Period: three weeks, 24 February to 14 March 2025 (three weeks)

Venue: onsite at DICAM, via Mesiano 77, 38123 Trento, Italy + online (Zoom)

Teaching language: English

Duration: 60 hours, including hands-on tutorials

Credits: 6 ECTS for MSc students (3 for UniTrento PhD students)

Participation fees: 216 € (how to enrol and other info)

Deadline for registration: 19th January 2025

Info: lorenzo.giovannini@unitn.it 

Detailed program

Introduction (8 hours) – prof. Massimo Cassiani

The main properties of turbulence will be outlined, along with phenomenological evidence and conceptual bases. A statistical analysis of turbulence will be presented, in particular Reynolds averaging approach. Turbulent kinetic energy (TKE) will be introduced along with its governing equation.

Numerical methods for turbulent flows (10 hours) – dr. Firas Dhaouadi

Semi-implicit finite volume and finite difference schemes on staggered meshes will be presented for the solution of the unsteady incompressible Reynolds-Averaged Navier-Stokes (RANS) equations, including a new provably positivity preserving (realizable) discretization of the k-ε turbulence model. A low Reynolds number version of the k-ε turbulence model needed to simulate turbulent boundary layers near the wall will be discussed. A discussion about direct numerical simulations (DNS) of the laminar-turbulent flow transition will follow. The numerical part contains extensive practical hands-on sessions at the computer.

Eddy covariance method (6 hours) – dr. Nadia Vendrame

The eddy covariance technique is a micrometeorological method for directly measuring turbulent exchanges of energy and mass between a surface and the atmosphere. The lectures will give an overview of the method, covering the theoretical framework, instrumentation setup, and a practical exercise of data processing to calculate fluxes.

Turbulence in the atmosphere (10 hours) – prof. Lorenzo Giovannini

This module will first provide an introduction to the atmospheric boundary layer, including a description of turbulence and its effects on mixing processes. Then the lectures will focus on state-of-the-art approaches used in numerical weather prediction models to parameterize turbulent processes taking place at the sub-grid scale in the atmospheric boundary layer. Practical examples will be provided considering the most used turbulence parameterizations implemented in the Weather Research and Forecasting (WRF) model. This module will be completed by a practical hands-on session at the computer using MATLAB.

Turbulence in lakes and stratified flows (10 hours) – prof. Marco Toffolon

This module will provide an overview of lake dynamics (e.g., stratification, layering, internal waves) and turbulence in stratified flows, combining theoretical and empirical observations. The development of Kelvin-Helmholtz instability across density interfaces will be discussed, together with some empirical formulas to estimate the inhibition of vertical turbulent fluxes in stratified flows depending on the Richardson number. The analysis of the most relevant terms in the TKE equation for stratified flows will be deepened.

Measuring turbulence in lakes and oceans (10 hours) – dr. Sebastiano Piccolroaz

This module will build on the introduction provided by the previous one to deepen the experimental point of view. The lectures will concentrate on the spectral analysis of turbulence time series, with a particular focus on the processing of microstructure profiles acquired in stratified flows (i.e., spectra of velocity shear and temperature gradient). This module will be completed by a practical component aimed at processing observed microstructure profiles to determine TKE dissipation rates and turbulent diffusivity, by implementing the proposed operational procedures.

Turbulence in multiphase flows (6 hours) – prof. Luigi Fraccarollo

The role of the solid phase in the generation of resistant tangential stresses in free surface flows with intense solid transport will be explained. The kinetic theory of gases offers the theoretical tool useful for the interpretation of the flow field through a continuous Eulerian model.

Contents

The course will offer an introduction to turbulence as it is found in environmental flows (including atmosphere, oceans, lakes, and rivers). The approach will couple the analysis of the most used numerical models (e.g., k-ε model) and the interpretation of real-world measurements, with a special focus on processes occurring in the atmosphere and in stratified water bodies such as lakes.

Students will learn the basics concepts of turbulence theory, of the main observational techniques and of the methods of analysis of data from turbulence measurements, as well as numerical methods for turbulence modelling.

Entrance requirements

Basics of calculus and numerical methods, physics, fluid mechanics and atmospheric physics.

Exam

Students that aim at obtaining the full course's credits need to submit two reports (one on a numerical exercise and one on the analysis of experimental data) on topics tackled during the course. The topics are to be chosen from this list (acronyms refer to instructors):

• numerical: FD, LG, MT

• experimental: NV, SP, LF

The exam has be taken by the end of July 2025. Students requiring an extension of the deadline must request for it.

Main references

- Stull C. D., An introduction to boundary layer meteorology, Springer, Dordrecht, The Netherlands, 1988.

- Tennekes, H. M and J. L. Lumley, 1975: A First Course in Turbulence. MIT Press.

- Panofsky, H. A., and J.A. Dutton, 1984: Atmospheric - Turbulence: Models and Methods for Engineering Applications. John Wiley & Sons.

- Wyngaard, J. C., 2011: Turbulence in the Atmosphere. Pennsylvania State University.

- Kaimal, J. C., and J. J. Finnigan, 1994: Atmospheric boundary layer flows—their structure and measurement. Oxford University Press.

- Imboden, D.M., Wüest, A., 1995, Mixing Mechanisms in Lakes, in: Lerman, A., Imboden, D.M., Gat, J.R. (eds.), Physics and Chemistry of Lakes, Springer Verlag.

- Wüest, A., Lorke, A., 2003, Small Scale Hydrodynamics in Lakes , Annual Review of Fluid Mechanics, 35, 373-412. doi:10.1146/annurev.fluid.35.101101.161220.