Monin and Obukhov Surface Layer Similarity Theory (MOST) and dimensional analysis for stratified fluids. Predictability of turbulent flow statistics from dimensional analysis.
7. Applications of MOST: estimation of CO2, water vapor, heat, and other passive admixtures fluxes from natural surfaces. Such applications are important in air pollution models, biosphere-atmosphere investigations, dispersion in rivers and estuaries, etc ....
8. Lagrangian models for air pollution. Brief introduction to stochastic calculus, quasi- markovian models for the Lagrangian acceleration term. Numerical simulations of contaminant dispersion from stacks (Project will deal with this topic).
9. The local structure of turbulence (if time permits): Kolmogorov's theory, energy-cascade and inertial subrange scaling. The use of Kolmogorov's theory to estimate turbulent production, dissipation, and surface fluxes are also discussed.
10. Field and laboratory measurements of turbulent flow variables: Field trips to the Duke Forest and the EPA Fluid Dynamics Modeling facility. Also, techniques developed in class will be applied to estimate momentum fluxes, CO2 fluxes, sensible heat fluxes, and latent heat fluxes for a "real-world" data set. The data used for this purpose will be provided within the second week of class.

References