Eddy genesis and manipulation in plane laminar shear flow

Eddy formation and presence in a plane laminar shear flow configuration consisting of two infinitely long plates orientated parallel to each other is investigated theoretically. The upper plate, which is planar, drives the flow; the lower one has a sinusoidal profile and is fixed. The governing equations are solved via a full finite element formulation for the general case and semi-analytically at the Stokes flow limit. The effects of varying geometry (involving changes in the mean plate separation or the amplitude and wavelength of the lower plate) and inertia are explored separately. For Stokes flow and varying geometry, excellent agreement between the two methods of solution is found. Of particular interest with regard to the flow structure is the importance of the clearance that exists between the upper plate and the tops of the corrugations forming the lower one. When the clearance is large, an eddy is only present at sufficiently large amplitudes or small wavelengths. However, as the plate clearance is reduced, a critical value is found which triggers the formation of an eddy in an otherwise fully attached flow for any finite amplitude and arbitrarily large wavelength. This is a precursor to the primary eddy to be expected in the lid-driven cavity flow which is formed in the limit of zero clearance between the plates. The influence of the flow driving mechanism is assessed by comparison with corresponding solutions for the case of gravity-driven fluid films flowing over an undulating substrate. When inertia is present, the flow generally becomes asymmetrical. However, it is found that for large mean plate separations the flow local to the lower plate becomes effectively decoupled from the inertia dominated overlying flow if the wavelength of the lower plate is sufficiently small. In such cases the local flow retains its symmetry. A local Reynolds number based on the wavelength is shown to be useful in characterising these large-gap flows. As the mean plate separation is reduced, the form of the asymmetry caused by inertia changes, and becomes strongly dependent on the plate separation. For lower plate wavelengths which do not exhibit a cinematically induced secondary eddy, an inertially induced secondary eddy can be created if the mean plate separation is sufficiently small and the global Reynolds number sufficiently large

Elastic turbulence in von Karman swirling flow between two disks

We discuss the role of elastic stress in the statistical properties of elastic turbulence, realized by the flow of a polymer solution between two disks. The dynamics of the elastic stress are analogous to those of a small scale fast dynamo in magnetohydrodynamics, and to those of the turbulent advection of a passive scalar in the Batchelor regime. Both systems are theoretically studied in literature, and this analogy is exploited to explain the statistical properties, the flow structure, and the scaling observed experimentally. Several features of elastic turbulence are confirmed experimentally and presented in this paper: (i) saturation of the rms of the vorticity and of velocity gradients in the bulk, leading to the saturation of the elastic stress; (ii) large rms of the velocity gradients in the boundary layer, linearly growth with Wi; (iii) skewed PDFs of the injected power, with exponential tails, which indicate intermittency; PDF of the acceleration exhibit well-pronounced exponential tails too; (iv) a new length scale, i.e the thickness of the boundary layer, as measured from the profile of the rms of the velocity gradient, is found to be relevant and much smaller than the vessel size; (v) the scaling of the structure functions of the vorticity, velocity gradients, and injected power is found to be the same as that of a passive scalar advected by an elastic turbulent velocity field.Comment: submitted to Physics of Fluids; 31 pages, 29 figures (resolution reduced to screen quality

Utilization of granular solidification during terrestrial locomotion of hatchling sea turtles

Biological terrestrial locomotion occurs on substrate materials with a range of rheological behaviour, which can affect limb-ground interaction, locomotor mode and performance. Surfaces like sand, a granular medium, can display solid or fluid-like behaviour in response to stress. Based on our previous experiments and models of a robot moving on granular media, we hypothesize that solidification properties of granular media allow organisms to achieve performance on sand comparable to that on hard ground. We test this hypothesis by performing a field study examining locomotor performance (average speed) of an animal that can both swim aquatically and move on land, the hatchling Loggerhead sea turtle (Caretta caretta). Hatchlings were challenged to traverse a trackway with two surface treatments: hard ground (sandpaper) and loosely packed sand. On hard ground, the claw use enables no-slip locomotion. Comparable performance on sand was achieved by creation of a solid region behind the flipper that prevents slipping. Yielding forces measured in laboratory drag experiments were sufficient to support the inertial forces at each step, consistent with our solidification hypothesis

Longitudinal flow evolution and turbulence structure of dynamically similar, sustained, saline density and turbidity currents

Experimental results are presented concerning flow evolution and turbulence structure of sustained saline and turbidity flows generated on 0°, 3°, 6°, and 9° sloping ramps that terminate abruptly onto a horizontal floor. Two-component velocity and current density were measured with an ultrasonic Doppler velocity profiler and siphon sampler on the slope, just beyond the slope break and downstream on the horizontal floor. Three main factors influence longitudinal flow evolution and turbulence structure: sediment transport and sedimentation, slope angle, and the presence of a slope break. These controls interact differently depending on flow type. Sediment transport is accompanied by an inertial fluid reaction that enhances Reynolds stresses in turbidity flows. Thus turbidity flows mix more vigorously than equivalent saline density flows. For saline flows, turbulent kinetic energy is dependent on slope, and rapid deceleration occurs on the horizontal floor. For turbidity flows, normalized turbulent kinetic energy increases downstream, and mean streamwise deceleration is reduced compared with saline flows. The slope break causes mean bed-normal velocity of turbidity flows to become negative and have a gentler gradient compared with other locations. A reduction of peak Reynolds normal stress in the bed-normal direction is accompanied by an increase in turbulent accelerations across the rest of the flow thickness. Thus the presence of particles acts to increase Reynolds normal stresses independently of gradients of mean velocity, and sediment transport increases across the break in slope. The experiments illustrate that saline density currents may not be good dynamic analogues for natural turbidity currents

Simple Viscous Flows: from Boundary Layers to the Renormalization Group

The seemingly simple problem of determining the drag on a body moving through a very viscous fluid has, for over 150 years, been a source of theoretical confusion, mathematical paradoxes, and experimental artifacts, primarily arising from the complex boundary layer structure of the flow near the body and at infinity. We review the extensive experimental and theoretical literature on this problem, with special emphasis on the logical relationship between different approaches. The survey begins with the developments of matched asymptotic expansions, and concludes with a discussion of perturbative renormalization group techniques, adapted from quantum field theory to differential equations. The renormalization group calculations lead to a new prediction for the drag coefficient, one which can both reproduce and surpass the results of matched asymptotics

Elastic turbulence in curvilinear flows of polymer solutions

Following our first report (A. Groisman and V. Steinberg, \sl Nature $\bf 405$, 53 (2000)) we present an extended account of experimental observations of elasticity induced turbulence in three different systems: a swirling flow between two plates, a Couette-Taylor (CT) flow between two cylinders, and a flow in a curvilinear channel (Dean flow). All three set-ups had high ratio of width of the region available for flow to radius of curvature of the streamlines. The experiments were carried out with dilute solutions of high molecular weight polyacrylamide in concentrated sugar syrups. High polymer relaxation time and solution viscosity ensured prevalence of non-linear elastic effects over inertial non-linearity, and development of purely elastic instabilities at low Reynolds number (Re) in all three flows. Above the elastic instability threshold, flows in all three systems exhibit features of developed turbulence. Those include: (i)randomly fluctuating fluid motion excited in a broad range of spatial and temporal scales; (ii) significant increase in the rates of momentum and mass transfer (compared to those expected for a steady flow with a smooth velocity profile). Phenomenology, driving mechanisms, and parameter dependence of the elastic turbulence are compared with those of the conventional high Re hydrodynamic turbulence in Newtonian fluids.Comment: 23 pages, 26 figure

Temperature dependence of bulk viscosity in water using acoustic spectroscopy

Despite its fundamental role in the dynamics of compressible fluids, bulk viscosity has received little experimental attention and there remains a paucity of measured data. Acoustic spectroscopy provides a robust and accurate approach to measuring this parameter. Working from the Navier-Stokes model of a compressible fluid one can show that the bulk viscosity makes a significant and measurable contribution to the frequency-squared acoustic attenuation. Here we employ this methodology to determine the bulk viscosity of Millipore water over a temperature range of 7 to 50 degrees Celsius. The measured attenuation spectra are consistent with the theoretical predictions, while the bulk viscosity of water is found to be approximately three times larger than its shear counterpart, reinforcing its significance in acoustic propagation. Moreover, our results demonstrate that this technique can be readily and generally applied to fluids to accurately determine their temperature dependent bulk viscosities.Comment: 7 pages, 4 figures. Proceedings of the Anglo-French Physical Acoustics Conference, January 201

Gas dynamics in high-luminosity polarized He-3 targets using diffusion and convection

The dynamics of the movement of gas is discussed for two-chambered polarized He-3 target cells of the sort that have been used successfully for many electron scattering experiments. A detailed analysis is presented showing that diffusion is a limiting factor in target performance, particularly as these targets are run at increasingly high luminosities. Measurements are presented on a new prototype polarized He-3 target cell in which the movement of gas is due largely to convection instead of diffusion. NMR tagging techniques have been used to visualize the gas flow, showing velocities along a cylindrically-shaped target of between 5-80 cm/min. The new target design addresses one of the principle obstacles to running polarized He-3 targets at substantially higher luminosities while simultaneously providing new flexibility in target geometry.Comment: First revision: 14 pages, 9 figures, submitted to Phys. Rev. C. We have shortened our discussion of the limitations inherent in various historical He-3 targets, and we have added a discussion exploring the optimal performance that can be expected from a suitably modified target based on diffusion-based mixing. A reference (Jones et. al.) was added. The results we present have not change

Dynamics and Excitation of Radio Galaxy Emission-Line Regions - I. PKS 2356-61

Results are presented from a programme of detailed longslit spectroscopic observations of the extended emission-line region (EELR) associated with the powerful radio galaxy PKS 2356-61. The observations have been used to construct spectroscopic datacubes, which yield detailed information on the spatial variations of emission-line ratios across the EELR, together with its kinematic structure. We present an extensive comparison between the data and results obtained from the MAPPINGS II shock ionization code, and show that the physical properties of the line-emitting gas, including its ionization, excitation, dynamics and overall energy budget, are entirely consistent with a scenario involving auto-ionizing shocks as the dominant ionization mechanism. This has the advantage of accounting for the observed EELR properties by means of a single physical process, thereby requiring less free parameters than the alternative scheme involving photoionization by radiation from the active nucleus. Finally, possible mechanisms of shock formation are considered in the context of the dynamics and origin of the gas, specifically scenarios involving infall or accretion of gas during an interaction between the host radio galaxy and a companion galaxy.Comment: 35 pages, LaTeX, uses aas2pp4.sty file, includes 9 PostScript figures. Two additional colour plates are available from the authors upon request. Accepted for publication in the Astrophysical Journa