Instabilities, transition to turbulence

Here we investigate flows dominated by rotation or shear effects. We use efficient cutting-edge numerical approaches to get a detailed characterization of such flows. We wish to gain some understanding on the way they destabilize in order to possibly elaborate control stategies. This concerns the dynamics of helical flows, also the subcritical transition to turbulence in wall shear flows, and chaotic advection. We also develop an experimental activity on a prototype flow, namely the flow above a rotating disk with free surface.


Helical flows

(I. Delbende)

Vortex system with 3 helical vortices (red) and a hub vortex (blue) simulated with the HELIX code (left: computational domain, middle: 3D representation). Dominant instability mode (right).
Vortex system with 3 helical vortices (red) and a hub vortex (blue) simulated with the HELIX code (left: computational domain, middle: 3D representation). Dominant instability mode (right).

The near wake of rotors involved in propulsion (ships, aircrafts, helicopters) or in energy production (wind and water turbines) is structured by helical tip and root vortices. Several instabilities have been evidenced experimentally in such systems, especially in Marseille. The HELIX code developped at LIMSI is able to simulate flows with a helical symmetry. It is thus possible to determine base flow states consisting of one or several viscous helical vortices and to characterize them. A linearized version of the code gives then access to their stability properties with respect to 2 types of perturbations: 1) perturbations with the same helical symmetry as the base flow, and 2) perturbations with an arbitrary wavelength, either larger or smaller than the helical pitch. In the first case, the modes generealize the inviscid Okulov modes to the viscous framework; in the nonlinear régime they lead to leapfrog dynamics and eventually to merging. These modes are present in wind turbine wakes. In the second case, the instabilities predicted by Widnall in helical vortices are generalized with the help of a dedicated numerical code HELIKZ. Other types of instabilities, namely elliptic instabilities are also investigated, as short wavelength modes are commonly observed in turbine wakes and play a role in their destruction. 


Subcritical transition to turbulence in wall flows

(Y. Duguet)

Transition from the (chaotic) localised edge state towards a turbulent slug regime in cylindrical pipe flow. Iso-axial vorticity perturbation in a meridian plane at Re=4500, periodic domain of length L=33.5D, time increasing downwards. (Ref: Duguet, Willis and Kerswell, JFM 663 (2010, JFM cover).

Transition to turbulence in the presence of a linearly stable laminar base flow (such as circular pipe flow, plane Couette flow, plane channels flow, boundary layer flows with or without wall suction) requires deeper theoretical understanding. The dynamics of coherent structures in the transitional regime is investigated in the light of the theory of dynamical systems using direct numerical simulations. The geometric structure of the associated phase space is investigated by identifying invariant solutions (fixed points, periodic orbits, basins of attraction). The physical mechanisms responsible for  the self-sustenance and the instability of such solutions are addressed.

The second approach developed at LIMSI in collaboration with KTH Stockholm (Sweden) and Universität Philipps Marburg (Germany) relies on a statistical description of the spatiotemporal dynamics of these same transitional flows. Close to the onset of turbulence, the flow usually features an alternation of laminar and turbulent patches, investigated using direct numerical simulations in spatially extended domains. Intermittent formation of localised turbulent patches in a boundar layer flow subject to incoming turbulence is investigated by large-eddy simulation. Quantitative results are modelled by techniques such as probabilistic cellular automata (PhD of T. Khapko, collaboration with KTH Stockholm).


Chaotic advection

(Y. Duguet)

The Lagrangian dynamics of passive tracers in incompressible flows is crucial for the prediction of the mixing properties in the high Schmidt number limit. The theoretical approach couples Hamiltonian theory with modern simulation techniques (spectral methods, bifurcation tools) and leads to predictions of the mixing rate and chaotic fraction. This approach has been tested for natural convection inside a differentially heated cavity (PhD of L. Oteski, funded by the Foundation Airbus Group).


Rotating disk flow with free surface

(L. Martin Witkowski)

The development of an experimental activity within the group has progressively been set up over recent years. Our main target is the study of first transitions to turbulence for flows in confined environments. The experiments are designed to be simple in their implementation. The study of a rotating disk in the presence of a free surface seems relevant in this context. The experiments are firstly those where the free surface is weakly deformed to supplement the studies already carried out numerically and experimentally at LIMSI and at IRPHE in Marseilles. These experiments are accompanied by linear stability studies as well as three-dimensional calculations. Then we study the regimes of large deformations of the free surface. These are situations where very little quantitative data (shape of the free surface, velocity field, stability thresholds) are available.


diskDetermination of the instability threshold in the flow generated by a rotating disk. A mode m = 4 appears at 7 rev / min, and a mode m = 3 becomes dominant for higher angular velocities (bottom right).

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100 Researchers
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