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Master internship & PhD on Space-time analysis for atmospheric data over North Atlantic, M2C laboratory, Rouen (France)

Du 1 février 2022 au 31 juillet 2024

Spring-Summer 2022
Site actualite
M2C Laboratory, Rouen (France)
Contacts :
L. Danaila,
N. Massei,


The aim of the internship will be to analyze data, compute space-time statistics, and answer questions pertaining to the underlying physics, such as the link between large and small-scale statistics at different ages of the flow.

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MASTER 2 Internship
Space-time analysis for atmospheric data over North Atlantic


Many natural processes and phenomena on Earth (such as sea waves, surges, precipitation and storms, floods, droughts, etc.) are closely linked to, and to some extent partially driven by variability of large-scale turbulent oceanic and atmospheric processes across time-scales. These processes can also be affected by periodicity at some scales (annual cycle, pseudo-periodic oscillations). Such variability eventually becomes more or less directly imprinted in a variety of natural processes as mentioned above.

Progress in rapidly expanding exploration of planetary atmospheric and oceanic environments demands an adequate qualitative and quantitative representation of various processes in anisotropic turbulence. The existing analytical theories are developed for homogeneous, isotropic flows. They quickly become very complicated when expanded to anisotropic flows with waves. Planetary circulations feature huge Reynolds numbers and are turbulent on almost all scales. In addition, the action of density stratification, rotation, streamline curvature, geometric confinement, magnetic fields, etc. renders these circulations anisotropic.

A systematic description of turbulence behavior in response to the impact exerted by extra strains is one of the important outstanding problems of fluid dynamics. Addressing this problem runs into difficulties already at the outset because proliferation of dimensional variables hinders the application of the dimensional analysis. Direct numerical simulations (DNS) are limited by the value of the resolvable Reynolds number even in relatively simple cases of channel flows. Linear and nonlinear theories of anisotropic turbulence have been developed (Cambon & Sagaut, 2019). However, clear understanding of the statistical behavior of such flows proved to be evasive. Further progress relies upon the development of self-consistent basic theories that make verifiable predictions suitable for testing against a large variety of data.


The aim of the internship will be to analyze data, compute space-time statistics, and answer questions pertaining to the underlying physics, such as the link between large and small-scale statistics at different ages of the flow. These large- scale might be of different kinds: stationary and stable (shear, stratification etc.), or time modulated (characterized by a quasi-periodic motion in space/time). An example of such flow is provided in Fig. 1, for time-averaged zonal flow in the atmosphere (at 500 mb), in comparison with an instantaneous velocity field (Fig.1, b). The case of large scales modulated in time is complex, but can be treated by extending the method developed in Thiesset & Danaila, 2020 for the simpler case of turbulence behind a cylinder with a large-scale Von Kármán street.

The following analysis will apply for different turbulent fields: sea-surface temperature (SST), atmospheric-ocean variables (i.e. velocity field, temperature, humidity, precipitations etc.), under variable density and viscosity conditions. Data will originate from one of the following sources: or Copernicus data (equivalent to ERA5 data). The latter concern mainly atmospheric data. Moreover, WRF simulations might be a source of data.

Methodology. Available data will be:

  1. i)  Filtered at a scale (through wavelets, increments, e.g. Massei et al. 2017);

  2. ii)  Scale-by-scale statistics will be computed at several orders: second-order (corresponding to spectra, or energy

    at a scale), third-order (reflecting energy fluxes at each scale) and higher-order statistics (fourth-order), e.g.

    Danaila et al., 2017, as a diagnostic of rare fluctuations, extreme events.

  3. iii)  Physical meaning of these statistics in terms of extreme events will be unraveled.

Required aptitudes. The candidate must possess basic skills such as: fluid mechanics, turbulence, data treatment. Bibliography

  1. Danaila L., Voivenel L., Varea E., 2017, Physics of Fluids, Vol.29, Issue 2, 020705, DOI: 10.1063/1.4974520.

  2. Galperin B., S. Sukoriansky, R. M. B. Young, R. Chemke, Y. Kaspi, P. L. Read, and N. Dikovskaya, in Zonal Jets:

    Phenomenology, Genesis, and Physics, edited by B. Galperin and P. L. Read (Cambridge University Press, 2019) pp.


  3. Galperin B. and Sukoriansky, Phys. Rev. Fluids, Vol. 5, issue 6, p. 063803, 2020.

  4. Ghil M., Groth A., Kondrashov D., Robertson A.W., Elsevier Inc., 2018.

  5. Kamenkovich I., Berloff P. and Pedlosky J., Journal of Physical Oceanography, Vol. 32, p. 1361, 2009.

  6. Chun et al. (2021) Drought variability driven by interannual and decadal teleconnection patterns in monsoon regions of

    Southeast China. In EGU General Assembly Conference Abstracts (pp. EGU21-9365).

  7. Massei N., Dieppois B., Hannah D.M, Lavers D.A., Fossa M., Laignel B., Debret M., J. of Hydrology, 546, 262-275,


  8. Sagaut P. and Cambon C., ‘Homogeneous turbulence dynamics’, Springer, 2018.

  9. Thiesset F. and Danaila L. 2020, J. Fluid Mech., Vol. 902,

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Spring/Summer 2022- for 6 months

Contacts :

L. Danaila,
N. Massei,
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The mastership will take benefit from our ongoing collaboration with Dr. K.P. Chun, The University of West England, Bristol, U.K., through weekly discussions and ‘work hard’ encouragements.