Turbulence in space plasmas (graduate course)

Turbulence in the expanding solar wind

General description

Time: 2022, August 22 - October 31

Credit points: 5 ECTS (Parts 1-2 only: 2.5 ECTS)

Prerequisites: basic course on plasma physics

Responsible department: Department of Physics and Astronomy, Uppsala University

Objectives: This course covers the theory, modeling and data analysis techniques of magnetohydrodynamic turbulence in space plasmas.

Learning Outcomes:

On completion of Part 1-2 of the course the student should:

1. Have a basic understanding of the general approach to turbulence in fluids and plasmas, including phenomenology and exact relations.

2. Handle basic models for the description of plasma turbulence.

3. Be able to select appropriate data intervals, use basic statistical analysis tools and assess their limitations and uncertainty.

On completion of Part 3-4 of the course the student should:

4. Be able to use advanced statistical analysis tools, model the observations and obtain relevant parameters to quantify turbulence and intermittency.

5. Be able to critically and comparatively describe the properties of turbulence of a specific sample.

6. Recognize the problem of dissipation, heating and particle energization in collisionless space plasma turbulence.

Evaluation: Students will be assigned data analysis projects to describe the properties of turbulence in experimental data or atmospheric/spacecraft measurements. They will prepare a final report including a description of the analysis and the interpretation in terms of models of turbulence. Optional active participation and tests during the course may replace part of the examination. Alternative forms of evaluation may be arranged in case of special needs. For students not completing parts 3-4, optional evaluation will be given at the end of part 2.

Suggested Literature: In addition to lecture notes, the course will be based on the following material:

1. Book: Frisch, Uriel, 1995, Turbulence: the legacy of A. N. Kolmogorov, Cambridge, UK: Cambridge University Press, 1995.

2. Book: Biskamp, Dieter, 2003, Magnetohydrodynamic turbulence, Cambridge, UK: Cambridge University Press, 2003.

3. Review article: Bruno, Roberto, and Carbone, Vincenzo, 2013: The Solar Wind as a Turbulence Laboratory, Living Reviews in Solar Physics 10, 2, 2013.

Teachers: Luca Sorriso-Valvo, Emiliya Yordanova.

Registration: Please email the teachers.


Part 1 - Theoretical framework: Kolmogorov phenomenology and intermittency

1. General introduction to fluid and magnetohydrodynamic homogeneous, isotropic, fully developed turbulence. Reynolds number.

2. Scale invariance of ideal Navier-Stokes and MHD equations: self-similarity and power laws in turbulence.

3. Representation of Navier-Stokes and MHD equations in the Fourier space: nonlinear interactions between wave vectors.

4. Phenomenology of turbulence: Kolmogorov hypotheses for fluids; Kolmogorov spectrum; Richardson’s cascade.

5. Model for Alfvénic MHD turbulence and Kraichnan spectrum; dynamic alignment.

6. Typical scales of turbulence: injection scale, Taylor microscale, dissipative scale.

7. Inhomogeneous dissipation: intermittency, scale-dependent statistics and loss of self-similarity; modified Richardson cascade.

Part 2 - Basic data analysis tools and modeling: global and local properties

1. Stationarity, homogeneity, ergodicity and the Taylor hypothesis.

2. Autocorrelation function and power spectral density.

3. Typical scales and Reynolds number estimates.

4. PDFs, structure functions, skewness, kurtosis; limitations and caveats.

5. Intermittent structures: PVI and LIM.

6. Statistical properties of intermittent structures: waiting times distributions, conditional statistical analysis.

Part 3 - Models for intermittent turbulence and exact laws

1. Standard phenomenological models for intermittency: log-normal, multifractal, She-Leveque, p-model, Castaing.

2. Third-order moment exact relations for fluids and plasmas: energy transfer rate.

3. The Politano-Pouquet law: global and local energy transfer rate in solar wind plasmas.

Part 4 - Observations of turbulence in space plasmas

1. Multi-scale turbulence and intermittency in space plasmas: 1/f range, ion-kinetic range, electron-kinetic range.

2. Anisotropy of solar wind turbulence.

3. Solar wind variability: fast/slow, Alfvénic, radial evolution.

4. Turbulence in the terrestrial magnetosheath.

5. Kinetic scale phenomenological models for turbulence.

6. Notes on particle energization in collisionless, turbulent space plasmas.

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last modified on Friday, 15-Jul-2022 10:59:03 CEST