European Turbulence Conference 2015

10:30 Instability and Transition 7
Chair: Rene Pecnik

10:30 15 mins	Roughness Induced Boundary Layer Transition in Incompressible Flow Qingqing Ye, Ferry F.J. Schrijer, Fulvio Scarano Abstract: The fluid dynamics process leading to laminar-turbulent transition behind an isolated roughness element is investigated in the incompressible regime using particle image velocimetry. The study covers the effect of roughness size and geometry on the promotion of transition. The measurement domain covers a large streamwise range from the near wake to the onset of the turbulent regime. Planar PIV measurements reveal the basic flow pattern and the turbulent structure of the flow characterizing by the velocity fluctuation statistics (RMS of the streamwise and wall-normal velocity component and Reynolds shear stress). The high Reynolds shear stress level reaching the region near the wall in the downstream area indicates the onset of turbulent boundary layer.
10:45 15 mins	ZERO-INERTIA INSTABILITIES IN RHEOPECTIC FLUIDS Simone Boi, Andrea Mazzino, Jan Oscar Pralits Abstract: The emergence of fluid instabilities in the relevant limit of vanishing fluid inertia (i.e., arbitrarily close to zero Reynolds number) has been investigated for the well-known Kolmogorov flow. The time-lagged viscosity change from lower to higher values due to shear changes is the crucial ingredient for the instabilities to emerge. This behavior characterizes the so-called rheopectic fluids. The instability does not emerge in shear-thinning or -thickening fluids where viscosity adjustment to local shear occurs instantaneously. No instability arbitrarily close to zero Reynolds number is either observed in thixotropic fluids, even though the viscosity adjustment time to shear is finite like in rheopectic fluids. Numerical tools (through suitable eigenvalue problems from the linear stability analysis) and multiple-scale homogenization techniques are utilized to lead to our conclusions. Our findings may have important consequences in all situations where purely hydrodynamic fluid instabilities or mixing are inhibited due to negligible inertia, such as in microfluidics. To trigger mixing in these situations, suitable (not necessarily viscoelastic) non-Newtonian fluid solutions appear as a valid answer. Our results open interesting questions and challenges in the field of smart (fluid) materials.
11:00 15 mins	FLOW INSTABILITIES AND REVERSALS IN NON-UNIFORMLY THERMOCAPILLARY DRIVEN MELT POOL Anton Kidess, Sasa Kenjeres, Chris R. Kleijn Abstract: With transient LES and DNS simulations, we investigate flow in melt pools driven by thermocapillary forces. The developing pool is at first axisymmetric as are the boundary conditions, but flow instabilities arise that lead to 3D oscillatory flow patterns. At higher laser powers a sign-change in the surface tension temperature coefficient occurs, resulting in a flow reversal in the pool and thus two counter-rotating vortices, which exhibit similar though more complex flow instabilities.
11:15 15 mins	Dispersive to nondispersive transition in the plane wake and channel flows Francesca De Santi, Federico Fraternale, Daniela Tordella Abstract: By varying the wavenumber over a large and finely discretized interval of values, we analyse the phase and group velocity of linear three-dimensional travelling waves both in the plane wake and channel flows to get the transition between dispersive and non-dispersive behaviour. The dispersion relation is computed from the Orr-Sommerfeld and Squire eigenvalue problem by observing the least stable mode, see figure 2, panels (a,b) and the comparison with [1, 2, 4–11, 15, 16]. The group velocity vg is also shown. The Reynolds number varies in the 20-100, 1000-8000 ranges for the wake and the channel flow, respectively, while we consider wavenumbers in the range 0.1-10. The wake basic flow consists of the first two orders of the Navier-Stokes matched asymptotic expansion described in [3, 13, 14]. At low wavenumbers we observe a dispersive behaviour where the phase speed and the group velocity substantially differ. The relevant perturbed solution is amenable to the typical solution belonging to the left branch of the eigenvalue spectrum, see the two examples shown in figure 1 (channel flow: Re = 6000, k = 1; wake Re = 100, k = 0.7). By rising the wave number value, we observe a sharp transition from the dispersive to the nondispersive regime. This transition is located at a critical wave number kd which is a function of the Reynolds number Re, the wave angle φ, and the wake downstream observation point x0. Precisely, kd increases with Re and decreases with φ for the wake flow, while these trends are reversed for the channel flow, see tables 1,2. Beyond the wavenumber threshold, the observed least-stable mode belongs to the right branch of the spectrum. The asymptotic solutions in the dispersive region are wall modes for the channel flow , and in-wake modes for the wake flow. This means that, for both the flows, the dispersive behaviour is related to perturbations with high momentum variations (high vorticity) in correspondence to the base flow high-shear region. On the contrary, if k > kd the solutions are central modes for the channel case, and out-of-wake modes for the wake flow. In these cases, the disturbance has high variations outside the base flow high-shear region. To understand the physical mechanism of the dispersive-nondispersive transition we focused on time variation of the wave kinetic energy associated to the convective transport. Figure 2 (c,d) shows the convective term as a function of the wavenumber for the two least stable modes. We observe that the dispersive-nondisperive transition allows waves k > kd to keep the lowest possible temporal variation of kinetic energy, i.e. the lowest decay. This remains true also when all the other more stable modes are considered. In practice nondispersive waves maintain their convective energy with k. [1] M. Asai and J. M. Floryan, Eur. J. Mech. B/Fluids, 25, 2006 [2] D. Barkley, Europhys. Lett., 75, 2006. [3] M. Belan and D. Tordella, J. Fluid Mech., 552, 2006. [4] F. Giannetti and P. Luchini, J. Fluid Mech., 581, 2007. [5] N. Ito, Trans. Japan Soc. Aero. Space Sci., 17:65, 1974. [6] M. Nishioka, S. Lida, and Y. Ichikawa, J. Fluid Mech., 72, 1975. [7] M. Nishioka and H. Sato, J. Fluid Mech.,65, 1974. [8] C. Norberg, J. Fluid Mech., 258, 1994. [9] P. Paranthoën, L. W. B. Browne, S. LeMasson, F. LeMasson, and J. C. Lecordie, Eur. J. Mech. B/Fluids, 18, 1999. [10] B. Pier, J. Fluid Mech., 458, 2002. [11] A. Roshko, NACA, 1932, 1954. [12] P. J. Schmid and D. S. Henningson. Stability and Transition in Shear Flows. Springer, 2001. [13] D. Tordella and M. Belan, Phys. Fluids,15. [14] D. Tordella, S. Scarsoglio, and M. Belan, Phys. Fluids, 18, 2006. [15] C. H. K. Williamson, J. Fluid Mech.,206, 1989. [16] A. Zebib, J. Engin. Maths, 21, 1987.
11:30 15 mins	Transient energy growth modulation by temperature dependent transport properties in a stratified plane Poiseuille flow Enrico Rinaldi, Bendiks Jan Boersma, Rene Pecnik Abstract: We investigate the effect of temperature dependent thermal conductivity $\lambda$ and isobaric specific heat $c_P$ on the transient amplification of perturbations in a thermally stratified laminar plane Poiseuille flow. It is shown that for decreasing thermal conductivity the maximum transient energy growth is amplified with respect to the $\lambda=1$ case, while the opposite occurs for increasing $\lambda$. A reversed mechanism is induced by a variable $c_p$. Substantial maximum growth enhancement/suppression is found in the range of Prandtl numbers $Pr$ which encompasses most fluids of practical interest. The relative growth modulation shows an optimum $Pr$ under spanwise perturbations. For energy amplifying property distributions a speed-up of the transient to reach the maximum energy growth is observed at low $Pr$, while a slow-down is found at large $Pr$. The opposite is true when the property variations suppress the growth of perturbations.
11:45 15 mins	LIFETIME OF TURBULENT PATCH IN TAYLOR COUETTE SETUP Arjang Alidai, René Delfos Abstract: In linearly stable shear ﬂows like pipe and plane Couette ﬂows, the transition from the laminar to the turbulent regime occurs abruptly. To better understand this transition, the time evolution of turbulent patches, created by controlled ﬁnite amplitude perturbations, have been studied in the literature. These studies mostly focused on pipe ﬂows for which a ﬁnite lifetime of the patch was proven. The same conclusion was drawn in the only available study performed in a Taylor Couette setup. Here, we measured the lifetime in a different size TC setup. We show that the lifetime is indeed ﬁnite and also very sensitive to the boundary condition, but not much to the perturbation mechanism. We suggest that in addition to the Reynolds number, the lifetime depends on the aspect ratio to the radius ratio of the setup.
12:00 15 mins	EXPLORING THE EFFECTS OF A RIGID BODY ON THE EVOLUTION OF THE RAYLEIGH-TAYLOR INSTABILITY Chris Brown, Stuart Dalziel Abstract: This talk discusses the effects of a rigid solid boundary impeding the evolution of the Rayleigh-Taylor (RT) instability. The introduction of an obstacle completely alters the evolution of RT growth, instead of mixing the domain rapidly, a quasi-steady flow, rich in dynamics is established for long periods of time. Using a combination of low Atwood number experiments and ILES simulations, this talk will present a non-dimensional analytical model for a multi-stage mixing process, discussing the effects of the opening size and topology on the density change of each layer, buoyancy driven flux through the opening and mixing efficiency.
12:15 15 mins	OBSERVATION OF PREDATOR-PREY DYNAMICS AND THE UNIVERSALITY CLASS IN TRANSITIONAL PIPE TURBULENCE Nigel Goldenfeld Abstract: Near the onset to turbulence in pipes, around Re = 1700-2000, turbulent puffs decay either directly or, at higher Reynolds numbers through splitting, with characteristic time-scales that exhibit a super-exponential dependence on Reynolds number [3, 1, 7]. The goal of our work [5] is to understand the phenomenology of this transition in terms of standard phase transition concepts, and to calculate the universality class from first principles. Using direct numerical simulations (DNS) of transitional pipe flow, we show that a collective mode, a so-called zonal flow emerges at large scales, activated by anisotropic turbulent fluctuations through an inverse cascade of energy. This zonal flow imposes a shear on the turbulent fluctuations that tends to suppress their anisotropy, leading to stochastic predator-prey dynamics. The effective stochastic theory for the predator-prey modes identified in the DNS reproduces the super-exponential lifetime statistics and phenomenology of pipe flow experiments, correctly predicts the phase diagram of transitional turbulence, and can be mapped exactly to the field theory of directed percolation.

Invited speakers: