arXiv subjects

Stephen Childress

Publications and source records attributed to Stephen Childress.

9 recordsLinked to original sources

arXiv2021

Flow rectification in loopy network models of bird lungs

We demonstrate flow rectification, valveless pumping or AC-to-DC conversion in macroscale fluidic networks with loops. Inspired by the unique anatomy of bird lungs and the phenomenon of directed airflow throughout the respiration cycle, we hypothesize, test and validate that multi-loop networks exhibit persistent circulation or DC flows when subject to oscillatory or AC forcing at high Reynolds numbers. Experiments reveal that disproportionately stronger circulation is generated for higher frequencies and amplitudes of the imposed oscillations, and this nonlinear response is corroborated by numerical simulations. Visualizations show that flow separation and vortex shedding at network junctions serve the valving function of directing current with appropriate timing in the oscillation cycle. These findings suggest strategies for controlling inertial flows through network topology and junction connectivity.

physics.flu-dyn↗

arXiv2019

A filamentary cascade model of the inertial range

This paper develops a simple model of the inertial range of turbulent flow, based on a cascade of vortical filaments. A binary branching structure is proposed, involving the splitting of filaments at each step into pairs of daughter filaments with differing properties, in effect two distinct simultaneous cascades. Neither of these cascades has the Richardson-Kolmogorov exponent of 1/3. This bimodal structure is also different from bifractal models as vorticity volume is conserved. If cascades are assumed to be initiated continuously and throughout space we obtain a model of the inertial range of stationary turbulence. We impose the constraint associated with Kolmogorov's four-fifths law and then adjust the splitting to achieve good agreement with the observed structure exponents $ζ_p$. The presence of two elements to the cascade is responsible for the nonlinear dependence of $ζ_p$ upon $p$. A single cascade provides a model for the initial-value problem of the Navier--Stokes equations in the limit of vanishing viscosity. To simulate this limit we let the cascade continue indefinitely, energy removal occurring in the limit. We are thus able to compute the decay of energy in the model.

physics.flu-dyn↗

arXiv2017

Eroding dipoles and vorticity growth for Euler flows in $ \scriptstyle{\mathbb{R}}^3$: The hairpin geometry as a model for finite-time blowup

A theory of an eroding "hairpin" vortex dipole structure in three dimensions is developed, extending our previous study of an axisymmetric eroding dipole without swirl. The hairpin is here similarly proposed as a model to produce large "self-stretching" of vorticity, with the possibility of finite-time blow-up. We derive a system of partial differential equations of "generalized" form, involving contour averaging of a locally two-dimensional Euler flow. We do not attempt here to solve the system exactly, but point out that non-existence of physically acceptable solutions would most probably be a result of the axial flow. Because of the axial flow the vorticity distribution within the dipole eddies is no longer of the simple Sadovskii type (vorticity constant over a cross-section) obtained in the axisymmetric problem. Thus the solution of the system depends upon the existence of a larger class of propagating two-dimensional dipoles. The hairpin model is obtained by formal asymptotic analysis. As in the axisymmetric problem a local transformation to "shrinking" coordinates is introduced, but now in a self-similar form appropriate to the study of a possible finite-time singularity. We discuss some properties of the model, including a study of the helicity and a first step in iterating toward a solution from the Sadovskii structure. We also present examples of two-dimensional propagating dipoles not previously studied, which have a vorticity profile consistent with our model. Although no rigorous results can be given, and analysis of the system is only partial, the formal calculations are consistent with the possibility of a finite time blowup of vorticity at a point of vanishing circulation of the dipole eddies, but depending upon the existence of the necessary two-dimensional propagating dipole.

physics.flu-dyn↗

arXiv2015

Eroding dipoles and vorticity growth for Euler flows in $ \scriptstyle{\mathbb{R}}^3$ I. Axisymmetric flow without swirl

A review of analyses based upon anti-parallel vortex structures suggests that structurally stable vortex structures with eroding circulation may offer a path to the study of rapid vorticity growth in solutions of Euler's equations in $ \scriptstyle{\mathbb{R}}^3$. We examine here the possible formation of such a structure in axisymmetric flow without swirl, leading to maximal growth of vorticity as $t^{4/3}$. Our study suggests that the optimizing flow giving the $t^{4/3}$ growth mimics an exact solution of Euler's equations representing an eroding toroidal vortex dipole which locally conserves kinetic energy. The dipole cross-section is a perturbation of the classical Sadovskii dipole having piecewise constant vorticity, which breaks the symmetry of closed streamlines. The structure of this perturbed Sadovskii dipole is analyzed asymptotically at large times, and its predicted properties are verified numerically.

physics.flu-dyn↗

arXiv2012

A model for singularity formation in three-dimensional Euler and Navier-Stokes flows

We present a formal, approximate model for singularity formation in classical fluid dynamics in three dimensions. The construction utilizes an approximation of local two-dimensionality to study an anti-parallel hairpin vortex structure with a cross-section equivalent to the 2D Chaplygin-Lamb dipole vortex. The model exhibits a finite time Euler singularity at an isolated point, with only finite local stretching of vortex lines. The model also suggests an associated Navier-Stokes problem, which exhibits a finite-time point singularity, provided that a Reynolds number is sufficiently large. The singularities are compatible with both the BKM [1] and CF[2] conditions. The vorticity support is infinite in volume but the singularity forms as a result of local processes requiring only finite energy input.

math-ph↗

arXiv2010

Stirring by squirmers

We analyse a simple 'Stokesian squirmer' model for the enhanced mixing due to swimming micro-organisms. The model is based on a calculation of Thiffeault & Childress [Physics Letters A, 374, 3487 (2010), arXiv:0911.5511], where fluid particle displacements due to inviscid swimmers are added to produce an effective diffusivity. Here we show that for the viscous case the swimmers cannot be assumed to swim an infinite distance, even though their total mass displacement is finite. Instead, the largest contributions to particle displacement, and hence to mixing, arise from random changes of direction of swimming and are dominated by the far-field stresslet term in our simple model. We validate the results by numerical simulation. We also calculate nonzero Reynolds number corrections to the effective diffusivity. Finally, we show that displacements due to randomly-swimming squirmers exhibit PDFs with exponential tails and a short-time superdiffusive regime, as found previously by several authors. In our case, the exponential tails are due to 'sticking' near the stagnation points on the squirmer's surface.

physics.flu-dyn↗

arXiv2010

Stirring by swimming bodies

We consider the stirring of an inviscid fluid caused by the locomotion of bodies through it. The swimmers are approximated by non-interacting cylinders or spheres moving steadily along straight lines. We find the displacement of fluid particles caused by the nearby passage of a swimmer as a function of an impact parameter. We use this to compute the effective diffusion coefficient from the random walk of a fluid particle under the influence of a distribution of swimming bodies. We compare with the results of simulations. For typical sizes, densities and swimming velocities of schools of krill, the effective diffusivity in this model is five times the thermal diffusivity. However, we estimate that viscosity increases this value by two orders of magnitude.

physics.flu-dyn↗

arXiv2009

Vortex shedding and hovering of a rigid body in an oscillating flow

The fluid dynamics video shows rigid, spatially asymmetric bodies interacting with oscillating background flows. A free rigid object, here a hollow "pyramid," can hover quite stably against gravity in the oscillating airflow with a zero mean, when its peak speed is sufficiently high. We further show in shadowgraph imaging how this asymmetric body sheds vortices in such an unsteady flow, thus enabling the body to "ratchet" itself through the background flow.

physics.flu-dyn↗

arXiv2003

Chaotic Mixing in a Torus Map

The advection and diffusion of a passive scalar is investigated for a map of the 2-torus. The map is chaotic, and the limit of almost-uniform stretching is considered. This allows an analytic understanding of the transition from a phase of constant scalar variance (for short times) to exponential decay (for long times). This transition is embodied in a short superexponential phase of decay. The asymptotic state in the exponential phase is an eigenfunction of the advection-diffusion operator, in which most of the scalar variance is concentrated at small scales, even though a large-scale mode sets the decay rate. The duration of the superexponential phase is proportional to the logarithm of the exponential decay rate; if the decay is slow enough then there is no superexponential phase at all.

nlin.CD↗