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We report experiments conducted in Taylor—Couette and plane Couette flows considering both the transition from laminar to turbulent flow and the reverse transition from turbulent to laminar flow. In the first case, the transition is discontinuous and is characterized by laminar-turbulent coexistence. The transition is controlled by the existence of finite amplitude solutions. In the second case, unexpectedly, the transition is continuous and leads to a periodical stripes pattern whose wavelength is large compared to the shear scale. This pattern can even be described in a generalized noisy Ginzburg—Landau formalism. In this context, the intermittent and disordered laminar-turbulent coexistence can be seen as the ultimate stage of the modulation of the turbulent flows.

Transitional pipe flow is investigated in two different experimental set-ups. In the first the stability threshold and the initial growth of localized perturbations are studied.

Good agreement is found with an earlier investigation of the transition threshold. The measurement technique applied in the last part of this study allows the reconstruction of the streamwise vorticity in a turbulent puff.

Non-linear stability bounds are derived for subcritical shear flows. First the methodology is exemplified using a model problem and then it is applied to plane Couette flow. The result is a lower bound which scales as Re. Upper bounds based on numerical simulations are found to be about Re, depending slightly on the transition scenario investigated. Bounds for plane Poiseuille flow are also presented.

Non-linear optimal perturbations are defined here as those of minimum energy leading to subcritical instability. We show that a necessary condition for an initial perturbation to be a non-linear optimal is that the initial perturbation energy growth is zero. The fulfillment of this condition does not depend on the disturbance amplitude but only on the linearized operator as long as the non-linearity conserves energy. Saddle point solutions and linear optimal perturbations leading to maximum transient growth both satisfy the non-linear optimality condition. We discuss these issues on low-dimensional models of subcritical transition for which non-linear optimals and the minimum threshold energy are computed.

The work is concerned with the theoretical and experimental study of laminarturbulent transition in the wind induced boundary layer in water beneath the free surface. The mechanism of this transition has not been identified yet and the present work is aimed to fill this gap. The experiments in the wave tank showed that the first perturbations which emerge out of natural primordial noise are long compared to the boundary layer thickness, then they gradually grow, become more nonlinear until suddenly a strong localised instability occurs. This instability results in almost immediate breakdown of the laminar boundary layer and formation of localised 3D turbulent spots. The spots slowly expand downstream forming turbulent streaks having the shape of upstream pointed arrowheads marked by the wind generated capillary-gravity waves on the water surface. The streaks merge further downstream creating basin-wide turbulence zone. The notable feature of the observed transition is that there is no universal critical Reynolds number, although the results are reproducible for the same values of wind. The critical distance where the turbulent spots first appear is found to be inversely proportional to the wind stress at the surface.

The theoretical study begins with the classical linear stability analysis carried out within the framework of Orr-Sommerfeld equation with the appropriate boundary conditions. In contrast to classical wall boundary layers, there are no linearly unstable modes. An analysis of weakly-nonlinear evolution of decaying perturbations under some unrestrictive assumptions suggests an unusual bypass scenario based on the explosive transverse instability of solitary waves as a plausible mechanism for the transition.

Nonlinear traveling wave solutions to the Navier—Stokes equations in the plane Poiseuille geometry (Waleffe, F. (2003), , 1517–1534) come into existence through a saddle-node bifurcation at a Reynolds number of 977, very close to the experimentally observed Reynolds number of ∼ 1000 for transition to turbulence in this geometry. These traveling waves are comprised of staggered counter-rotating streamwise vortices with a spanwise wavelength of 106 wall units, in good agreement with the experimentally observed value of ∼ 100 wall units for buffer layer structures. In the present work, the effect of viscoelasticity on these states is examined, using the FENE-P constitutive model of polymer solutions. The changes to the velocity field for the viscoelastic traveling waves mirror those experimentally observed in fully turbulent flows of polymer solutions near the onset of turbulent drag reduction: drag is reduced, streamwise velocity fluctuations increase and wall-normal fluctuations decrease. The mechanism underlying theses changes is elucidated through an examination of the forces exerted by the polymer molecules on the fluid. The onset Weissenberg number (shear rate times polymer relaxation time) for drag reduction is insensitive to polymer extensibility or concentration. Above the onset Weissenberg number, there is a dramatic increase in the critical wall-normal length scale at which the nonlinear traveling waves can exist. This sharp increase in length scale directly correlates with the extensibility and concentration of the polymer molecules and is consistent with the observed shift to higher Reynolds numbers of the transition to turbulence in polymer solutions. The balance of turbulent kinetic energy for the nonlinear traveling waves shows the same qualititative changes as are found in full turbulence, as do the overall kinematics of stretching and rotation in the flow. These observations suggest that the mechanism of near-onset drag reduction in flow over smooth walls is captured by the effect of viscoelasticity on these nonlinear traveling waves.

A non-linear stability analysis of plane Couette flow of the Upper-Convected Maxwell model is performed. The amplitude equation describing time-evolution of a finite-size perturbation is derived. It is shown that above the critical Weissenberg number, a perturbation in the form of an eigenfunction of the linearized equations of motion becomes subcritically unstable, and the threshold value for the amplitude of the perturbation decreases as the Weissenberg number increases.