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Dwight Barkley

Publications and source records attributed to Dwight Barkley.

27 records · Page 2Linked to original sources
arXiv2011

Simplifying the complexity of pipe flow

Transitional pipe flow is modeled as a one-dimensional excitable and bistable medium. Models are presented in two variables, turbulence intensity and mean shear, that evolve according to established properties of transitional turbulence. A continuous model captures the essence of the puff-slug transition as a change from excitability to bistability. A discrete model, that additionally incorporates turbulence locally as a chaotic repeller, reproduces almost all large-scale features of transitional pipe flow. In particular it captures metastable localized puffs, puff splitting, slugs, a continuous transition to sustained turbulence via spatiotemporal intermittency (directed percolation), and a subsequent increase in turbulence fraction towards uniform, featureless turbulence.

physics.flu-dyn↗
arXiv2010

Convective instability in inhomogeneous media: impulse response in the subcritical cylinder wake

We study experimentally the impulse response of a cylinder wake below the critical Reynolds number of the Bénard-von Kármán instability. In this subcritical regime, a localized inhomogeneous region of convective instability exists which causes initial perturbations to be transiently amplified. The aim of this work is to quantify the evolution resulting from this convective instability using two-dimensional particle image velocimetry in a hydrodynamic tunnel experiment. The velocity fields allow us to describe the evolution of wave packets in terms of two control parameters: the Reynolds number and the magnitude of the imposed perturbation. The temporal evolution of energy exhibits a transient algebraic growth at short times followed by an exponential decay.

physics.flu-dyn↗
arXiv2010

Alternative Stable Scroll Waves and Conversion of Autowave Turbulence

Rotating spiral and scroll waves (vortices) are investigated in the FitzHugh-Nagumo model of excitable media. The focus is on a parameter region in which there exists bistability between alternative stable vortices with distinct periods. Response Functions are used to predict the filament tension of the alternative scrolls and it is shown that the slow-period scroll has negative filament tension, while the filament tension of the fast-period scroll changes sign within a hysteresis loop. The predictions are confirmed by direct simulations. Further investigations show that the slow-period scrolls display features similar to delayed after-depolarisation (DAD) and tend to develop into turbulence similar to Ventricular Fibrillation (VF). Scrolls with positive filament tension collapse or stabilize, similar to monomorphic Ventricular Tachycardia (VT). Perturbations, such as boundary interaction or shock stimulus, can convert the vortex with negative filament tension into the vortex with positive filament tension. This may correspond to transition from VF to VT unrelated to pinning.

nlin.PS↗
arXiv2007

Mean flow of turbulent-laminar patterns in plane Couette flow

A turbulent-laminar banded pattern in plane Couette flow is studied numerically. This pattern is statistically steady, is oriented obliquely to the streamwise direction, and has a very large wavelength relative to the gap. The mean flow, averaged in time and in the homogeneous direction, is analysed. The flow in the quasi-laminar region is not the linear Couette profile, but results from a non-trivial balance between advection and diffusion. This force balance yields a first approximation to the relationship between the Reynolds number, angle, and wavelength of the pattern. Remarkably, the variation of the mean flow along the pattern wavevector is found to be almost exactly harmonic: the flow can be represented via only three cross-channel profiles as U(x,y,z) = U_0(y) + U_c(y) cos(kz) + U_s(y) sin(kz). A model is formulated which relates the cross-channel profiles of the mean flow and of the Reynolds stress. Regimes computed for a full range of angle and Reynolds number in a tilted rectangular periodic computational domain are presented. Observations of regular turbulent-laminar patterns in other shear flows -- Taylor-Couette, rotor-stator, and plane Poiseuille -- are compared.

physics.flu-dyn↗
arXiv2005

Turbulent-laminar patterns in plane Couette flow

Regular patterns of turbulent and laminar fluid motion arise in plane Couette flow near the lowest Reynolds number for which turbulence can be sustained. We study these patterns using an extension of the minimal flow unit approach to simulations of channel flows pioneered by Jimenez and Moin. In our case, computational domains are of minimal size in only two directions. The third direction is taken to be large. Furthermore, the long direction can be tilted at any prescribed angle to the streamwise direction. We report on different patterned states observed as a function of Reynolds number, imposed tilt, and length of the long direction. We compare our findings to observations in large aspect-ratio experiments.

physics.flu-dyn↗
arXiv2004

Computational Study of Turbulent-Laminar Patterns in Couette Flow

Turbulent-laminar patterns near transition are simulated in plane Couette flow using an extension of the minimal flow unit methodology. Computational domains are of minimal size in two directions but large in the third. The long direction can be tilted at any prescribed angle to the streamwise direction. Three types of patterned states are found and studied: periodic, localized, and intermittent. These correspond closely to observations in large aspect ratio experiments.

physics.flu-dyn↗
arXiv2003

Symmetry breaking and turbulence in perturbed plane Couette flow

Perturbed plane Couette flow containing a thin spanwise-oriented ribbon undergoes a subcritical bifurcation at Re = 230 to a steady 3D state containing streamwise vortices. This bifurcation is followed by several others giving rise to a fascinating series of stable and unstable steady states of different symmetries and wavelengths. First, the backwards-bifurcating branch reverses direction and becomes stable near Re = 200. Then, the spanwise reflection symmetry is broken, leading to two asymmetric branches which are themselves destabilized at Re = 420. Above this Reynolds number, time evolution leads first to a metastable state whose spanwise wavelength is halved and then to complicated time-dependent behavior. These features are in agreement with experiments.

physics.flu-dyn↗
arXiv2003

Stability analysis of perturbed plane Couette flow

Plane Couette flow perturbed by a spanwise oriented ribbon, similar to a configuration investigated experimentally at the Centre d'Etudes de Saclay, is investigated numerically using a spectral-element code. 2D steady states are computed for the perturbed configuration; these differ from the unperturbed flows mainly by a region of counter-circulation surrounding the ribbon. The 2D steady flow loses stability to 3D eigenmodes at Re = 230, beta = 1.3 for rho = 0.086 and Re = 550, beta = 1.5 for rho = 0.043, where Re is the Reynolds number, beta is the spanwise wavenumber and rho is the half-height of the ribbon. For rho = 0.086, the bifurcation is determined to be subcritical by calculating the cubic term in the normal form equation from the timeseries of a single nonlinear simulation; steady 3D flows are found for Re as low as 200. The critical eigenmode and nonlinear 3D states contain streamwise vortices localized near the ribbon, whose streamwise extent increases with Re. All of these results agree well with experimental observations.

physics.flu-dyn↗