Projects
Rotating turbulent flows
Rotating turbulent flows are ubiquitous in geophysics, astrophysics and engineering. Consider, for example, flows in the oceans, in the atmosphere or in turbomachinery. Understanding and being able to predict the behavior of such flows is of great importance for many applications. However, despite the increased fundamental understanding, predicting rotating turbulent flows remains a challenge. This is mainly because such flows often contain a large range of scales of motion, which cannot be resolved using direct numerical simulations. With the aim to improve the numerical prediction of incompressible rotating turbulent flows, we, therefore, turn to largeeddy simulation.
In largeeddy simulation, the large scales of motion in a flow are explicitly computed, whereas the effects of the smallscale motions are modeled using subgridscale models. Eddy viscosity models are commonly used subgridscale models. These subgridscale models prescribe the net dissipation of kinetic energy caused by smallscale turbulent motions. Although eddy viscosity models are effective in many cases, they have an important drawback. They model turbulence as an essentially dissipative process. Given the importance of energy transfer in rotating turbulent flows, it seems unlikely that eddy viscosity models are always suitable for largeeddy simulations of such flows.
In this project, we, therefore, propose a new subgridscale model for largeeddy simulations of incompressible rotating turbulent flows. This subgridscale model consists of a dissipative eddy viscosity term as well as a nondissipative term that is nonlinear in the rateofstrain and rateofrotation tensors. We study and validate this subgridscale model using detailed direct numerical and largeeddy simulations of two canonical rotating turbulent flows, namely, rotating decaying turbulence and spanwiserotating planechannel flow. We also provide a comparison with the commonly used dynamic Smagorinsky model, the scaled anisotropic minimumdissipation model and the vortexstretchingbased eddy viscosity model.
Selected publications

Silvis, M. H., Bae, H. J., Trias, F. X., Abkar, M., Verstappen, R. (2019). “A nonlinear subgridscale model for largeeddy simulations of rotating turbulent flows”. arXiv: 1904.12748 [physics.fludyn]. Abstract PDF BibTeX BibLaTeX Cited by 2+

Silvis, M. H., Verstappen, R. (2019). “Nonlinear SubgridScale Models for LargeEddy Simulation of Rotating Turbulent Flows”. In: Direct and LargeEddy Simulation XI. Ed. by Salvetti, M. V., Armenio, V., Fröhlich, J., Geurts, B. J., Kuerten, H. Springer International Publishing, pp. 129–134. DOI: 10.1007/9783030049157_18. Abstract PDF BibTeX BibLaTeX Cited by 5+

Silvis, M. H., Trias, F. X., Abkar, M., Bae, H. J., LozanoDurán, A., Verstappen, R. W. C. P. (2016). “Exploring nonlinear subgridscale models and new characteristic length scales for largeeddy simulation”. In: Studying Turbulence Using Numerical Simulation Databases  XVI: Proceedings of the 2016 Summer Program. Ed. by Moin, P., Urzay, J. Center for Turbulence Research, Stanford University, pp. 265–274. Abstract PDF BibTeX BibLaTeX Cited by 12+
Physicsbased turbulence models
The Navier–Stokes equations form a very accurate mathematical model for turbulent flows. The behavior of most turbulent flows can, however, not (yet) directly be predicted using these equations, because the current computational power does not suffice to resolve all physically relevant scales of motion in such flows. We, therefore, turn to largeeddy simulation to predict the largescale behavior of incompressible turbulent flows. In largeeddy simulation, the large scales of motion in a flow are explicitly computed, whereas effects of smallscale motions have to be modeled. Here, the question is: how to model these effects? Moreover, one can wonder: what defines a welldesigned subgridscale model?
In this project, we aim to answer these questions by following a systematic approach, based on the idea that subgridscale models should respect the fundamental physical and mathematical properties of the Navier–Stokes equations and the turbulent stresses. We thereby obtain a framework of constraints for the construction of physicsbased subgridscale models. We apply this framework to a general class of subgridscale models based on the local velocity gradient. We also analyze the properties of a number of existing models from this class. Finally, we illustrate how new physicsbased subgridscale models with desired builtin properties can be created.
Selected publications

Silvis, M. H., Remmerswaal, R. A., Verstappen, R. (2017). “Physical consistency of subgridscale models for largeeddy simulation of incompressible turbulent flows”. Physics of Fluids 29, 015105. DOI: 10.1063/1.4974093. Abstract PDF BibTeX BibLaTeX Cited by 34+

Silvis, M. H., Remmerswaal, R. A., Verstappen, R. (2017). “A Framework for the Assessment and Creation of SubgridScale Models for LargeEddy Simulation”. In: Progress in Turbulence VII: Proceedings of the iTi Conference in Turbulence 2016. Ed. by Örlü, R., Talamelli, A., Oberlack, M., Peinke, J. Springer International Publishing, pp. 133–139. DOI: 10.1007/9783319579344_19. Abstract PDF BibTeX BibLaTeX Cited by 2+

Silvis, M. H., Verstappen, R. (2018). “Constructing Physically Consistent SubgridScale Models for LargeEddy Simulation of Incompressible Turbulent Flows”. In: Turbulence and Interactions: Proceedings of the TI 2015 Conference. Ed. by Deville, M. O., Couaillier, V., Estivalezes, J.L., Gleize, V., Lê, T.H., Terracol, M., Vincent, S. Springer International Publishing, pp. 241–247. DOI: 10.1007/9783319603872_26. Abstract PDF BibTeX BibLaTeX Cited by 3+

Silvis, M. H., Verstappen, R. (2015). “Physicallyconsistent subgridscale models for largeeddy simulation of incompressible turbulent flows”. arXiv: 1510.07881 [physics.fludyn]. Abstract PDF BibTeX BibLaTeX Cited by 4+