arXiv subjects

William R. Young

Publications and source records attributed to William R. Young.

23 records · Page 2Linked to original sources

arXiv2014

Refraction of swell by surface currents

Using recordings of swell from pitch-and-roll buoys, we have reproduced the classic observations of long-range surface wave propagation originally made by Munk et al. (1963) using a triangular array of bottom pressure measurements. In the modern data, the direction of the incoming swell fluctuates by about $\pm 10^\circ$ on a time scale of one hour. But if the incoming direction is averaged over the duration of an event then, in contrast with the observations by Munk et al. (1963), the sources inferred by great-circle backtracking are most often in good agreement with the location of large storms on weather maps of the Southern Ocean. However there are a few puzzling failures of great-circle backtracking e.g., in one case, the direct great-circle route is blocked by the Tuamoto Islands and the inferred source falls on New Zealand. Mirages like this occur more frequently in the bottom-pressure observations of Munk et al. (1963), where several inferred sources fell on the Antarctic continent. Using spherical ray tracing we investigate the hypothesis that the refraction of waves by surface currents produces the mirages. With reconstructions of surface currents inferred from satellite altimetry, we show that mesoscale vorticity significantly deflects swell away from great-circle propagation so that the source and receiver are connected by a bundle of many rays, none of which precisely follow a great circle. The $\pm 10^\circ$ directional fluctuations at the receiver result from the arrival of wave packets that have travelled along the different rays within this multipath. The occasional failure of great-circle backtracking, and the associated mirages, probably results from partial topographic obstruction of the multipath, which biases the directional average at the receiver.

physics.flu-dyn↗

arXiv2014

Mixing by microorganisms in stratified fluids

We examine the vertical mixing induced by the swimming of microorganisms at low Reynolds and Péclet numbers in a stably stratified ocean, and show that the global contribution of oceanic microswimmers to vertical mixing is negligible. We propose two approaches to estimating the mixing efficiency, $η$, or the ratio of the rate of potential energy creation to the total rate-of-working on the ocean by microswimmers. The first is based on scaling arguments and estimates $η$ in terms of the ratio between the typical organism size, $a$, and an intrinsic length scale for the stratified flow, $\ell = \left ( νκ/ N^2 \right )^{1/4}$, where $ν$ is the kinematic viscosity, $κ$ the diffusivity, and $N$ the buoyancy frequency. In particular, for small organisms in the relevant oceanic limit, $a / \ell \ll 1$, we predict the scaling $η\sim (a / \ell)^3$. The second estimate of $η$ is formed by solving the full coupled flow-stratification problem by modeling the swimmer as a regularized force dipole, and computing the efficiency numerically. Our computational results, which are examined for all ratios $a/\ell$, validate the scaling arguments in the limit $a / \ell \ll 1$ and further predict $η\approx 1.2 \left ( a / \ell \right )^3$ for vertical swimming and $η\approx 0.15 \left ( a / \ell \right )^3$ for horizontal swimming. These results, relevant for any stratified fluid rich in biological activity, imply that the mixing efficiency of swimming microorganisms in the ocean is at very most 8\% and is likely smaller by at least two orders of magnitude.

physics.flu-dyn↗

arXiv2011

The advection-condensation model and water vapour PDFs

The statistically steady humidity distribution resulting from an interaction of advection, modeled as an uncorrelated random walk of moist parcels on an isentropic surface, and a vapour sink, modeled as immediate condensation whenever the specific humidity exceeds a specified saturation humidity, is explored with theory and simulation. A source supplies moisture at the deep-tropical southern boundary of the domain, and the saturation humidity is specified as a monotonically decreasing function of distance from the boundary. The boundary source balances the interior condensation sink, so that a stationary spatially inhomogeneous humidity distribution emerges. An exact solution of the Fokker-Planck equation delivers a simple expression for the resulting probability density function (PDF) of the water vapour field and also of the relative humidity. This solution agrees completely with a numerical simulation of the process, and the humidity PDF exhibits several features of interest, such as bimodality close to the source and unimodality further from the source. The PDFs of specific and relative humidity are broad and non-Gaussian. The domain averaged relative humidity PDF is bimodal with distinct moist and dry peaks, a feature which we show agrees with middleworld isentropic PDFs derived from the ERA interim dataset.

physics.flu-dyn↗

arXiv2008

Energy-Enstrophy Stability of beta-plane Kolmogorov Flow with Drag

We develop a new nonlinear stability method, the Energy-Enstrophy (EZ) method, that is specialized to two-dimensional hydrodynamics; the method is applied to a beta-plane flow driven by a sinusoidal body force, and retarded by drag with damping time-scale mu^{-1}. The standard energy method (Fukuta and Murakami, J. Phys. Soc. Japan, 64, 1995, pp 3725) shows that the laminar solution is monotonically and globally stable in a certain portion of the (mu,beta)-parameter space. The EZ method proves nonlinear stability in a larger portion of the (mu,beta)-parameter space. And by penalizing high wavenumbers, the EZ method identifies a most strongly amplifying disturbance that is more physically realistic than that delivered by the energy method. Linear instability calculations are used to determine the region of the (mu,beta)-parameter space where the flow is unstable to infinitesimal perturbations. There is only a small gap between the linearly unstable region and the nonlinearly stable region, and full numerical solutions show only small transient amplification in that gap.

physics.flu-dyn↗

arXiv2007

Bounding biomass in the Fisher equation

The FKPP equation with a variable growth rate and advection by an incompressible velocity field is considered as a model for plankton dispersed by ocean currents. If the average growth rate is negative then the model has a survival-extinction transition; the location of this transition in the parameter space is constrained using variational arguments and delimited by simulations. The statistical steady state reached when the system is in the survival region of parameter space is characterized by integral constraints and upper and lower bounds on the biomass and productivity that follow from variational arguments and direct inequalities. In the limit of zero-decorrelation time the velocity field is shown to act as Fickian diffusion with an eddy diffusivity much larger than the molecular diffusivity and this allows a one-dimensional model to predict the biomass, productivity and extinction transitions. All results are illustrated with a simple growth and stirring model.

q-bio.PE↗