Publications 1999 – 2010

Mercier M.J., Martinand D., Mathur M., Gostiaux L., Peacock T. & Dauxois T.

Journal of Fluid Mechanics, 657, 309 (2010)

We present the results of a combined experimental and numerical study of the generation of internal waves using the novel internal wave generator design of Gostiaux et al. (Exp. Fluids, vol. 42, 2007, pp. 123–130). This mechanism, which involves a tunable source composed of oscillating plates, has so far been used for a few fundamental studies of internal waves, but its full potential is yet to be realized. Our study reveals that this approach is capable of producing a wide variety of two-dimensional wave fields, including plane waves, wave beams and discrete vertical modes in finite-depth stratifications. The effects of discretization by a finite number of plates, forcing amplitude and angle of propagation are investigated, and it is found that the method is remarkably efficient at generating a complete wave field despite forcing only one velocity component in a controllable manner. We furthermore find that the nature of the radiated wave field is well predicted using Fourier transforms of the spatial structure of the wave generator.

https://doi.org/10.1017/S0022112010002454

Allshouse M.R., Barad M.F. & Peacock T.

Nature Physics, 6, 516 (2010)

Buoyancy-driven flow, which is flow driven by spatial variations in fluid density, lies at the heart of a variety of physical processes, including mineral transport in rocks, the melting of icebergs and the migration of tectonic plates4. Here we show that buoyancy-driven flows can also generate propulsion. Specifically, we find that when a neutrally buoyant wedge-shaped object floats in a density-stratified fluid, the diffusion-driven flow at its sloping boundaries generated by molecular diffusion produces a macroscopic sideways thrust. Computer simulations reveal that thrust results from diffusion-driven flow creating a region of low pressure at the front, relative to the rear of an object. This discovery has implications for transport processes in regions of varying fluid density, such as marine snow aggregation at ocean pycnoclines, and wherever there is a temperature difference between immersed objects and the surrounding fluid, such as particles in volcanic clouds.

https://doi.org/10.1038/nphys1686

Mathur M. & Peacock T.

Physical Review Letters, 104, 118501 (2010)

Internal waves are a ubiquitous and significant means of momentum and energy transport in the oceans, atmosphere, and astrophysical bodies. Here, we show that internal wave propagation in nonuniform density stratifications, which are prevalent throughout nature, has a direct mathematical analogy with the classical optical problem of a Fabry-Perot multiple-beam light interferometer. We rigorously establish this correspondence, and furthermore provide the first experimental demonstration of an internal wave interferometer, based on the theory of resonant transmission of internal waves.

http://hdl.handle.net/1721.1/58604

Peacock T. & Dabiri J.

CHAOS, 20, 017501 (2010)

The topic of Lagrangian coherent structures (LCS) has been a rapidly growing area of research in nonlinear dynamics for almost a decade. It provides a means to rigorously define and detect transport barriers in dynamical systems with arbitrary time dependence and has a wealth of applications, particularly to fluid flow problems. Here, we give a short introduction to the topic of LCS and review the new work presented in this Focus Issue.

https://doi.org/10.1063/1.3278173

Tang W.E. & Peacock T.

CHAOS, 20, 017508 (2010)

For a nonuniformly stratified layer of fluid, internal gravity waves propagate at varying angles depending on the local buoyancy and Coriolis (in geophysical applications) frequencies. Relatively confined geometries, such as multiple submarine ridges, can support internal wave attractors, which can be viewed as Lagrangian coherent structures for the energy density flux. Since traditional approaches for locating these structures prove cumbersome, here we develop an approach that efficiently extracts the locations of internal wave attractors, as well as quantifying the rate of attraction. Using realistic geometry and stratification from ocean observations, we find that a significant northern portion of the Luzon ridge can support internal wave attractors.

https://doi.org/10.1063/1.3273054

Mathur M. & Peacock T.

Journal of Fluid Mechanics, 639, 133-152 (2009)

In addition to being observable in laboratory experiments, internal wave beams are reported in geophysical settings, which are characterized by non-uniform density stratifications. Here, we perform a combined theoretical and experimental study of the propagation of internal wave beams in non-uniform density stratifications. Transmission and reflection coefficients, which can differ greatly for different physical quantities, are determined for sharp density-gradient interfaces and finite-width transition regions, accounting for viscous dissipation. Thereafter, we consider even more complex stratifications to model geophysical scenarios. We show that wave beam ducting can occur under conditions that do not necessitate evanescent layers, obtaining close agreement between theory and quantitative laboratory experiments. The results are also used to explain recent field observations of a vanishing wave beam at the Keana Ridge, Hawaii.

https://doi.org/10.1017/S0022112009991236

Echeverri P., Flynn M.R., Winters K.B. & Peacock, T.

Journal of Fluid Mechanics, 636, 91-108 (2009)

We analyse the low-mode structure of internal tides generated in laboratory experiments and numerical simulations by a two-dimensional ridge in a channel of finite depth. The height of the ridge is approximately half of the channel depth and the regimes considered span sub- to supercritical topography. For small tidal excursions, of the order of 1% of the topographic width, our results agree well with linear theory. For larger tidal excursions, up to 15% of the topographic width, we find that the scaled mode 1 conversion rate decreases by less than 15%, in spite of nonlinear phenomena that break down the familiar wave-beam structure and generate harmonics and inter-harmonics. Modes two and three, however, are more strongly affected. For this topographic configuration, most of the linear baroclinic energy flux is associated with the mode 1 tide, so our experiments reveal that nonlinear behaviour does not significantly affect the barotropic to baroclinic energy conversion in this regime, which is relevant to large-scale ocean ridges. This may not be the case, however, for smaller scale ridges that generate a response dominated by higher modes.

https://doi.org/10.1017/S0022112009007654

Peacock T., Mercier M.J., Didelle H., Viboud S. & Dauxois T.

Physics of Fluids, 21, 121702 (2009)

We present the first laboratory experimental results concerning the scattering of a low-mode internal tide by finite-amplitude Gaussian topography. Experiments performed at the Coriolis Platform in Grenoble used a recently conceived internal wave generator as a means of producing a high-quality mode-1 wave field. The evolution of the wave field in the absence and presence of a Gaussian was studied by performing spatiotemporal modal decompositions of velocity field data obtained using particle image velocimetry. The results support the belief that finite-amplitude topography produces significant reflection of the internal tide and transfer of energy from low to high modes.

http://hdl.handle.net/1721.1/62004

Balmforth N.J. & Peacock T.

Journal of Physical Oceanography, 39, 1965-1974 (2009)

Calculations are presented of the rate of energy conversion of the barotropic tide into internal gravity waves above topography on the ocean floor. The ocean is treated as infinitely deep, and the topography consists of periodic obstructions; a Green function method is used to construct the scattered wavefield. The calculations extend the previous results of for subcritical topography (wherein waves propagate along rays whose slopes exceed that of the topography everywhere), by allowing the obstacles to be arbitrarily steep or supercritical (so waves propagate at shallower angles than the topographic slopes and are scattered both up and down). A complicated pattern is found for the dependence of energy conversion on ϵ, the ratio of maximum topographic slope to wave slope, and the ratio of obstacle amplitude and separation. This results from a sequence of constructive and destructive interferences between scattered waves that has implications for computing tidal conversion rates for the global ocean.

https://doi.org/10.1175/2009JPO4057.1

Yick K.Y., Torres C.R., Peacock T. & Stocker R.

Journal of Fluid Mechanics, 632, 49-68 (2009)

We present a combined experimental and numerical investigation of a sphere settling in a linearly stratified fluid at small Reynolds numbers. Using time-lapse photography and numerical modelling, we observed and quantified an increase in drag due to stratification. For a salt stratification, the normalized added drag coefficient scales as Ri^0.51, where Ri = a³N²/(νU) is the viscous Richardson number, a the particle radius, U its speed, ν the kinematic fluid viscosity and N the buoyancy frequency. Microscale synthetic schlieren revealed that a settling sphere draws lighter fluid downwards, resulting in a density wake extending tens of particle radii. Analysis of the flow and density fields shows that the added drag results from the buoyancy of the fluid in a region of size (ν/N)^1/2 surrounding the sphere, while the bulk of the wake does not influence drag. A scaling argument is provided to rationalize the observations. The enhanced drag can increase settling times in natural aquatic environments, affecting retention of particles at density interfaces and vertical fluxes of organic matter.

https://doi.org/10.1017/S0022112009007332

Weldon M., Peacock T., Jacobs, G.B., Helu M. & Haller, G.

Journal of Fluid Mechanics, 611, 1-11 (2008)

We present the results of a combined experimental and numerical study of flow separation in the unsteady two-dimensional rotor-oscillator flow. Experimentally detected material spikes are directly compared to separation profiles predicted from numerical shear-stress and pressure data, using a recent kinematic theory of unsteady separation. For steady, periodic, quasi-periodic and random forcing, fixed separation is observed, and experimental observations and theoretical predictions are in close agreement. The transition from fixed to moving separation is also reported.

https://doi.org/10.1017/S0022112008002395

Blanchette F., Peacock T. & Cousin R.

Journal of Fluid Mechanics, 609, 305-317 (2008)

We present the results of a combined theoretical and experimental study of the stability of a uniformly stratified fluid bounded by a sidewall moving vertically with constant velocity. This arrangement is perhaps the simplest in which boundary effects can drive instability and, potentially, layering in a stratified fluid. Our investigations reveal that for a given stratification and diffusivity of the stratifying agent, the sidewall boundary-layer flow becomes linearly unstable when the wall velocity exceeds a critical value. The onset of instability is clearly observed in the experiments, and there is good quantitative agreement with some predictions of the linear stability analysis.

https://doi.org/10.1017/S0022112008002164

Peacock T. & Bradley E.

Science, 320, (5881), 1302-1303 (2008)

Scientists have made great progress in controlling flow in many systems, but general strategies with feedback remain the ultimate goal.

https://www.jstor.org/stable/20054880

Peacock T., Echeverri P. & Balmforth, N.J.B.

Journal of Physical Oceanography, 38, (1), 235-242 (2008)

Experimental results of internal tide generation by two-dimensional topography are presented. The synthetic Schlieren technique is used to study the wave fields generated by a Gaussian bump and a knife edge. The data compare well to theoretical predictions, supporting the use of these models to predict tidal conversion rates. In the experiments, viscosity plays an important role in smoothing the wave fields, which heals the singularities that can appear in inviscid theory and suppresses secondary instabilities of the experimental wave field.

https://doi.org/10.1175/2007JPO3738.1

Alford M.H., MacKinnon J.A., Zhao Z., Pinkel R., Klymak J. & Peacock T.

Geophysical Research Letters, 34, (24), L24601 (2007)

The long-range propagation of the semidiurnal internal tide northward from the Hawaiian ridge and its susceptibility to parametric subharmonic instability (PSI) at the “critical latitude,” λc = 28.8°N, were examined in spring 2006 with intensive shipboard and moored observations spanning 25–37°N along a tidal beam. Velocity and shear at λc were dominated by intense vertically-standing, inertially-rotating bands of several hundred meters vertical wavelength. These occurred in bursts following spring tide, contrasting sharply with the downward-propagating, wind-generated features seen at other latitudes. These marginally-stable layers (which have inverse 16-meter Richardson number Ri16−1 = 0.7) are interpreted as the inertial waves resulting from PSI of the internal tide. Elevated near-inertial energy and parameterized diapycnal diffusivity, and reduced asymmetry in upgoing/downgoing energy, were also observed at and equatorward of λc. Yet, simultaneous moored measurements of semidiurnal energy flux and 1-km-deep velocity sections measured from the ship indicate that the internal tide propagates at least to 37°N, with no detectable energy loss or phase discontinuity at λc. Our observations indicate that PSI occurs in the ocean with sufficient intensity to substantially alter the inertial shear field at and equatorward of λc, but that it does not appreciably disrupt the propagation of the tide at our location.

https://doi.org/10.1029/2007GL031566

Mathur M., Haller G., Peacock T., Ruppert-Felsot J.E. & Swinney H.L.

Physical Review Letters, 98, (14), Art. No. 144502 (2007)

We present a technique that uncovers the Lagrangian building blocks of turbulence, and apply this technique to a quasi-two-dimensional turbulent flow experiment. Our analysis identifies an intricate network of attracting and repelling material lines. This chaotic tangle, the Lagrangian skeleton of turbulence, shows a level of complexity found previously only in theoretical and numerical examples of strange attractors. We quantify the strength (hyperbolicity) of each material line in the skeleton and demonstrate dramatically different mixing properties in different parts of the tangle.

https://doi.org/10.1103/PhysRevLett.98.144502

Yick, K.Y., Stocker, R. & Peacock, T.

Experiments in Fluids, 42, (1), 41-48 (2007)

We develop the axisymmetric Synthetic Schlieren technique to study the wake of a microscale sphere settling through a density stratification. A video-microscope was used to magnify and image apparent displacements of a micron-sized random-dot pattern. Due to the nature of the wake, density gradient perturbations in the horizontal greatly exceed those in the vertical, requiring modification of previously developed axisymmetric techniques. We present results for 780 and 383 μm spheres, and describe the limiting role of noise in the system for a 157 μm sphere. This technique can be instrumental in understanding a range of ecological and environmental oceanic processes on the microscale.

https://doi.org/10.1007/s00348-006-0217-7

Heitz R., Peacock T. & Stocker, R.

Physics of Fluids, 17, Art. No. 128104 (2005)

Diffusion-driven flow arises when a stably stratified fluid is bounded by an inclined wall. For a stratified fluid in an inclined fissure, in which fluid is confined to a gap between two inclined parallel walls, the flow field is determined by the gap width and the angle of inclination. When the gap width is much wider than the buoyancy layer thickness, the problem reduces to that of a semi-infinite fluid. As the gap width decreases, interaction between the boundary layer flows on the upper and lower walls increasingly influences the velocity profile, affecting transport within the fissure. We have obtained supporting experimental results that show these trends, demonstrating the existence of optimum conditions for dye transport.

https://doi.org/10.1063/1.2142833

Peacock T. & Tabaei A.

Physics of Fluids, 17, Art. No. 061702 (2005)

Recent theoretical and numerical investigations predict that localized nonlinear effects in the overlapping region of an incoming and reflected internal wave beam can radiate higher-harmonic beams. We present the first set of experimental visualizations, obtained using the digital Schlieren method, that confirm the existence of radiated higher-harmonic beams. For arrangements in which the angle of propagation of the second harmonic exceeds the slope angle, radiated beams are visualized. When the propagation angle of the second harmonic deceeds the slope angle no radiated beams are detected, as the associated density gradient perturbations are too weak for the experimental method. The case of a critical slope is also reported.

https://doi.org/10.1063/1.1932309

Peacock T. & Weidman, P.

Experiments in Fluids, 39, 32-37 (2005)

Experiments are conducted to test extant theory on the effect of uniform rotation Ω on the angle θ of conical beam wave propagation excited by a sphere vertically oscillating at frequency ω in a density stratified fluid. The near-constant Brunt–Väisälä frequency stratification N produced in situ in a rotating cylindrical tank exhibits no effect of residual motion for the range of Froude numbers investigated. Good agreement between experiment and theory is found over the range of angles 15°<θ<65° using the “synthetic schlieren” visualization technique. In particular, the cut-off for wave propagation at ω=2Ω, below which waves do not propagate, is clearly observed.

https://doi.org/10.1007/s00348-005-0955-y

Peacock T., Blanchette F. & Bush J.W.M.

Journal of Fluid Mechanics, 529, 33-49 (2005)

We present the results of an experimental investigation of the flows generated by monodisperse particles settling at low Reynolds number in a stably stratified ambient with an inclined sidewall. In this configuration, upwelling beneath the inclined wall associated with the Boycott effect is opposed by the ambient density stratification. The evolution of the system is determined by the relative magnitudes of the container depth, $h$, and the neutral buoyancy height, $h_n\,{=}\,c_0(\rho_p-\rho_f)/|{\rm d}\rho/{\rm d}z|$, where $c_0$ is the particle concentration, $\rho_p$ the particle density, $\rho_f$ the mean fluid density and ${\rm d}\rho/{\rm d}z\,{}\,h_n$, layering occurs. The lowermost layer is created by clear fluid transported from the base to its neutral buoyancy height, and has a vertical extent $h_n$; subsequently, smaller overlying layers develop. Within each layer, convection erodes the initially linear density gradient, generating a step-like density profile throughout the system that persists after all the particles have settled. Particles are transported across the discrete density jumps between layers by plumes of particle-laden fluid.

https://doi.org/10.1017/S002211200500337X

Peacock T., Stocker R. & Aristoff J.

Physics of Fluids, 16, 3503-3505 (2004)

We present experimental results on diffusion-driven flow along an inclined wall in a stably stratified fluid. The experiments focus on the dependence of the velocity in the buoyancy layer on the angle of inclination. The increase of velocity with decreasing angle is in agreement with theory for larger angles. For small angles, where current theory breaks down, the velocity tends to zero and an angle of maximum velocity exists.

https://doi.org/10.1063/1.1763091

Peacock T., Bradley E., Hertzberg J. & Lee Y.C.

Experiments in Fluids, 37, 22-28 (2004)

We present the results of an experimental study in which a planar laminar jet of air was forced by an array of micro-electromechanical systems (MEMS) micro-actuators. In the absence of forcing, the velocity profile of the experimental jet matched the classic analytic solution. Driving actuators on either side of the jet in-phase or anti-phase, respectively, excited the symmetric or anti-symmetric mode of instability of the jet. Asymmetric forcing, using MEMS actuators on only one side of the jet, was also investigated.

https://doi.org/10.1007/s00348-004-0780-8

Blanchette F., Peacock T. & Bush J.W.M.

Geophysical Research Letters, 31, L05611 (2004)

We investigate the plausibility of the stratified Boycott effect as a source of layering in magma chambers. Crystal settling within the magma chamber will generate buoyant fluid near the sloping sidewalls whose vertical ascent may be limited by the ambient stratification associated with vertical gradients in SiO2. The resulting flow may be marked by a layered structure, each layer taking the form of a convection cell spanning the lateral extent of the magma chamber. Using parameters relevant to magma chambers, we estimate that such convection cells would be established over a timescale of a month and have a depth on the order of 4m, which is roughly consistent with field observations of strata within solidified chambers.

https://doi.org/10.1029/2003GL019235

Ma Z.C., Bradley E., Peacock T., Hertzberg J.R. & Lee Y.C.

IEEE Transactions on Advanced Packaging, 23, 3, 268-276 (2003)

We describe surface-micromachined thermal actuator-based micro-electro-mechanical systems (MEMS) flaps with a length scale of 1,000 /spl mu/m. These flaps were developed for the enhancement of fluid mixing in an experimental study of a planar air jet. The scales of the flow physics required the actuators to be much larger than the typical MEMS scales, and the experiment required an array of 10 flaps (1 cm in length) to be soldered onto a ceramic substrate with high precision. These unusual requirements made it difficult to achieve good assembly yields that could provide large deflections. To improve the yields and deflections, we modified the initial flap design by reducing the size of the solder pads, removing sharp corners, changing the number and the width of the actuator’s hot arms, and strengthening the support beams. In addition, we developed a controllable assembly process to reflow tin/lead solder on gold pads, and we used numerical simulations extensively in the design process to improve the performance. The experimental measurements corroborated these simulations: the deflection was increased from 6.4 to 11.1 /spl mu/m under a 5 V applied voltage. Flow velocity measurements showed that these MEMS flaps amplified the natural instabilities of the planar jet.

https://doi.org/10.1109/TADVP.2003.817966

Peacock T. & Mullin T.

Journal of Fluid Mechanics, 432, 369-386 (2000)

The results of an experimental study of electrohydrodynamic convection in a liquid crystal are presented. Investigations concerned a small-aspect-ratio device so that finite geometry effects could be exploited to study the mechanisms by which complicated flows were organized. The results have been related to ideas on Shil’nikov dynamics and gluing bifurcations in low-dimensional dynamical systems.

https://doi.org/10.1017/S0022112000003293

Peacock T. & Mullin T.

Physics of Fluids, 12, S8 (2000)

https://doi.org/10.1063/1.4757294

Mullin T. & Peacock T.

Proceedings of the Royal Society of London A, 455, 2635-2653 (1999)

We present the results of an experimental study of hydrodynamic instabilities in two classes of nematic liquid crystal material subjected to linear oscillatory shear. The materials are distinguished by their viscosity coefficient α3, which is negative in one case and positive in the other. The instabilities appear above a critical amplitude of the shear whose value also depends on the applied frequency. In the material with negative α3, the instability has the form of microscopic Williams domains, which align with the shear and are uniformly spread throughout the sample. The principal set of results relate to instabilities in a material with positive α3. They concern two qualitatively distinct macroscopic features that are on the length-scale of hundreds of layer thicknesses. One of them consists of a uniform distortion of the director, and the other contains microscopic structures in the form of Williams domains. It is proposed that an observed large scale mean flow is responsible for the modulation of the latter instability.

http://rspa.royalsocietypublishing.org/content/455/1987/2635.abstract

Peacock T., Binks D.J. & Mullin T.

Physical Review Letters, 82, 1446-1449 (1999)

The results of an experimental study of flow in a small aspect ratio liquid crystal cell are presented where the dimensions of the device are on the same scale as the width of a human hair. This system is found to display wide ranging dynamical behavior, from simple oscillations to seemingly homogeneous turbulence. Through a systematic study of the low-dimensional behavior we uncover an organizing center for the dynamics.

https://doi.org/10.1103/PhysRevLett.82.1446

Peacock T. & Mullin T.

International Journal of Bifurcations and Chaos, 9, 427-441 (1999)

Results are presented of an experimental investigation of cellular flows in a nematic liquid crystal cell with physical dimensions comparable to the thickness of a human hair. Finite geometry effects have been exploited to investigate detailed bifurcation events which combine to give complicated flows in some parameter regimes. Initially observed flows consist of either six or eight convection cells which possess maximum symmetry consistent with the boundary conditions. These states undergo symmetry-breaking and Hopf bifurcations as the control parameter is continuously changed and interactions of the critical events are found to generate Silnikov dynamics. At stronger forcing it is possible to obtain both ordered fluid motion, consisting of square convection cells, and microturbulence. 

https://doi.org/10.1142/S0218127499000286