Liquid oil painting: Free and forced convection in an enclosure with mechanical and thermal forcing

A fluid dynamics video is linked to this article, which have been submitted to the Gallery of Fluid Motion as part of the 65th American Physical Society meeting of the Division of Fluid Dynamics, held in San Diego, California, USA, over 17-20 November 2012. The video serves to visualize flows generated in a rectangular enclosure that are subjected to both mechanical and thermal forcing through a common horizontal boundary. This system exhibits features consistent with either horizontal convection or lid-driven cavity flows depending on the ratio between thermal and mechanical stirring, and three different cases are visualized in the linked videos.Comment: 2 video files attached, 4 pages, 1 figure. This article is submitted accompanying a video submitted to the Gallery of Fluid Motion as part of the 65th Division of Fluid Dynamics meeting of the American Physical Society (17-20 November, San Diego, CA, USA

Non-linear growth of short-wave instabilities in a Batchelor vortex pair

Recent investigations have identified a variety of instability modes which may develop to enhance dispersion of co- and counter-rotating vortex pairs. This has application in the aviation industry, where an aircraft’s trailing vortices pose a significant hazard for other nearby aircraft. Batchelor vortices adopt the radial velocity field of Lamb – Oseen vortices, but with an axial velocity component through the core of the vortex, and are often used to represent vortices within an aircraft wake. Recently, the vortex swirl ratio of the Batchelor vortex pair has been identified as a key parameter which may be used to select the mode of instability which develops. Several modes have recently been identified via linear stability analysis. This study extends these prior investigations by considering the non-linear growth of the three-dimensional instabilities acting to disperse the vortex pair. Here, we validate prior linear instability investigations, and compare and contrast the relative ability of several instability modes to achieve improved vortex dispersion. The study has been conducted using a high-order, three-dimensional spectral element method to solve the timedependent incompressible Navier – Stokes equations. The study is conducted at a circulation Reynolds number of 2 800

Cylinders with Square Cross Section: Paths to Turbulence with Various Angles of Incidence

The path to turbulence in the wake of cylinders with square crosssection is investigated by means of direct numerical simulation, employing a two-dimensional spectral element method and Floquet linear stability analysis. The critical Reynolds number for the onset of the three-dimensional instability modes A, B, C and QP are reported for cylinder incidence angles between 0° and 45°. The Strouhal—Reynolds number relationship, and lift and drag coefficients are also investigated for these incidence angles. Reynolds numbers (based on the side length of the square) up to Re=300 are considered, and a significant variation in bifurcation scenarios are observed for the various incidence angles. At Reynolds numbers greater than Re ≈ 225 for an incidence angle of 45°, a previously unreported asymmetry is detected in the von Kármán vortex street. The cause of this asymmetry is investigated as it presents a possible alternative path to turbulence to that reported in the wakes of other bluff bodies

Trapping Ultracold Atoms in a Time-Averaged Adiabatic Potential

We report the first experimental realization of ultracold atoms confined in a time-averaged, adiabatic potential (TAAP). This novel trapping technique involves using a slowly oscillating ($\sim$ kHz) bias field to time-average the instantaneous potential given by dressing a bare magnetic potential with a high frequency ($\sim$ MHz) magnetic field. The resultant potentials provide a convenient route to a variety of trapping geometries with tunable parameters. We demonstrate the TAAP trap in a standard time-averaged orbiting potential trap with additional Helmholtz coils for the introduction of the radio frequency dressing field. We have evaporatively cooled 5 $\times 10^4$ atoms of $^{87}$Rb to quantum degeneracy and observed condensate lifetimes of over \unit[3]{s}.-Comment: 4 pages, 6 figure

Strain-rate development between a co-rotating Lamb-Oseen vortex pair of unequal strength.

To date, several investigations have considered the prospect of enhanced dissipation of a vortex pair due to elliptic (short wave) instabilities. Recent studies indicate that these modes have the potential to significantly reduce the time taken to dissipate vortex pairs. This has generated interest in the aviation industry, where aircraft trailing wakes pose a significant hazard for nearby aircraft. Of note, recent studies have indicated that the growth rate of these short-wave instability modes depends strongly on the strain-rate developed within the core of each vortex. This strainrate has been shown to develop naturally simply due to the presence of both vortices. Studies to date have concentrated on vortex pairs where each vortex has the same magnitude of circulation. We extend this by varying the circulation ratio of the two vortices; the circulation of one vortex is varied while the circulation of the other remains constant. The effect on the strain-rate which develops within each core is considered. Of particular interest are the time-scales involved in both the strain-rate development and in the twodimensional merging process, as sufficient time is required for short-wavelength instabilities to occur prior to merging for the process to successfully reduce dissipation time. A spectral-element method is used to conduct the DNS investigation at a circulation Reynolds number of ReΓ = 20,000

Linear stability of horizontal, laminar fully developed, quasi-two-dimensional liquid metal duct flow under a transverse magnetic field and heated from below

This study considers the linear stability of Poiseuille-Rayleigh-B\'enard flows, subjected to a transverse magnetic field to understand the instabilities that arise from the complex interaction between the effects of shear, thermal stratification and magnetic damping. This fundamental study is motivated in part by the desire to enhance heat transfer in the blanket ducts of nuclear fusion reactors. In pure MHD flows, the imposed transverse magnetic field causes the flow to become quasi-2D and exhibit disturbances that are localised to the horizontal walls. However, the vertical temperature stratification in Rayleigh-B\'enard flows feature convection cells that occupy the interior region and therefore the addition of this aspect provides an interesting point for investigation. The linearised governing equations are described by the \qtwod\ model proposed by Sommeria and Moreau (1982) which incorporates a Hartmann friction term, and the base flows are considered fully developed and 1D. The neutral stability curves for critical Reynolds and Rayleigh numbers, $Re_c$ and $Ra_c$, respectively, as functions of Hartmann friction parameter $H$ have been obtained over $10^{-2}\leq H\leq10^4$. Asymptotic trends are observed as $H\rightarrow\infty$ following $Re_c\propto H^{\,1/2}$ and $Ra_c\propto H$. The linear stability analysis reveals multiple instabilities which alter the flow both within the Shercliff boundary layers and the interior flow, with structures consistent with features from plane Poiseuille and Rayleigh-B\'enard flows

Subcritical transition to turbulence in quasi-two-dimensional shear flows

The transition to turbulence in ducts, pipes or other conduits is a crucial phenomenon. It determines the energy consumption and heat or mass exchange in countless processes: whether cooling circuits of heat exchangers, pipelines or chemical reactors to cite but a few. The transition occurs at relatively low flow rates as a response to perturbations exceeding a critical amplitude (such transitions are subcritical) through an intrinsically three-dimensional (3D) mechanism. However, fluid motion can be restricted to two dimensions, if it is stratified, subject to rapid rotation or intense magnetic fields, for example in rotating machines or in the liquid metal cooling circuits of nuclear fusion reactors. Subcritical turbulence has yet to be observed in 2D or quasi-2D flows, let alone a transition to it. Here we use stability analysis and direct numerical simulations on the example of a duct flow driven by the motion of its lateral walls to provide the first evidence of turbulence in subcritical quasi-2D shear flows. We further show that the scenario leading to turbulence mostly relies on the nonlinear dynamics of so-called Tollmien-Schlichting waves, rather than on perturbations experiencing fast, transient growth. Although the transition is subcritical, it cannot take place at such low flow rates as in 3D flows, because these waves are severly damped. This alternative scenario opens a new route to turbulence that calls for exploration. This new landscape may reset current strategies to promote or to hinder quasi-2D turbulence in practical applications, including in fusion reactors.Comment: Combined main paper (7 pages, 5 figures) and supplementary information (16 pages, 6 figures, 5 tables), submitted for consideration to Nature Physic

Nonlinear resonant tunneling in systems coupled to quantum reservoirs

An adiabatic approximation in terms of instantaneous resonances is developed to study the steady-state and time-dependent transport of interacting electrons in biased resonant tunneling heterostructures. The resulting model consists of quantum reservoirs coupled to regions where the system is described by nonlinear ordinary differential equations and has a general conceptual interest.Comment: 4 pages, 3 postscript figure

From three-dimensional to quasi-two-dimensional:Transient growth in magnetohydrodynamic duct flows

This study seeks to elucidate the linear transient growth mechanisms in a uniform duct with square cross-section applicable to flows of electrically conducting fluids under the influence of an external magnetic field. A particular focus is given to the question of whether at high magnetic fields purely two-dimensional mechanisms exist, and whether these can be described by a computationally inexpensive quasi-two-dimensional model. Two Reynolds numbers of $5000$ and $15\,000$ and an extensive range of Hartmann numbers $0 \leq Ha \leq 800$ were investigated. Three broad regimes are identified in which optimal mode topology and non-modal growth mechanisms are distinct. These regimes corresponding to low, moderate and high magnetic field strengths are found to be governed by the independent parameters, Hartmann number, Reynolds number based on the Hartmann layer thickness $R_H$, and Reynolds number built upon the Shercliff layer thickness $R_S$, respectively. Transition between regimes respectively occurs at $Ha \approx 2$ and no lower than $R_H \approx 33.\dot{3}$. Notably for the high Hartmann number regime, quasi-two-dimensional magnetohydrodynamic models are shown to be an excellent predictor of not only transient growth magnitudes, but also the fundamental growth mechanisms of linear disturbances. This paves the way for a precise analysis of transition to quasi-two-dimensional turbulence at much higher Hartmann numbers than is currently achievable.Comment: Accepted for publication in Journal of Fluid Mechanics (2018

The validity of axisymmetric assumptions when investigating pulsatile biological flows

Computational fluid simulations of biological flows is increasingly popular due to its inexpense and ability to define the flow throughout the entire domain---both common limiting factors for experimental work. A common assumption has been that both the geometry and the flow field through an aneurysm is axisymmetric; however, investigations into non-biological flows have seen that even with an axisymmetric geometry, non-axisymmetric flow may develop. Idealised geometries are used to investigate these biological flows as it simplifies the model to enable an improved understanding of the effect geometry has on the flow. Additionally this simplification allows the implementation of a computationally cheaper axisymmetric code. We test this axisymmetric assumption by applying Floquet stability analysis to investigate the stability of the flow and thus determine when an axisymmetric aneurysmal flow is unstable to non-axisymmetric instabilities. Dimensions of the model are selected to be consistent with a high risk aneurysm in the human abdominal aorta and Reynolds numbers relevant to aneurysms in large arteries are examined. The presence of three dimensional instabilities has a significant impact on the validity of the assumption of axisymmetry. The maximum streamwise vorticity in the perturbation fields is found to occur at the downstream section of the aneurysm, implying that it is in these areas that the results of axisymmetric simulations differ the most from fully three dimensional flow. References Barkley, D. and Henderson, R. D., Three-dimensional Floquet stability analysis of the wake of a circular cylinder. J. Fluid Mech. 322 (1996), 215--241. doi:10.1017/S0022112096002777 Brown, P. M., Zelt D. T., Sobolev B., The risk of rupture in untreated aneurysms: The impact of size, gender, and expansion rate. J. Vasc. Surg. 37 (2003), 280--284. doi:10.1067/mva.2003.119 Cowling R., Soria J., Flow Visualisation through Model Abdominal Aortic Aneurysm, Fourth Australian Conference on Laser Diagnostics in Fluid Mechanics and Combustion, The University of Adelaide, South Australia, Australia, 7--9 December 2005, 33--36. Egelhoff C. J., Budwig R. S., Elger D. F., Khraishi T. A., Model studies of the flow in abdominal aortic aneurysms during resting and exercise conditions. J. Biomech, 32 (1999), 1319-1329. doi:10.1016/S0021-9290(99)00134-7 Karniadakis, G. E. and Triantafyllou, G. S., Frequency selection and asymptotic states in laminar wakes. J. Fluid Mech. 199 (1989), 441--469. doi:10.1017/S0022112089000431 Karniadakis, G. E., Israeli, M. and Orszag, S. A., High-order splitting methods for the incompressible Navier-Stokes equations, J. Comp. Phys. 97 (1991), 414--443. doi:10.1016/0021-9991(91)90007-8 Ku, D. N., Blood flow in arteries, Annual review of Fluid Mechanics, 29 (1997), 399--434. doi:10.1146/annurev.fluid.29.1.399 Lasheras J., The Biomechanics of Arterial Aneurysms, Annual Review of Fluid Mechanics, 39 (2007), 293--319 doi:10.1146/annurev.fluid.39.050905.110128 Salsac, A. V., Sparks, S. R., Chomaz, J. M. and Lasheras, J. C., Evolution of the wall shear stresses during the progressive enlargement of symmetric abdominal aortic aneurysms, J. Fluid Mech., 560 (2006), 19--51. doi:10.1017/S002211200600036X Sheard, G. J., Evans, R. G., Denton, K. M. and Hourigan, K., Undesirable Haemodynamics in Aneurysms, In Proceedings of the IUTAM Symposium on Unsteady Separated Flows and Their Control, Hotel Corfu Chandris, Corfu, Greece, 18--22 June 2007 Sheard, G. J. and Ryan, K., Pressure-driven flow past spheres moving in a circular tube, J. Fluid Mech. 592 (2007), 233--262. doi:10.1017/S0022112007008543 Stedman, 2002, The American HeritageÆ Stedmanís Medical Dictionary, Houghton Mifflin Company, Massachusetts. Steinman, D. A., Vorp, D. A. and Ethier, C. R., Computational modelling of arterial biomechanics: Insights into pathogenesis and treatment of vascular disease, J. Vascular Surgery, 37 (2003), 1118--1128. doi:10.1067/mva.2003.122 Waite, L. and Fine, J. (2007). Applied biofluid mechanics. United Stated of America: McGraw-Hill