Although the equations governing fluid flow are well known, there are no analytical expressions that describe the complexity of turbulent motion. A recent proposition is that in analogy to low dimensional chaotic systems, turbulence is organized around unstable solutions of the governing equations which provide the building blocks of the disordered dynamics. We report the discovery of periodic solutions which just like intermittent turbulence are spatially localized and show that turbulent transients arise from one such solution branch.

Direct numerical simulation of transitional pipe flow is carried out in a long computational domain in order to characterize the dynamics within the saddle region of phase space that separates laminar flow from turbulent intermittency. For Reynolds numbers ranging from Re=1800 to 2800, a shoot and bisection method is used to compute critical trajectories. The chaotic saddle or edge state approached by these trajectories is studied in detail. For Re< or =2000 the edge state and the corresponding intermittent puff are shown to share similar averaged global properties. For Re> or =2200, the puff length grows unboundedly whereas the edge state varies only little with Re. In this regime, transition is shown to proceed in two steps: first the energy grows to produce a localized turbulent patch, which then, during the second stage, spreads out to fill the pipe.

Glucocorticoids, widely used in inflammatory disorders, rapidly increase bone fragility and, therefore, fracture risk. However, common bone densitometry measurements are not sensitive enough to detect these changes. Moreover, densitometry only partially recognizes treatment-induced fracture reductions in osteoporosis. Here, we tested whether the reference point indentation technique could detect bone tissue property changes early after glucocorticoid treatment initiation. After initial laboratory and bone density measurements, patients were allocated into groups receiving calcium þ vitamin D (CaþD) supplements or antiosteoporotic drugs (risedronate, denosumab, teriparatide). Reference point indentation was performed on the cortical bone layer of the tibia by a handheld device measuring bone material strength index (BMSi). Bone mineral density was measured by dualenergy X-ray absorptiometry (DXA). Although CaþD-treated patients exhibited substantial and significant deterioration, risedronate-treated patients exhibited no significant change, and both denosumab-and teriparatide-treated participants exhibited significantly improved BMSi 7 weeks after initial treatment compared with baseline; these trends remained stable for 20 weeks. In contrast, no densitometry changes were observed during this study period. In conclusion, our study is the first to our knowledge to demonstrate that reference point indentation is sensitive enough to reflect changes in cortical bone indentation after treatment with osteoporosis therapies in patients newly exposed to glucocorticoids.

Alternating laminar and turbulent helical bands appearing in shear flows between counterrotating cylinders are accurately computed and the near-wall instability phenomena responsible for their generation identified for the first time. The computations show that this intermittent regime can only exist within large domains and that its spiral coherence is not dictated by endwall boundary conditions. A supercritical transition route, consisting of a progressive helical alignment of localised turbulent spots, is carefully studied. Subcritical routes disconnected from secondary laminar flows have also been identified. 47.20.Lz, 47.27.Cn A comprehensive understanding of turbulent phenomena necessarily requires a previous explanation of the mechanisms that mediate between laminar and fully disordered fluid motion. One of the most challenging shear flow problems is the understanding of laminar-turbulent coexistence phenomena or intermittency, i.e., spatio-temporal coexistence between laminar and turbulent regions in a fluid flow. Canonical shear flows such as plane Couette flow between inertially countersliding parallel plates or pipe flow in a very long straight pipe of circular cross section exhibit localised turbulence as a prelude to fully developed turbulent flow [1][2][3][4][5][6]. Open shear flows share many common drawbacks when studying the long term behaviour of turbulent or intermittent regimes, since localised turbulent spots are often advected downstream and leave the domain. Computation of these flows usually assumes streamwise periodicity, overlooking the real boundary conditions at the entrance and exit of the domains and potentially leading to artificial interaction of the leading and trailing edges of localised turbulent spots. A naturally streamwise-periodic problem such as the Taylor-Couette system between independently rotating concentric cylinders solves these difficulties. Furthermore, while transition in open shear flows is typically subcritical, i.e., bypassing linear stability, Taylor-Couette flow exhibits a huge variety of secondary supercritical steady, time periodic, or almost periodic laminar flows before an eventual transition to chaotic regimes [7]. This enables to study transition in a supercritical setting, along with degeneration into subcriticality. We refer the reader to standard monographs and references therein [8,9].Laminar-turbulent coexistence in Taylor-Couette flow was originally reported by Coles and Van Atta in the 1960s [10,11]. They observed interlaced laminar-turbulent helical patterns (see Fig. 1a) so called spiral turbulence or barber pole turbulence, according to Feynman [12]. This pattern has been studied experimentally by many authors later in the 1980s [7,13] and during the current decade [1,14]. Spiral turbulence, henceforth termed as SPT, may exhibit hysteretic subcritical behaviour, being sustained even in situations where linear theory predicts stability of the base laminar flow. Linear non-modal analysis has shown a strong correlation between the hysteretic ...

Recent numerical studies suggest that in pipe and related shear flows, the region of phase space separating laminar from turbulent motion is organized by a chaotic attractor, called an edge state, which mediates the transition process. We here confirm the existence of the edge state in laboratory experiments. We observe that it governs the dynamics during the decay of turbulence underlining its potential relevance for turbulence control. In addition we unveil two unstable traveling wave solutions underlying the experimental flow fields. This observation corroborates earlier suggestions that unstable solutions organize turbulence and its stability border. DOI: 10.1103/PhysRevLett.108.214502 PACS numbers: 47.27.Cn, 47.27.NÀ, 47.52.+j In most situations of practical interest fluid flows are turbulent. Often transition to turbulence occurs despite the linear stability of the laminar state [1,2] such as in flows through pipes, ducts or even in astrophysical Keplerian flows. In some other cases turbulence occurs well below the critical point given by linear instability analysis, such as in flows through channels. Moreover, it has been shown for these shear flows that the turbulent state has unstable characteristics [3][4][5][6][7] and that localized turbulent patches eventually decay back to laminar. That at higher Reynolds numbers turbulence is still the rule rather than the exception is due to its invasive nature which causes laminar gaps to be quickly consumed by adjacent turbulent domains [8,9]. The observation that localized turbulent domains are intrinsically unstable [3,4,10,11] offers prospects to control and relaminarize flows [12]. Such potential methods are of great practical interest because the drag in turbulent flows is significantly larger and this causes higher energy consumption and limits transport rates.From a dynamical point of view the stability boundary separating laminar from turbulent motion plays a key role in how flows transit to and from turbulence. This laminarturbulent boundary is highly convoluted and most likely possesses a fractal structure as shown in simulations [13]. Some signatures of this have also been observed in experiments [14]. Hence its complexity puts a complete description for transition in shear flows beyond reach in the foreseeable future. However, using a tracking method first proposed and applied to plane Poiseuille flow [15,16], it has been possible to compute phase-space trajectories on the laminar-turbulent boundary of pipe flow [17,18]. Surprisingly, the dynamics at this boundary, or edge, are organized by a single state: This so-called ''edge state'' [13] is a chaotic attractor within the edge, whereas in the full phase-space it is a repeller with a single unstable direction pointing towards turbulence on one side and towards laminar flow on the other.According to dynamical systems theory the disordered dynamics of turbulence as well as of its edge are organized around unstable solutions of the Navier-Stokes equations [19]. For pipe flow mainly traveling wave s...