Bulletin of the American Physical Society
67th Annual Meeting of the APS Division of Fluid Dynamics
Volume 59, Number 20
Sunday–Tuesday, November 23–25, 2014; San Francisco, California
Session G22: Instability: Transition to Turbulence |
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Chair: Jim Riley, University of Washington Room: 2012 |
Monday, November 24, 2014 8:00AM - 8:13AM |
G22.00001: Coherent structures in stratified plane Couette flows Daniel Olvera, Rich Kerswell Wall--bounded shear flows typically follow a subcritical transition scenario where finite amplitude solutions unconnected to the basic flow play a key role. Edge tracking has been very useful in finding some of these by following the laminar--turbulent boundary in phase space for many canonical shear flows. However, it has yet to be used to probe stratified flows. We will discuss the results of edge tracking in stably--stratified plane Couette flow over large and small domains. [Preview Abstract] |
Monday, November 24, 2014 8:13AM - 8:26AM |
G22.00002: Critical Reynolds number for global instability of channel flow in subcritical scenario Takahiro Ishida, Takahiro Tsukahara We perform direct numerical simulations for the transitional pressure-driven channel flow and investigate the critical Reynolds number for global instability (Re$_{\mathrm{G}})$. In the channel flow, the critical Reynolds number relevant to local (infinitesimal) instability (Re$_{\mathrm{L}})$ is known as 5772, which is based on the channel half width ($h$/2) and the channel centerline velocity in laminar flow, by the linear stability theory. However, the understanding of Re$_{\mathrm{G}}$ is still unresolved because it is inherently non-linear. In this study, temporal progress of a turbulent spot that grows from finite disturbance in the laminar flow is analyzed. We use the small and the large computational boxes for identifying the lower critical number, which are $L_{x}$*$L_{y}$*$L_{z}=$6.4$h$*$h$*3.2$h$ and 102.4$h$*$h$*51.2$h$, respectively. For the small box, we determine Re$_{\mathrm{G}}$\textbar $_{\mathrm{S}}$ is 1400. The flow regime observed in the small box is only either laminar flow or fully-developed turbulence. As for the large box, we obtain Re$_{\mathrm{G}}$\textbar $_{\mathrm{L}}$ of 875 because of the emergence of the transitional structure named ``turbulent stripe,'' or a coexistence of oblique turbulent and laminar region. Because the spatial size of turbulent stripe is much larger than the small box, Re$_{\mathrm{G}}$\textbar $_{\mathrm{S}}$ indicates the critical Reynolds number for the flow without large-scale intermittency. Therefore, we found that the existence of turbulent stripe caught in large box would decrease the Re$_{\mathrm{G}}$ value compared to those proposed by previous studies. [Preview Abstract] |
Monday, November 24, 2014 8:26AM - 8:39AM |
G22.00003: Nonlinear optimal perturbations of stratified plane Couette flow T.S. Eaves, C.P. Caulfield The stability properties of shear flows have received wide attention due to the important engineering applications of understanding how and when turbulence might emerge in a given flow geometry. Research has recently focused on identifying ``minimal seeds,'' i.e. the initial perturbations to a laminar state with the smallest initial perturbation energy $E_0=E_c$ that ultimately trigger the transition to turbulence. In unstratified plane Couette flow, Rabin, Caulfield \& Kerswell ({\it J. Fluid Mech.} 2012 {\bf 712}) identified both such a minimal seed, and other ``nonlinear optimal perturbations'' (NLOPS) with $E_0 < E_c$ which maximised the gain in kinetic energy over some finite time while the flow still remained laminar. We use the same variational method of ``nonlinear adjoint looping'' to identify NLOPS and minimal seeds in stably stratified plane Couette flow, where a constant (stabilising) density difference is maintained across the flow. We also identify the mechanisms through which such perturbations may transiently gain both kinetic and potential energy as the bulk Richardson number is varied, identifying how stratification changes the qualitative characteristics of the optimal perturbations. [Preview Abstract] |
Monday, November 24, 2014 8:39AM - 8:52AM |
G22.00004: Singularity of Navier-Stokes Equations Leading to Turbulent Transition Hua-Shu Dou As is well known, there is discontinuity during the transition from laminar flow to turbulence in the time-averaged Navier-Stokes equations. In other words, singularity may implicitly exist in the Navier-Stokes equations. Transition of a laminar flow to turbulence must be implemented via the singularity. However, how the singularity of Navier-Stokes equations is related to the turbulent transition is not understood. In this study, the singularity possibly hidden in the Navier-Stokes equation is exactly derived by mathematical treatment. Then, it is found that for pressure driven flows, the singularity of Navier-Stokes equations corresponds to the inflection point on the velocity profile. Since the rate of amplification to a disturbance at the inflection point is infinite, the laminar flow is able to involve into turbulence at this point firstly at a sufficient high Reynolds number. This is the reason why turbulent spot is formed at the location of inflection point. It is further demonstrated that the existence of the singularity in the time-averaged Navier-Stokes equations is the necessary and sufficient condition for the turbulent transition in pressure driven flows. These results agrees well with the findings from the recent proposed energy gradient method. [Preview Abstract] |
Monday, November 24, 2014 8:52AM - 9:05AM |
G22.00005: The competition of convective and absolute instabilities in rotating-disk flow transition Shintaro Imayama, P. Henrik Alfredsson, R.J. Lingwood The main objective of this experimental study is to investigate laminar-turbulent transition mechanisms in the rotating-disk boundary-layer flow. Lingwood (1995) found that the flow becomes locally absolutely unstable above a critical Reynolds number and suggested that absolutely unstable travelling waves triggered nonlinearity leading to transition. However, the growth of convectively unstable stationary vortices is also a possible alternative route if the surface roughness of the disk is sufficiently large. The convectively unstable stationary vortices are attributed to an inviscid crossflow mechanism. Flow-visualization studies and hot-wire measurements of the rotating-disk boundary layer typically capture 28-32 stationary vortices in the transition regime (e.g. Imayama et al. 2014). The hot-wire measurements presented here were performed on a smooth glass disk with a diameter of 474 mm. To excite stationary vortices disk-shaped roughness elements with a diameter of 2 mm and a height of 5 micron were put on the disk at a radial position of 110 mm. In the presentation, the details of the convectively unstable stationary vortices in the rotating-disk boundary layer are shown and compared with travelling waves and similarities/differences in the turbulent transition discussed. [Preview Abstract] |
Monday, November 24, 2014 9:05AM - 9:18AM |
G22.00006: Fully localised nonlinear energy growth optimals in pipe flow Chris Pringle, Ashley Willis, Rich Kerswell In wall-bounded shear flows such as pipe flow, transition to turbulence remains a problem of great theoretical and practical importance. The transition is typically abrupt, occurs at flow rates for which the underlying base flow is stable, and is triggered by disturbance amplitudes much smaller that the ensuing turbulent state. Progress has recently been made in identifying the smallest perturbation capable of triggering turbulence (the minimal seed) using energy growth optimals, but only in small periodic domains. Here we present a new fully-localised (non-periodic in the streamwise direction) energy growth optimal for pipe flow. The perturbation approaches the experimentally-relevant minimal seed for transition in long pipes. [Preview Abstract] |
Monday, November 24, 2014 9:18AM - 9:31AM |
G22.00007: Transition to sustained turbulence in pipe flow: a second order phase transition? Mukund Vasudevan, Bj\"orn Hof In a recent study, the critical point for sustained turbulence in a pipe was estimated to be Re $\approx$ 2040, by balancing the times scales for turbulence growth and decay processes. This work brought into focus the spatio-temporal aspects of the transition and suggested the possibility that the transition is a second order non-equilibrium phase transition. The present contribution aims to experimentally characterize the transition to sustained turbulence in pipe flow in greater detail and explore the analogy to a phase transition. However, the long time scales near the critical point ($\sim 10^{7}$ advective time units) pose a challenge in realizing this. We circumvent this problem by constructing a set-up with a quasi-periodic pipe, that exploits the memoryless nature of the turbulence spreading and decay processes in the vicinity of the critical point. In conjunction with an accurate control of the Reynolds number, it is then possible to monitor the spatio-temporal dynamics for arbitrarily long times, and obtain quantities such as the equilibrium turbulent fraction. We present evidence to support the idea that the transition to sustained turbulence in pipe flow is a phase transition of second order and provide first estimates of some of the associated critical exponents. [Preview Abstract] |
Monday, November 24, 2014 9:31AM - 9:44AM |
G22.00008: Investigation of Turbulent Laminar Patterns in Poiseuille-Couette flow Quoc Nguyen, Dimitrios Papavassiliou Laminar-turbulent intermittency has recently been observed in the transitional regime of pipe ...[1-2] and plane Couette flow ...[3-7]. While many works focus on behavior of these patterns in plane Couette flow, little attention has been paid to Poiseuille flow and transition from Couette to Poiseuille flow. In this study, we investigate behavior of turbulent laminar patterns in Poiseuille-Couette flow, including pure Poiseuille and Couette flows at two limits. Direct Numerical Simulation (DNS) is used to simulate a Poiseuille-Couette channel at a size of 16$\pi $h x 2h x 2$\pi $h (corresponding to a resolution of 512x129x128 in x, y and z directions), with periodic boundary condition applied in the x and z directions (h is half of the channel height). The Reynolds number is 300, and the flow is at transitional regime in all simulations. Behavior of laminar turbulent patterns as the flow goes from Couette to Poiseuille flow will be presented in details. This would shed some light on the effect of different types of flow on these patterns, as well as how these patterns vary from fully Poiseuille flow to fully Couette flow. Bibliography .1. Moxey D {\&} Barkley D (2009), \textit{PNAS} 107(18). 2. Samanta D, Lozar AD, {\&} Hof B (2011). \textit{J. Fluid Mech.} 681. 3. Barkley D {\&} Tuckerman LS (2005) \textit{Phys. Rev. Lett.} 94. 4. Duguet Y {\&} Schlatter P (2013) \textit{Phys. Rev. Lett.} 110. 5. Philip J {\&} Manneville P (2011). \textit{Phys. Rev. E} 83. 6. Tuckerman LS {\&} Barkley D (2011) \textit{Phys. Fluids} 23. 7. Shi L, Avila M, {\&} Hof B (2013) \textit{Phys. Rev. Lett.} 110. [Preview Abstract] |
Monday, November 24, 2014 9:44AM - 9:57AM |
G22.00009: Effects of Longitudinal Grooves on the Stability of Channel Flow H. Vafadar Moradi, Jerzy M. Floryan The travelling wave instability in a channel with small-amplitude longitudinal grooves of arbitrary shape has been studied. The disturbance velocity field is always three-dimensional with disturbances which connect to the two-dimensional waves in the limit of zero groove amplitude playing the critical role. The presence of grooves destabilizes the flow if the groove wave number $\beta$ is larger than $\beta_{tran} \approx 4.22$, but stabilizes the flow for smaller $\beta$. It has been found that $\beta_{tran}$ does not depend on the groove amplitude. The dependence of the critical Reynolds number on the groove amplitude and wave number has been determined. Special attention has been paid to the drag-reducing long wavelength grooves, including the optimal grooves. It has been demonstrated that such grooves slightly increase the critical Reynolds number, i.e., such grooves do not cause an early breakdown into turbulence. [Preview Abstract] |
Monday, November 24, 2014 9:57AM - 10:10AM |
G22.00010: Secondary instability and tertiary states in rotating plane Couette flow Conor Daly, Tobias Schneider, Philipp Schlatter, Nigel Peake Recent experimental studies have shown rich transition behaviour in rotating plane Couette flow (RPCF). In this paper we study the transition in supercritical RPCF theoretically by determination of various equilibria and periodic orbit tertiary states via Floquet analysis on secondary Taylor vortex solutions. Two new tertiary states are discovered which we name oscillatory wavy vortex flow (oWVF) and skewed vortex flow (SVF). We present the bifurcation routes and stability properties of these new tertiary states, alongside a bifurcation procedure whereby a set of defected wavy twist vortices are approached. [Preview Abstract] |
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