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Turbulence in environmental flows

Lecturers:  Michael Dumbser (UNITN/DICAM); Luigi Fraccarollo (UNITN/DICAM); Lorenzo Giovannini (UNITN/DICAM); Sebastiano Piccolroaz (UNITN/DICAM); Marco Toffolon (UNITN/DICAM); Nadia Vendrame (UNITN/DICAM); Dino Zardi (UNITN/DICAM)

Timetable: end of May - beginning of June 2023

Schedule: see the link to the course here

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.


- Introduction (Prof. D. Zardi)

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 (Prof. M. Dumbser)

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 (Dr. N. 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 (Prof. L. Giovannini)

This module will first provide an introduction to the atmospheric boundary layer, including the 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 (Prof. M. 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 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 (Dr. S. Piccolroaz)

This module will build on the introduction provided by the previous one to deepen the experimental point of view. The lectures will be focused 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 (Prof. L. 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.

Duration: 60 hours (6 credits)

Registration: in order to register for the course, please send an email to dicamphd [at]