2,221 research outputs found
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) ≈ U0(y) + Uc(y) cos(kz) + Us(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
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
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
Turbulent-laminar patterns in shear flows without walls
Turbulent-laminar intermittency, typically in the form of bands and spots, is
a ubiquitous feature of the route to turbulence in wall-bounded shear flows.
Here we study the idealised shear between stress-free boundaries driven by a
sinusoidal body force and demonstrate quantitative agreement between turbulence
in this flow and that found in the interior of plane Couette flow -- the region
excluding the boundary layers. Exploiting the absence of boundary layers, we
construct a model flow that uses only four Fourier modes in the shear direction
and yet robustly captures the range of spatiotemporal phenomena observed in
transition, from spot growth to turbulent bands and uniform turbulence. The
model substantially reduces the cost of simulating intermittent turbulent
structures while maintaining the essential physics and a direct connection to
the Navier-Stokes equations.
We demonstrate the generic nature of this process by introducing stress-free
equivalent flows for plane Poiseuille and pipe flows which again capture the
turbulent-laminar structures seen in transition.Comment: 13 pages, 9 figure
Universal continuous transition to turbulence in a planar shear flow
We examine the onset of turbulence in Waleffe flow -- the planar shear flow
between stress-free boundaries driven by a sinusoidal body force. By truncating
the wall-normal representation to four modes, we are able to simulate system
sizes an order of magnitude larger than any previously simulated, and thereby
to attack the question of universality for a planar shear flow. We demonstrate
that the equilibrium turbulence fraction increases continuously from zero above
a critical Reynolds number and that statistics of the turbulent structures
exhibit the power-law scalings of the (2+1)-D directed percolation universality
class
Specialization or Diversification? A Basic Policy Decision Confronting Economically Underdeveloped Countries
Paper delivered before the Historical Society of the Rice Institute on May 8, 195
Life History Analysis And Individual Differences In Humans: A Test Of The Application Of An R/k Analysis
A number of psychologists have begun to apply principles from evolutionary biology to their domains in an attempt to provide an integrated model of human behaviour. One such application, a theory based on the r/K continuum of reproductive strategies, postulates that a single heritable reproductive dimension underlies a broad range of individual differences in life histories, physiological functioning, and social behaviour (Rushton, 1985). The two experiments reported here provide a test of this theory. Experiment 1 was conducted to determine if such a reproductive dimension exists and the extent of its heritability. Numerous reproductive and other variables from a sample of 7620 twins were subjected to principal component analyses. The obtained solutions for both male and female twins revealed factors which resembled the proposed dimension. Comparisons of aggregated standard scores for monozygotic twin pairs and same-sexed dizygotic pairs indicated that the dimension was moderately heritable. The second experiment replicated and extended the first study using a broader range of variables from a sample of 250 university undergraduates. In both experiments, strongest support for the theory was found for the physiological and sexual-reproductive variables, with the findings for personality variables being less supportive. The results were generally interpreted as providing initial support for the application of r/K theory to humans
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