William R. Young

Bio: William R. Young is an academic researcher from Brunel University London. The author has contributed to research in topics: Geostrophic wind & Internal wave. The author has an hindex of 48, co-authored 192 publications receiving 7916 citations. Previous affiliations of William R. Young include École Normale Supérieure & University of Birmingham.

Homogenization of potential vorticity in planetary gyres

Abstract: The mean circulation of planetary fluids tends to develop uniform potential vorticity q in regions where closed time-mean streamlines or closed isolines of mean potential vorticity exist. This state is established in statistically steady flows by geostrophic turbulence or by wave-induced potential-vorticity flux. At the outer edge of the closed contours the expelled gradients of q are concentrated. Beyond this transition lies motionless fluid, or a different flow regime in which the planetary gradient of q may be dominant. The homogenized regions occur where direct forcing by external stress or heating within the closed isoline is negligible, upon the potential-density surface under consideration. In the stably stratified ocean such regions are found at depths greater than those of direct wind-induced stress or penetrative cooling. In ‘channel’ models of the atmosphere we again find constant q when mesoscale eddies cause the dominant potential-vorticity flux. In the real atmosphere the results here can apply only where internal heating is negligible. The derivations given here build upon the Prandtl–Batchelor theorem, which applies to non-rotating, steady two-dimensional flow. Supporting evidence is found in numerical circulation models and oceanic observations.

How rapidly is a passive scalar mixed within closed streamlines

Abstract: The homogenization of a passive ‘tracer’ in a flow with closed mean streamlines occurs in two stages: first, a rapid phase dominated by shear-augmented diffusion over a time ≈P1/3(L/U), where the Peclet number P=LU/κ (L,U and κ are lengthscale, velocity scale and diffusivity), in which initial values of the tracer are replaced by their (generalized) average about a streamline; second, a slow phase requiring the full diffusion time ≈ L2/κ. The diffusion problem for the second phase, where tracer isopleths are held to streamlines by shear diffusion, involves a generalized diffusivity which is proportional to κ, but exceeds it if the streamlines are not circular. Expressions are also given for flow fields that are oscillatory rather than steady.

Modes of optical waveguides

Abstract: A simple method is presented for finding the modes on those optical waveguides with a cladding refractive index that differs only slightly from the refractive index of the core. The method applies to waveguides of arbitrary refractive index profile, arbitrary number of propagating modes, and arbitrary cross section. The resulting modal fields and their progagation constants display the polarization properties of the waveguide contained within the ∇ ∊ term of the vector wave equation. Examples include modes on waveguides with circular symmetry and waveguides with two preferred axes of symmetry, e.g., an elliptical core. Only a minute amount of eccentricity is necessary for the well-known LP modes to be stable on an elliptical core, while the circle modes couple power among themselves.

Evolution of vortex statistics in two-dimensional turbulence.

Abstract: Freely evolving two-dimensional turbulence is dominated by coherent vortices. The density of these vortices decays in time as \ensuremath{\rho}\ensuremath{\sim}${\mathit{t}}^{\mathrm{\ensuremath{-}}\ensuremath{\xi}}$ with \ensuremath{\xi}\ensuremath{\approxeq}0.75. A new scaling theory is proposed which expresses all statistical properties in terms of \ensuremath{\xi}. Thus the average circulation of the vortices increases as ${\mathit{t}}^{\ensuremath{\xi}/2}$ and their average radius as ${\mathit{t}}^{\ensuremath{\xi}/4}$. The total energy is constant, the enstrophy decreases as ${\mathit{t}}^{\mathrm{\ensuremath{-}}\ensuremath{\xi}/2}$, and the vorticity kurtosis increases as ${\mathit{t}}^{\ensuremath{\xi}/2}$. These results are supported both by numerical simulations of the fluid equations and by solutions of a modified point-vortex model.

Using Multivariate Statistics

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Microfluidics: Fluid physics at the nanoliter scale

Abstract: Microfabricated integrated circuits revolutionized computation by vastly reducing the space, labor, and time required for calculations. Microfluidic systems hold similar promise for the large-scale automation of chemistry and biology, suggesting the possibility of numerous experiments performed rapidly and in parallel, while consuming little reagent. While it is too early to tell whether such a vision will be realized, significant progress has been achieved, and various applications of significant scientific and practical interest have been developed. Here a review of the physics of small volumes (nanoliters) of fluids is presented, as parametrized by a series of dimensionless numbers expressing the relative importance of various physical phenomena. Specifically, this review explores the Reynolds number Re, addressing inertial effects; the Peclet number Pe, which concerns convective and diffusive transport; the capillary number Ca expressing the importance of interfacial tension; the Deborah, Weissenberg, and elasticity numbers De, Wi, and El, describing elastic effects due to deformable microstructural elements like polymers; the Grashof and Rayleigh numbers Gr and Ra, describing density-driven flows; and the Knudsen number, describing the importance of noncontinuum molecular effects. Furthermore, the long-range nature of viscous flows and the small device dimensions inherent in microfluidics mean that the influence of boundaries is typically significant. A variety of strategies have been developed to manipulate fluids by exploiting boundary effects; among these are electrokinetic effects, acoustic streaming, and fluid-structure interactions. The goal is to describe the physics behind the rich variety of fluid phenomena occurring on the nanoliter scale using simple scaling arguments, with the hopes of developing an intuitive sense for this occasionally counterintuitive world.

Stochastic Processes in Physics and Chemistry

Abstract: N G van Kampen 1981 Amsterdam: North-Holland xiv + 419 pp price Dfl 180 This is a book which, at a lower price, could be expected to become an essential part of the library of every physical scientist concerned with problems involving fluctuations and stochastic processes, as well as those who just enjoy a beautifully written book. It provides an extensive graduate-level introduction which is clear, cautious, interesting and readable.

Chaotic Mixer for Microchannels

Abstract: It is difficult to mix solutions in microchannels. Under typical operating conditions, flows in these channels are laminar—the spontaneous fluctuations of velocity that tend to homogenize fluids in turbulent flows are absent, and molecular diffusion across the channels is slow. We present a passive method for mixing streams of steady pressure-driven flows in microchannels at low Reynolds number. Using this method, the length of the channel required for mixing grows only logarithmically with the Pe «clet number, and hydrodynamic dispersion along the channel is reduced relative to that in a simple, smooth channel. This method uses bas-relief structures on the floor of the channel that are easily fabricated with commonly used methods of planar lithography.