Bulletin of the American Physical Society
68th Annual Meeting of the APS Division of Fluid Dynamics
Volume 60, Number 21
Sunday–Tuesday, November 22–24, 2015; Boston, Massachusetts
Session R17: Flow Instability: Transition to Turbulence 
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Chair: Nigel Goldenfeld, Univeristy of Illinois, UrbanaChampaigne Room: 205 
Tuesday, November 24, 2015 12:50PM  1:03PM 
R17.00001: Predatorprey effective model for the laminarturbulent transition in a pipe HongYan Shih, TsungLin Hsieh, Nigel Goldenfeld The goal of our work is to understand the phenomenology of the laminarturbulent transition in terms of standard phase transition concepts, and to calculate the universality class from first principles. Direct numerical simulations (DNS) of transitional pipe flow show that a collective mode  a zonal flow  is activated by Reynolds stress and suppresses turbulence subsequently, leading to stochastic predatorpreylike oscillations. Here we describe in detail the effective stochastic theory for such spatialextended predatorprey modes. We present Monte Carlo simulations of the effective theory, showing that it reproduces the phenomenology of pipe flow experiments, including the phase diagram of puff decay and splitting. In particular, the theory predicts a superexponential lifetime statistics for both puff decay and puffsplitting, in agreement with experimental data on pipe flow, and can be mapped exactly to the field theory of directed percolation. Our calculations strongly suggest that transitional turbulence in pipes is in the universality class of directed percolation. [Preview Abstract] 
Tuesday, November 24, 2015 1:03PM  1:16PM 
R17.00002: Linear stability analysis of flows in a grooved channel Alireza Mohammadi, Jerzy Maciej Floryan It is known that longitudinal grooves which are parallel to the flow direction may either stabilize or destabilize the travelling wave instability in a pressuregradientdriven channel flow depending on the groove wave number. These waves reduce to the classical TollmienSchlichting (TS) waves in the smooth channel limit. It is shown that another class of travelling wave instability exists if grooves with sufficiently high amplitude and proper wavelengths are used. It is demonstrated that the new instability is driven by inviscid mechanisms, with the disturbance motion having the form of a wave propagating in the streamwise direction with the phase speed approximately four times larger than the TS wave speed and with its streamwise wavelength being approximately twice the spanwise groove wavelength. The instability motion is concentrated mostly in the middle of the channel and has a primarily planar character, i.e. the dominant velocity components are parallel to the walls. A significant reduction of the corresponding critical Reynolds number can be achieved by increasing the groove amplitude. This mode reduces to the highly attenuated Squire mode in the smooth channel limit. [Preview Abstract] 
Tuesday, November 24, 2015 1:16PM  1:29PM 
R17.00003: Transition to turbulence in pipe flow as a phase transition Mukund Vasudevan, Bj\"orn Hof In pipe flow, turbulence first arises in the form of localized turbulent patches called puffs. The flow undergoes a transition to sustained turbulence via spatiotemporal intermittency, with puffs splitting, decaying and merging in the background laminar flow. However, the due to mean advection of the puffs and the long timescales involved ($\sim 10^{7}$ advective time units), it is not possible to study the transition in typical laboratory setups. So far, it has only been possible to indirectly estimate the critical point for the transition. Here, we exploit the stochastic memoryless nature of the puff decay and splitting processes to construct a pipe flow setup, that is periodic in a statistical sense. It then becomes possible to study the flow for sufficiently long times and characterize the transition in detail. We present measurements of the turbulent fraction as a function of Reynolds number which in turn allows a direct estimate of the critical point. We present evidence that the transition has features of a phase transition of second order. [Preview Abstract] 
Tuesday, November 24, 2015 1:29PM  1:42PM 
R17.00004: Turbulent structures in Kolmogorovian shear flows: DNS Laurette S Tuckerman, Matthew Chantry, Dwight Barkley Patterns of turbulent and laminar flow form a vital step in the transition to turbulent in wallbounded shear flows. In flows with two unconstrained directions these patterns form oblique bands, whereas in pipe flow the structures are streamwiselocalized puffs. To understand these structures we examine Waleffe flow, a sinusoidal shear flow, $U\sin \left( \frac{\pi}{2} y \right)$, driven by a body force and stressfree boundary conditions at $y=\pm 1$. Introduced as a model for plane Couette flow we demonstrate the existence of turbulence bands which match those found in plane Couette flow, excluding the boundary layer regions of the latter flow. This agreement is reiterated in the studies of uniform turbulence and linear stability; highlighting the surprising unimportance of this region to transitional turbulence. Building upon this we consider two other canonical flows: plane Pouiseuille flow and pipe flow. Attacking these flows with the approach that succeeded in plane Couette flow we attempt to clarify the role of boundary layers to transitionally turbulent shear flows. [Preview Abstract] 
Tuesday, November 24, 2015 1:42PM  1:55PM 
R17.00005: Turbulent structures in Kolmogorovian shear flows: Models Matthew Chantry, Laurette S Tuckerman, Dwight Barkley Oblique patterns of turbulence are observed immediately beyond transition in wallbounded shear flows with two unconstrained directions. Despite the ubiquitous nature of these structures, simple descriptions obtained directly from the NavierStokes equations are lacking. To this aim we examine Waleffe flow, a sinusoidal shear flow, $U\sin \left( \frac{\pi}{2} y \right)$, driven by a body force and stressfree boundary conditions at $y=\pm 1$. After establishing the ability of Waleffe flow to capture turbulent bands we study a series of models, capturing the shear dependent direction with a small number of Fourier modes. With only one nonzero Fourier wavenumber the fundamentals of bands are already observed. This minimal system offers the perfect testbed to study the emergence of bands. Considering small increases to the number of modes we find the rich behaviour associated with plane Couette flow. These models form a fascinating midpoint between the full NavierStokes equations and the minimal SSP model. [Preview Abstract] 
Tuesday, November 24, 2015 1:55PM  2:08PM 
R17.00006: Determining the universality class of the transition to turbulence Gr\'egoire Lemoult, Bj\"orn Hof In the counterrotating regime of TaylorCouette (TC) flow, turbulence appears abruptly through spatiotemporal intermittency (STI). STI is observed during the subcritical transition to turbulence in many wall bounded shear flows, most notably pipe flow and Couette flows. K. Avila \textit{et al.} (Science 333, 192196 (2011)) recently characterized the onset of sustained turbulence in pipe flow and suggested that the transition could be a second order nonequilibrium phase transition. We explore this proposition in a TC experiment. Our TC setup has an aspect ratio of 8 and an azimuthal length of more than 1300 gapwidths, minimizing the finite size effects and keeping the spatiotemporal dynamics 1D. We measured three independent critical exponents and they are in very good agreement with those of the directed percolation universality class in 1+1 dimensions. These experimental results strongly suggest that the transition to turbulence is a second order nonequilibrium phase transition. [Preview Abstract] 
Tuesday, November 24, 2015 2:08PM  2:21PM 
R17.00007: The behavior of dropletladen pipe flow at the onset of turbulence Kyle Winters, Ellen Longmire The addition of either dispersed fluid droplets or solid particles to a pipe flow can modify the Reynolds number at which the flow transitions to turbulence, $Re_c$. For dispersed solid particles, Matas et al. (2003) studied the behavior of $Re_c$ as a function of volume fraction and particle size, and found that for certain regimes particles can promote transition, while for others, transition was delayed to higher values of $Re_c$. To explore the phenomenon in dropletladen flows, pressure and PIV measurements are taken in facility comprised of a pumpdriven circuit with a 44mm diameter, D, and with an 8.8m (200D) development and test section. Static mixers are placed upstream to generate an even dispersion of silicone oil in a refractive index matched waterglycerin flow. Pressure signals were used to identify transitional structures and trigger a high repetition rate PIV system downstream. Information from the pressure drop traces is used to determine $Re_c$ for various droplet sizes and volume fractions. Additionally, PIV data provide detailed information about velocity variations and the transitional structures in the flow. Pressure and PIV data from droplet laden flow are compared to similar data from single phase flows in our facility and in the literature. [Preview Abstract] 
Tuesday, November 24, 2015 2:21PM  2:34PM 
R17.00008: New experiment in Plane Poiseuille flow with zero mean advection velocity: observation of stationary turbulent spots Lukasz Klotz, Gregoire Lemoult, Jose Eduardo Wesfreid We describe a new experimental setup which allows us to study the subcritical transition to turbulence in a two dimensional shear flow (including plane Couette, plane CouettePoiseuille and plane Poiseuille flows). Our facility is an extension of a classical plane Couette experiment, in which one uses a single closed loop of plastic belt to generate the opposite sign velocity at each wall of the test section. However, in our case, we use two independent closed loops of plastic belt, one at each wall of the test section. The speed of these belts may be controlled separately. That enables to set two different velocities (in value and direction) as a boundary conditions at each of two test section's walls. In addition the pressure gradient in streamwise direction can be controlled. In particular, the plane Poiseuille flow with zero mean advection velocity can be created. We characterize by PIV the basic flow for different configurations. For a plane Poiseuille flows as base flow, we were able to observe for the first time the nearly stationary turbulent spots in this flow, with structures of characteristic wavelength $\sim $ the distance between the two plates. [Preview Abstract] 

R17.00009: ABSTRACT WITHDRAWN 
Tuesday, November 24, 2015 2:47PM  3:00PM 
R17.00010: Transition to turbulence in pulsatile pipe flow Bjorn Hof, Duo Xu Pulsating flows are common in nature and applications, the most prominent example being cardiovascular flow. Often such flows are at the verge of becoming turbulent yet the influence of pulsation on the transition process is unclear. We present detailed experiments carried out in a straight pipe of circular crosssection with a sinusoidally modulated flow rate. With decreasing frequencies (Wo $<$ 10) the transition is delayed considerably to larger mean Reynolds numbers, however the qualitative transition scenario remains unchanged. Like for steady flows puffs are the first observable turbulent structures but their lifetimes are shorter and turbulence only becomes sustained at larger Re. For fixed frequency and increasing pulsation amplitude on the other hand a different transition process is found. Here turbulence only occurs during the decelerating flow phase. Like the steady flow transition also this transition appears to require finite amplitude perturbations. The structure of the resulting turbulent flow however differs considerably for the pulsatile case. We map out the stability threshold for both instabilities in Refrequencyamplitude parameter space. Particular attention is paid to the regime where both transition types coexist and compete. [Preview Abstract] 
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