102 research outputs found
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Vortex-ring-induced stratified mixing
There is tantalizing evidence that some mechanically driven stratified flows tend towards a state of constant mixing efficiency. We provide insight into the energy balance leading to the constant mixing efficiency and isolate the responsible mechanism. The work presented demonstrates an important mixing efficiency regime for periodically forced externally driven stratified flows. Externally forced stratified turbulent mixing is often characterized by the associated eddies within the flow, which are the dominant mixing mechanism (Turner, J. Fluid Mech., vol. 173, 1986, pp. 431â471). Here, we study mixing induced by vortex rings in order to characterize the mixing induced by an individual eddy. By generating a long sequence of independent vortex-ring mixing events in a density-stratified fluid with a sharp interface, we determine the mixing efficiency of each ring. After an initial adjustment phase, we find that the mixing efficiency of each vortex ring is independent of the Richardson number. By studying the mixing mechanism here, we demonstrate consistent features of a volumetrically confined, periodically forced external mixing regime.This work was funded through the support of the Natural Sciences and Engineering Research Council of Canada (NSERC) and the Engineering and Physical Sciences Research Council (EPSRC). The experimental data associated with this study is made available at https://www.repository.cam.ac.uk/handle/1810/249285.This is the author accepted manuscript. The final version is available from Cambridge University Press via http://dx.doi.org/10.1017/jfm.2015.49
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Efficient mixing in stratified flows: Experimental study of a Rayleigh-Taylor unstable interface within an otherwise stable stratification
AbstractBoussinesq salt-water laboratory experiments of RayleighâTaylor instability (RTI) can achieve mixing efficiencies greater than 0.75 when the unstable interface is confined between two stable stratifications. This is much greater than that found when RTI occurs between two homogeneous layers when the mixing efficiency has been found to approach 0.5. Here, the mixing efficiency is defined as the ratio of energy used in mixing compared with the energy available for mixing. If the initial and final states are quiescent then the mixing efficiency can be calculated from experiments by comparison of the corresponding density profiles. Varying the functional form of the confining stratifications has a strong effect on the mixing efficiency. We derive a buoyancy-diffusion model for the rate of growth of the turbulent mixing region, (where is the Atwood number across the mixing region when it extends a height , is acceleration due to gravity and is a constant). This model shows good agreement with experiments when the value of the constant is set to 0.07, the value found in experiments of RTI between two homogeneous layers (where the height of the turbulent mixing region increases as , an expression which is equivalent to that derived for ).This work was funded by EPSRC (grant number EP/P505445/1) and
an AWE CASE award (AWE contract number 30174006).This is the accepted manuscript. The final version is available from CUP at http://journals.cambridge.org/action/displayAbstract?fromPage=online&aid=9346643&fileId=S0022112014003085. This work is © British Crown Copyright 2014/AWE
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The synthesis of di-carboxylate esters using continuous flow vortex fluidics
Faraday wave assisted flow chemistry. Vibrations and shear stress drive the synthesis of di-esters in minutes using room temperature vortex fluidics.We acknowledge support from the Government of South Australia and
the Australian Research Council.This is the author accepted manuscript. The final version is available from the Royal Society of Chemistry via http://dx.doi.org/10.1039/C5GC02494
Cleaning of viscous drops on a flat inclined surface using gravity-driven film flows
We investigate the fluid mechanics of cleaning viscous drops attached to a flat inclined
surface using thin gravity-driven film flows. We focus on the case where the drop cannot be
detached from the surface by the mechanical forces exerted by the cleaning fluid on the drop
surface. The fluid in the drop dissolves into the cleaning film flow, which then transports it
away. To assess the impact of the drop on the velocity of the cleaning fluid, we have
developed a novel experimental technique based on particle image velocimetry. We show the
velocity distribution at the film surface in the situations both where the film is flowing over a
smooth surface, and where it is perturbed by a solid obstacle representing a very viscous
drop. We find that at intermediate Reynolds numbers the acceleration of the starting film is
overestimated by a plane model using the lubrication approximation. In the perturbed case,
the streamwise velocity is strongly affected by the presence of the obstacle. The upstream
propagation of the disturbance is limited, but the disturbance extends downstream for
distances larger than 10 obstacle diameters. Laterally, we observe small disturbances in both
the streamwise and lateral velocity, owing to stationary capillary waves. The flow also
exhibits a complex three-dimensional converging pattern immediately below the obstacle.J. R. Landel acknowledges financial support from Magdalene College, Cambridge, through a
Nevile Research Fellowship in Applied Mathematics. This material is based upon work
supported by the Defense Threat Reduction Agency under Contract No. HDTRA1-12-D-
0003-0001.This is the accepted manuscript. The final version is available from Elsevier at http://www.sciencedirect.com/science/article/pii/S0960308514001175
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The magic carpet: an arbitrary spectrum wave maker for internal waves
Abstract
We present a novel apparatus for generating internal waves of arbitrary size and shape, including both phase-locked and propagating waves. It is an actively driven, flexible âmagic carpetâ in the base of a tank. Our wave maker is computer-controlled to enable easy configuration. The actuation of a smooth, flexible surface produces clean waveforms with a predictable spectrum, for which we derive a theoretical model. We demonstrate the versatility of our wave maker through an experimental study of linear and nonlinear, isolated, and combined internal waves, including some that are sufficiently nonlinear to break remote from their source.
Graphic abstract</jats:p
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A hierarchical decomposition of internal wave fields
Internal gravity wave fields are decomposed into temporal modes revealing the hierarchical structure of nonlinear waveâwave interactions. We present a novel fusion of Green's functions for solving the forced internal wave equation with a weakly nonlinear perturbation expansion. Our approach is semi-analytical, based on integration over finite elements with the perturbation expansion ensuring source terms at each order are only dependent on the solutions at lower orders. Thus, the procedure is purely inductive and efficient to compute. To perform a thorough validation of our new method, we diagnose experiments using synthetic Schlieren and apply sophisticated post-processing techniques, including dynamic mode decomposition, to obtain these temporal modes for systems with discrete input frequencies. By decomposing the experimental field and comparing individual constituents against equivalents synthesised by our model, we are able to present the first truly comprehensive, validated, mechanistic picture of waveâwave interactions to arbitrary order. This synergy enables us to identify non-wave oscillatory behaviour at frequencies shared by waves in the hierarchy and leads us to discover an important open question regarding transmission efficiency within individual waveâwave interactions. Although our experiments are generated by boundary displacements, we present equivalences between source terms and boundary displacements so that the class of applicable systems may be broadened. Our technique also generalises to aperiodic and unbounded configurations and to any weakly nonlinear wave-governed system for which there is an available Green's function.</jats:p
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Interaction between the Blasius boundary layer and a free surface
We consider the steady supercritical flow of a fluid layer. The layer is bounded above by a free surface and below by a rigid no-slip base. The base is in two parts: the downstream part of the base is stationary, while the upstream part translates in the streamwise direction with a uniform speed; there is an abrupt transition. At high Reynolds number, a boundary layer forms in the fluid above the base downstream of the transition point. The displacement due to this boundary layer creates a perturbation to the outer flow and therefore to the free surface. We show that the Blasius boundary layer solution, which applies in an infinitely deep fluid, also applies at high Froude numbers. The Blasius solution no longer applies for flows that are just supercritical, as the outer flow is strongly affected by the presence of the boundary layer. We outline possible applications of this work to depth-averaged models of gravity currents.JMFT is funded by an EPSRC Studentship (EP/M508007/1) and NMV is a Royal Society Dorothy Hodgkin Research Fellow (DH120121)
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The granular Blasius problem
We consider the steady flow of a granular current over a uniformly sloped surface that is smooth upstream (allowing slip for x<0) but rough downstream (imposing a no-slip condition on x>0), with a sharp transition at . This problem is similar to the classical Blasius problem, which considers the growth of a boundary layer over a flat plate in a Newtonian fluid that is subject to a similar step change in boundary conditions. Our discrete particle model simulations show that a comparable boundary-layer phenomenon occurs for the granular problem: the effects of basal roughness are initially localised at the base but gradually spread throughout the depth of the current. A rheological model can be used to investigate the changing internal velocity profile. The boundary layer is a region of high shear rate and therefore high inertial number ; its dynamics is governed by the asymptotic behaviour of the granular rheology for high values of the inertial number. The \unicode[STIX]{x1D707}(I) rheology (Jop et al., Nature, vol. 441 (7094), 2006, pp. 727â730) asserts that \text{d}\unicode[STIX]{x1D707}/\text{d}I=O(1/I^{2}) as , but current experimental evidence is insufficient to confirm this. We show that this rheology does not admit a self-similar boundary layer, but that there exist generalisations of the \unicode[STIX]{x1D707}(I) rheology, with different dependencies of \unicode[STIX]{x1D707}(I) on , for which such self-similar solutions do exist. These solutions show good quantitative agreement with the results of our discrete particle model simulations.J.M.F.T. is funded by an EPSRC Studentship (EP/M508007/1)
N.M.V. is a Royal Society Dorothy Hodgkin Research Fellow (DH120121)
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On the meaning of mixing efficiency for buoyancy-driven mixing in stratified turbulent flows
The concept of a mixing efficiency is widely used to relate the amount of irreversible diabatic mixing in a stratified flow to the amount of energy available to support mixing. This common measure of mixing in a flow is based on the change in the background potential energy, which is the minimum gravitational potential energy of the fluid that can be achieved by an adiabatic rearrangement of the instantaneous density field. However, this paper highlights examples of mixing that is primarily âbuoyancy-drivenâ (i.e. energy is released to the flow predominantly from a source of available potential energy) to demonstrate that the mixing efficiency depends not only on the specific characteristics of the turbulence in the region of the flow that is mixing, but also on the density profile in regions remote from where mixing physically occurs. We show that this behaviour is due to the irreversible and direct conversion of available potential energy into background potential energy in those remote regions (a mechanism not previously described). This process (here termed ârelabellingâ) occurs without requiring either a local flow or local mixing, or any other process that affects the internal energy of that fluid. Relabelling is caused by initially available potential energy, associated with identifiable parcels of fluid, becoming dynamically inaccessible to the flow due to mixing elsewhere. These results have wider relevance to characterising mixing in stratified turbulent flows, including those involving an external supply of kinetic energy.G.O.H. was supported by Australian Research Council Future Fellowship FT100100869 and was hosted by DAMTP during this work. M.S.D.W. was funded by EPSRC (grant number EP/P505445/1) and an AWE CASE award (AWE contract number 30174006).This is the author accepted manuscript. The final version is available from Cambridge University Press via http://dx.doi.org/10.1017/jfm.2015.46
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Particle organization after viscous sedimentation in tilted containers
A series of sedimentation experiments and numerical simulations have been conducted
to understand the factors that control the final angle of a static sediment
layer formed by quasi-monodisperse particles settling in an inclined container. The
set of experiments includes several combinations of fluid viscosity, container angle,
and solids concentration. A comparison between the experiments and a set of twodimensional
numerical simulations shows that the physical mechanism responsible
for the energy dissipation in the system is the collision between the particles.
The results provide new insights into the mechanism that sets the morphology of
the sediment layer formed by the settling of quasi-monodisperse particles onto the
bottom of an inclined container. Tracking the interface between the suspension solids
and the clear fluid zone reveals that the final angle adopted by the sediment layer
shows strong dependencies on the initial particle concentration and the container
inclination, but not the fluid viscosity. It is concluded that (1) the hindrance function
plays an important role on the sediment bed angle, (2) the relation between the
friction effect and the slope may be explained as a quasi-linear function of the
projected velocity along the container bottom, and (3) prior to the end of settling
there is a significant interparticle interaction through the fluid affecting to the final
bed organization.We can express the sediment bed slope as a function of two dimensionless
numbers, a version of the inertial number and the particle concentration.
The present experiments confirm some previous results on the role of the interstitial
fluid on low Stokes number flows of particulate matter.The authors acknowledge the support of the National Commission for Scientific and Techno-
logical Research of Chile, CONICYT, Grant N⊠21110766, Fondecyt Projects N⊠11110201
and N⊠1130910, the Department of Civil Engineering, the Department of Mining Engineering and the Advanced Mining Technology Center of the University of Chile, as well the staff
of the G.K. Batchelor Laboratory, Department of Applied Mathematics and Theoretical
Physics, University of Cambridge.This is the author accepted manuscript. The final version is available from AIP at http://dx.doi.org/10.1063/1.4958722
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