Stabilisation and drag reduction of pipe flows by flattening the base profile

Recent experimental observations (Kuehnen et al., 2018) have shown that flattening a turbulent streamwise velocity profile in pipe flow destabilises the turbulence so that the flow relaminarises. We show that a similar phenomenon exists for laminar pipe flow profiles in the sense that the nonlinear stability of the laminar state is enhanced as the profile becomes more flattened. Significant drag reduction is also observed for the turbulent flow when triggered by sufficiently large disturbances. The flattening is produced by an artificial body force designed to mimick a baffle used in the experiments of Kuehnen et al. (2018) and the nonlinear stability measured by the size of the energy of the initial perturbations needed to trigger transition. In order to make the latter computation more efficient, we examine how indicative the minimal seed for transition is in measuring transition thresholds. We first show that the minimal seed is relatively robust to base profile changes and spectral filtering. We then compare the (unforced) transition behaviour of the minimal seed with several forms of randomised initial conditions in the range of Reynolds numbers Re=2400 to 10000 and find that the energy of the minimal seed after the Orr and oblique phases of its evolution is close to that of a localised random disturbance. In this sense, the minimal seed at the end of the oblique phase can be regarded as a good proxy for typical disturbances (here taken to be the localised random ones) and is thus used as initial condition in the simulations with the body force. The enhanced nonlinear stability and drag reduction predicted in the present study are an encouraging first step in modelling the experiments of Kuehnen et al. and should motivate future developments to fully exploit the benefits of this promising direction for flow control

Transition to magnetorotational turbulence in Taylor-Couette flow with imposed azimuthal magnetic field

The magnetorotational instability (MRI) is thought to be a powerful source of turbulence and momentum transport in astrophysical accretion discs, but obtaining observational evidence of its operation is challenging. Recently, laboratory experi-ments of Taylor–Couette flow with externally imposed axial and azimuthal magnetic fields have revealed the kinematic and dynamic properties of the MRI close to the instability onset. While good agreement was found with linear stability analyses, little is known about the transition to turbulence and transport properties of the MRI. We here report on a numerical investigation of the MRI with an imposed azimuthal magnetic field. We show that the laminar Taylor–Couette flow becomes unstable to a wave rotating in the azimuthal direction and standing in the axial direction via a supercritical Hopf bifurcation. Subsequently, the flow features a catastrophic transition to spatio-temporal defects which is mediated by a subcritical subharmonic Hopf bifurcation. Our results are in qualitative agreement with the PROMISE ex-periment and dramatically extend their realizable parameter range. We find that as the Reynolds number increases defects accumulate and grow into turbulence, yet the momentum transport scales weakly

Dynamo action in a quasi-Keplerian Taylor-Couette flow

We numerically compute the flow of an electrically conducting fluid in a Taylor-Couette geometry where the rotation rates of the inner and outer cylinders satisfy \Omega_o/\Omega_i=(r_o/r_i)-3/2. In this quasi-Keplerian regime a non-magnetic system would be Rayleigh-stable for all Reynolds numbers Re, and the resulting purely azimuthal flow incapable of kinematic dynamo action for all magnetic Reynolds numbers Rm. For Re=10^4 and Rm=10^5 we demonstrate the existence of a finite-amplitude dynamo, whereby a suitable initial condition yields mutually sustaining turbulence and magnetic fields, even though neither could exist without the other. This dynamo solution results in significantly increased outward angular momentum transport, with the bulk of the transport being by Maxwell rather than Reynolds stresses

Designing a minimal baffle to destabilise turbulence in pipe flows

Motivated by the results of recent experiments (K\"uhnen et al., Flow Turb. Combust., vol. 100, 2018, pp. 919-943), we consider the problem of designing a baffle (an obstacle to the flow) to relaminarise turbulence in pipe flows. Modelling the baffle as a spatial distribution of linear drag $\mathbf{f}(\mathbf{x},t)=-\chi(\mathbf{x})\mathbf{u}_{tot}(\mathbf{x},t)$ within the flow ($\mathbf{u}_{tot}$ is the total velocity field and $\chi \ge 0$ a scalar field), two different optimisation problems are considered to design $\chi$ at a Reynolds number $Re=3000$. In the first, the smallest baffle defined in terms of a $L_1$ norm of $\chi$ is sought which minimises the viscous dissipation rate of the flow. In the second, a baffle which minimises the total energy consumption of the flow is treated. Both problems indicate that the baffle should be axisymmetric and radially localised near the pipe wall, but struggle to predict the optimal streamwise extent. A manual search finds an optimal baffle one radius long which is then used to study how the amplitude for relaminarisation varies with $Re$ up to $15\,000$. Large stress reduction is found at the pipe wall, but at the expense of an increased pressure drop across the baffle. Estimates are then made of the break even point downstream of the baffle where the stress reduction at the wall due to the relaminarised flow compensates for the extra drag produced by the baffle.EPSR

Non-local effects in the mean-field disc dynamo. II. Numerical and asymptotic solutions

The thin-disc global asymptotics are discussed for axisymmetric mean-field dynamos with vacuum boundary conditions allowing for non-local terms arising from a finite radial component of the mean magnetic field at the disc surface. This leads to an integro-differential operator in the equation for the radial distribution of the mean magnetic field strength, $Q(r)$ in the disc plane at a distance $r$ from its centre; an asymptotic form of its solution at large distances from the dynamo active region is obtained. Numerical solutions of the integro-differential equation confirm that the non-local effects act similarly to an enhanced magnetic diffusion. This leads to a wider radial distribution of the eigensolution and faster propagation of magnetic fronts, compared to solutions with the radial surface field neglected. Another result of non-local effects is a slowly decaying algebraic tail of the eigenfunctions outside the dynamo active region, $Q(r)\sim r^{-4}$, which is shown to persist in nonlinear solutions where $\alpha$-quenching is included. The non-local nature of the solutions can affect the radial profile of the regular magnetic field in spiral galaxies and accretion discs at large distances from the centre.Comment: Revised version, as accepted; Geophys. Astrophys. Fluid Dyna

The rise of fully turbulent flow

Over a century of research into the origin of turbulence in wallbounded shear flows has resulted in a puzzling picture in which turbulence appears in a variety of different states competing with laminar background flow. At slightly higher speeds the situation changes distinctly and the entire flow is turbulent. Neither the origin of the different states encountered during transition, nor their front dynamics, let alone the transformation to full turbulence could be explained to date. Combining experiments, theory and computer simulations here we uncover the bifurcation scenario organising the route to fully turbulent pipe flow and explain the front dynamics of the different states encountered in the process. Key to resolving this problem is the interpretation of the flow as a bistable system with nonlinear propagation (advection) of turbulent fronts. These findings bridge the gap between our understanding of the onset of turbulence and fully turbulent flows.Comment: 31 pages, 9 figure

Factor structure and construct validity of the Adult Social Care Outcomes Toolkit for Carers (ASCOT-Carer)

Background: The ASCOT-Carer is a self-report instrument designed to measure social care-related quality of life (SCRQoL). This article presents the psychometric testing and validation of the ASCOT-Carer four response-level interview (INT4) in a sample of unpaid carers of adults who receive publicly-funded social care services in England. Methods: Unpaid carers were identified through a survey of users of publicly-funded social care services in England. 387 carers completed a face-to-face or telephone interview. Data on variables hypothesised to be related to SCRQoL (for example, characteristics of the carer, cared-for person and care situation) and measures of carer experience, strain, health-related quality of life and overall QoL were collected. Relationships between these variables and overall SCRQoL score were evaluated through correlation, ANOVA and regression analysis to test the construct validity of the scale. Internal reliability was assessed using Cronbach’s alpha and feasibility by the number of missing responses. Results: The construct validity was supported by statistically significant relationships between SCRQoL and scores on instruments of related constructs, as well as with characteristics of the carer and care recipient in univariate and multivariate analyses. A Cronbach’s alpha of 0.87 (7 items) indicates that the internal reliability of the instrument is satisfactory and a low number of missing responses (<1%) indicates a high level of acceptance. Conclusions: The results provide evidence to support the construct validity, factor structure, internal reliability and feasibility of the ASCOT-Carer INT4 as an instrument for measuring social care-related quality of life of unpaid carers who care for adults with a variety of long-term conditions, disability or problems related to old age

Destabilizing turbulence in pipe flow

Turbulence is the major cause of friction losses in transport processes and it is responsible for a drastic drag increase in flows over bounding surfaces. While much effort is invested into developing ways to control and reduce turbulence intensities, so far no methods exist to altogether eliminate turbulence if velocities are sufficiently large. We demonstrate for pipe flow that appropriate distortions to the velocity profile lead to a complete collapse of turbulence and subsequently friction losses are reduced by as much as 90%. Counterintuitively, the return to laminar motion is accomplished by initially increasing turbulence intensities or by transiently amplifying wall shear. Since neither the Reynolds number (Re) nor the shear stresses decrease (the latter often increase), these measures are not indicative of turbulence collapse. Instead an amplification mechanism, measuring the interaction between eddies and the mean shear is found to set a threshold below which turbulence is suppressed beyond recovery

Functional Interactions between KCNE1 C-Terminus and the KCNQ1 Channel

The KCNE1 gene product (minK protein) associates with the cardiac KvLQT1 potassium channel (encoded by KCNQ1) to create the cardiac slowly activating delayed rectifier, IKs. Mutations throughout both genes are linked to the hereditary cardiac arrhythmias in the Long QT Syndrome (LQTS). KCNE1 exerts its specific regulation of KCNQ1 activation via interactions between membrane-spanning segments of the two proteins. Less detailed attention has been focused on the role of the KCNE1 C-terminus in regulating channel behavior. We analyzed the effects of an LQT5 point mutation (D76N) and the truncation of the entire C-terminus (Δ70) on channel regulation, assembly and interaction. Both mutations significantly shifted voltage dependence of activation in the depolarizing direction and decreased IKs current density. They also accelerated rates of channel deactivation but notably, did not affect activation kinetics. Truncation of the C-terminus reduced the apparent affinity of KCNE1 for KCNQ1, resulting in impaired channel formation and presentation of KCNQ1/KCNE1 complexes to the surface. Complete saturation of KCNQ1 channels with KCNE1-Δ70 could be achieved by relative over-expression of the KCNE subunit. Rate-dependent facilitation of K+ conductance, a key property of IKs that enables action potential shortening at higher heart rates, was defective for both KCNE1 C-terminal mutations, and may contribute to the clinical phenotype of arrhythmias triggered by heart rate elevations during exercise in LQTS mutations. These results support several roles for KCNE1 C-terminus interaction with KCNQ1: regulation of channel assembly, open-state destabilization, and kinetics of channel deactivation

Order-of-magnitude speedup for steady states and traveling waves via Stokes preconditioning in Channelflow and Openpipeflow

Steady states and traveling waves play a fundamental role in understanding hydrodynamic problems. Even when unstable, these states provide the bifurcation-theoretic explanation for the origin of the observed states. In turbulent wall-bounded shear flows, these states have been hypothesized to be saddle points organizing the trajectories within a chaotic attractor. These states must be computed with Newton's method or one of its generalizations, since time-integration cannot converge to unstable equilibria. The bottleneck is the solution of linear systems involving the Jacobian of the Navier-Stokes or Boussinesq equations. Originally such computations were carried out by constructing and directly inverting the Jacobian, but this is unfeasible for the matrices arising from three-dimensional hydrodynamic configurations in large domains. A popular method is to seek states that are invariant under numerical time integration. Surprisingly, equilibria may also be found by seeking flows that are invariant under a single very large Backwards-Euler Forwards-Euler timestep. We show that this method, called Stokes preconditioning, is 10 to 50 times faster at computing steady states in plane Couette flow and traveling waves in pipe flow. Moreover, it can be carried out using Channelflow (by Gibson) and Openpipeflow (by Willis) without any changes to these popular spectral codes. We explain the convergence rate as a function of the integration period and Reynolds number by computing the full spectra of the operators corresponding to the Jacobians of both methods.Comment: in Computational Modelling of Bifurcations and Instabilities in Fluid Dynamics, ed. Alexander Gelfgat (Springer, 2018