Stochastic Modelling and Simulation of Atmospheric Boundary Layer Processes Dr. rer. nat. Marten Klein

The Division of Stochastic Modelling and Simulation of Atmospheric Boundary Layer Processes investigates small-scale turbulence effects in the planetary boundary layer and its coupling to the large-scale dynamics.

Current research activities are focusing on the mass, momentum, and heat transport in shear flows, rotating and stratified boundary layers, as well as free and forced convection. We strive to numerically capture fundamental statistical properties of theses flows by physics-based modelling approaches.

Numerical challenges with respect to atmospheric flows arise due to the presence of

  • turbulence,
  • multiscale dynamics,
  • scale interactions and intermittency, as well as
  • multiphysics  phenomena.

Idealization and model reduction is used to focus on certain dynamical properties. But even then it is often not feasible to resolve the flow on all relevant scales so that turbulence modelling is required.

Turbulence models should be numerically efficient but, in order to possess predictive capabilities, they should as well obey some fundamental physical principles. These requirements are addressed by stochastic turbulence models. Some of these models are further developed by the group and are being applied to various flows that are related to atmospheric boundary layers.

Furthermore, also direct numericalsimulation (DNS) and large-eddy simulation (LES) are utilized, for example, to obtain reference solutions for parameter ranges that are accessible to both conventional and stochastic simulation approaches.



M. Sc. Sreenivasa Chary Thatikonda

B. Sc. Thierry Tchouto

B. Sc. Sascha Zell

B. Sc. Roland E. Maier

M. Sc. Christian Zenker

Relevant publications


  • M. Klein, H. Schmidt, and D. O. Lignell. Stochastic modeling of surface scalar-flux fluctuations in turbulent channel flow using one-dimensional turbulence. Int. J. Heat Fluid Flow, 93:108889, 2022. DOI: 10.1016/j.ijheatfluidflow.2021.108889. Preprint: arXiv:2111.15359


  • M. Klein, and H. Schmidt. Stochastic modeling of passive scalars in turbulent channel flows: predictive capabilities of one-dimensional turbulence. In: A. Dillmann, G. Heller, E. Krämer, C. Wagner (Eds.), New Results in Numerical and Experimental Fluid Mechanics XIII, volume 151 of Notes on Numerical Fluid Mechanics and Multidisciplinary Design, Springer Nature, Cham, 2021, pp. 47–57. STAB/DGLR Symposium 2020. URL: doi:10.1007/978-3-030-79561-0_5. Preprint: arXiv:2011.04818
  • M. Klein, and H. Schmidt. Investigating Schmidt number effects in turbulent electroconvection using one-dimensional turbulence. Proc. Appl. Math. Mech., 21:e202100147, 2021. DOI: 10.1002/pamm.202100147
  • M. Klein, Roland E. Maier, and H. Schmidt. Stochastic modeling of transient neutral and stably-stratified Ekman boundary layers. Proc. Appl. Math. Mech., 21:e202100146, 2021. DOI: 10.1002/pamm.202100146
  • S. Sharma, M. Klein, and H. Schmidt. Modelling turbulent jets at high-Reynolds number using one-dimensional turbulence. AIAA 2021-2104. AIAA AVIATION 2021 FORUM. August 2021. URL:
  • M. Klein, C. Zenker, K. Hertha, and H. Schmidt. Modeling one and two passive scalar mixing in turbulent jets using one-dimensional turbulence. In: WCCM-ECCOMAS 2020, published online, 2021. URL:
  • H. Schmidt, J. A. Medina Méndez, and M. Klein. EHD Turbulence in channel flows with inhomogeneous electrical fields: a one-dimensional turbulence study. In: WCCM-ECCOMAS 2020, published online, 2021. URL:
  • J. A. Medina Méndez, M. Klein, and H. Schmidt. The one-dimensional turbulence aspects of internal forced convective flows. In: WCCM-ECCOMAS 2020, published online, 2021. URL:


  • M. V. Kurgansky, T. Seelig, M. Klein, A. Will, and U. Harlander. Mean flow generation due to longitudinal librations of sidewalls of a rotating annulus. Geophys. Astro. Fluid Dyn.114(6), 742–762, 2020. DOI: 10.1080/03091929.2019.1692829
  • M. Klein, and H. Schmidt. Towards a stochastic model for electrohydrodynamic turbulence with application to electrolytes. Proc. Appl. Math. Mech., 20:e202000128, 2020. DOI: 10.1002/pamm.202000128
  • M. Klein, and H. Schmidt. A stochastic modeling strategy for intermittently unstable Ekman boundary layers. Proc. Appl. Math. Mech., 20:e202000127, 2020. DOI: 10.1002/pamm.202000127


  • M. Vincze, N. Fenyvesi, M. Klein, J. Sommeria, S. Viboud, and Y. Ashkenazy. Evidence for wind-induced Ekman layer resonance based on rotating tank experiments. EPL, 125:44001, 2019.
  • Rakhi, M. Klein, J. A. Medina M., and H. Schmidt. One-dimensional turbulence modeling of incompressible temporally developing turbulent boundary layers with comparison to DNS. J. Turbul., 20(8):506–543, 2019.
  • M. Klein, C. Zenker, and H. Schmidt. Small-scale resolving simulations of the turbulent mixing in confined planar jets using one-dimensional turbulence. Chem. Eng. Sci., 204:186–202, 2019.
  • M. Klein, and H. Schmidt. Investigating Rayleigh–Bénard convection at low Prandtl numbers using one-dimensional turbulence modeling. In: 11th Int. Symp. Turb. Shear Flow Phen. (TSFP11), 1:1–6, 2019.


  • A. Ghasemi, M. Klein, A. Will, and U. Harlander. Mean flow generation by an intermittently unstable boundary layer over a sloping wall. J. Fluid Mech., 853:111–149, 2018.
  • D. O. Lignell, V. Lansinger, J. Medina, M. Klein, A. R. Kerstein, H. Schmidt, M. Fistler, and M. Oevermann. One-dimensional turbulence modeling for cylindrical and spherical flows: model formulation and application. Theo. Comp. Fluid Dyn., 32(4):495–520, 2018.
  • M. Klein, H. Schmidt, and D. O. Lignell. Map-based modeling of high-Rayleigh-number turbulent convection in planar and spherical confinements. In: Conf. Model. Fluid Flow (CMFF’18), J. Vad (Ed.), 2018. ISBN: 978-963313297-5
  • M. Klein, and H. Schmidt. Investigating the Reynolds number dependency of the scalar transfer to a wall using a stochastic turbulence model. Proc. Appl. Math. Mech., 18:e201800238, 2018.


  • M. Klein, and H. Schmidt. Stochastic modeling of passive scalar transport in turbulent channel flows at high Schmidt numbers.In: 10th Int. Symp. Turb. Shear Flow Phen. (TSFP10), 1:1B-2, 2017.
  • M. Klein, and H. Schmidt. Stochastic modeling of passive scalar transport at very high Schmidt numbers. Proc. Appl. Math. Mech., 17(1):639–640, 2017.


  • M. Klein (2016). Inertial wave attractors, resonances, and wave excitation by libration: direct numerical simulations and theory. Ph.D. thesis. Faculty 2, Brandenburg University of Technology Cottbus-Senftenberg, Cottbus, Germany. Published online. URN:
  • A. Ghasemi, M. Klein, U. Harlander, E. Schaller, and A. Will. Mean flow generation by Görtler vortices in a rotating annulus with librating side-walls. Phys. Fluids, 28(5):055603, 2016.


  • M. Klein, T. Seelig, M. V. Kurgansky, A. Ghasemi, I. D. Borcia, A. Will, E. Schaller, C. Egbers, and U. Harlander. Inertial wave excitation and focusing in a liquid bounded bounded by a frustum and a cylinder. J. Fluid Mech., 751:255–297, 2014.

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