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Stratified turbulence in the 21st century – new insights on an increasingly important problem
Theo Murphy scientific meeting organised by Professor Paul Linden FRS, Professor Richard Kerswell FRS, Dr Colm-cille Caulfield, Dr Stuart Dalziel and Dr John Taylor
A key issue in climate science is the rate at which heat is transported by turbulent motions in a density stratified environment. This rate determines the uptake of heat by the oceans and is critical for accurate climate predictions. This multidisciplinary meeting discussed new mathematical approaches and encouraged cross-fertilisation of ideas by bringing together theoretical, experimental and computational scientists with practitioners.
Speaker biographies, abstracts and the schedule of talks are available below. Alternatively you can download the draft programme (PDF).
Attending this event
This meeting has taken place. Recorded audio of the presentations can be found below.
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Organisers
Schedule
Chair
Dr Colm-cille Caulfield, University of Cambridge, UK
Dr Colm-cille Caulfield, University of Cambridge, UK
Dr Colm-cille Caulfield holds a joint appointment in the Department of Applied Mathematics and Theoretical Physics and the BP Institute at the University of Cambridge. The BP Institute is a multi-disciplinary research centre devoted to fundamental studies of problems related to the energy industry, defined in the broadest sense. It brings together industrialists and academics with expertise in applied mathematics, earth sciences, engineering and chemistry.
Dr Caulfield is interested in working as part of such diverse teams to study various fluid flows in the environment, particularly in cases where density differences play a dynamical role. Of course, density differences, (due to temperature or composition variation) are ubiquitous in the environment. Understanding the fundamental properties of the associated fluid dynamics is key to ensuring sustainable human activity. To name just three important examples, understanding how density differences affect fluid flows can allow strategies to be developed to model the climate system, to deal with the dispersion of pollutants, or to minimise energy consumption within buildings.
| 09:05 - 09:40 |
Stratified turbulent mixing in the ocean: patterns, processes, and parameterisation
Though average observed diapycnal mixing rates in the ocean interior are consistent with values required by inverse models, recent focus has been on the dramatic spatial variability of mixing rates in both the upper and deep ocean, which spans several orders of magnitude. Global ocean models have been shown to be very sensitive not only to the overall level but to the detailed distribution of mixing. Some of these patterns are driven by the geography of generation, propagation and destruction of internal waves, which are thought to supply much of the power for turbulence in the ocean interior. I will briefly review some results from the last five years of a Climate Process Team tasked with improving representations of internal-wave driven mixing in the oceanic component of climate models. Another set of recent and ongoing work has turned to the poorly understood role of mesoscale and sub-mesoscale features in stratified oceanic turbulence. In some situations, the interplay between internal waves and mesoscale vorticity can noticeably enhance turbulent mixing rates. In other situations, sub-mesoscale instabilities act to re-stratify the ocean, a counter-balance of sorts to one-dimensional vertical mixing schemes. Recent observational examples of both situations will be presented, and discussed in the broader framework of global mixing rates. 
Dr Jennifer MacKinnon, University of California San Diego, Scripps Institution of Oceanography, USA
Dr Jennifer MacKinnon, University of California San Diego, Scripps Institution of Oceanography, USAJennifer MacKinnon studies small-scale dynamical processes in the ocean, primarily internal waves and turbulence. Her main interests lie in integrating ocean observations, process studies and numerical simulations to understand the dynamics of high-frequency ocean processes and their relationship to lower-frequency global phenomena. MacKinnon has been involved with numerical process studies of nonlinear interactions between internal waves, with ocean-going observations of internal-wave driven turbulent mixing, and has recently become interested in sub-mesosacle instabilities as observed in the upper ocean. Simultaneously, MacKinnon is working with collaborators to use numerical and observational results to develop analytical parameterisations of turbulent diffusivity for use in large-scale climate models. |
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| 09:40 - 10:20 |
Mixing in density-stratified, free shear flows and the implications for mixing in the ocean
To first order, in the interior of the ocean the mean density and horizontal velocity fields can be considered a function of the vertical coordinate z. For this simple shearing flow, we introduce a new mixing length model to describe the mixing of density and momentum. We introduce a mixing length Lp controlling mixing in the density field and a mixing length Lm controlling mixing in the momentum field. There are no undetermined coefficients in the model, and no need to make any assumptions about the value of the flux Richardson number Rif. The model determines Rif and demonstrates Rif is dependent on the relative magnitudes of three length scales: Lp, Lo, and Ls , where Lo is the Ozmidov scale and Ls the Corrsin shear scale. The model predictions are in good agreement with published laboratory observations. We discuss the implications of the model for the interpretation of oceanic turbulent microstructure measurements and the description of mixing in numerical ocean models. 
Professor Greg Ivey, University of Western Australia, Australia
Professor Greg Ivey, University of Western Australia, AustraliaGreg Ivey is a member of the School of Civil, Environmental and Mining Engineering and the Oceans Institute at University of Western Australia (UWA). Greg has a BE and a MEng Science from UWA, and a PhD from the University of California at Berkeley. His research interests are in the area of physical oceanography, with particular focus on ocean turbulence and mixing, internal wave dynamics, and coastal ocean dynamics. In recent years his work has focused on observations at sea, mainly on the Australian North West Shelf (NWS). The NWS is density-stratified year-round, stirred by strong tidal currents and episodic tropical cyclones in the summer months. The research challenges of the region are both to undertake engineering developments, and to manage the unique marine ecosystems of the region. |
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| 10:50 - 11:30 |
Parameterising mixing in the stably stratified ocean interior
Vertical mixing is suppressed in the stable density stratification of the ocean interior, yet the vertical turbulent diffusion of heat and salt still plays a significant role in the thermohaline circulation. Ocean climate models cannot explicitly resolve the mixing processes, so must employ parameterisations relating the mixing to resolved parameters. Such mixing requires a source of energy, supplied by sheared flow; when this shear is resolved, for example in large-scale ocean currents, the parameterised turbulent diffusion can be expressed in terms of the resolved flow and stratification. However, in much of the ocean, the shear responsible for mixing is due to internal waves, which are rarely simulated in climate models. These waves are generated by the tides and wind, propagate around the ocean, and eventually lead to mixing when they break. Parameterisation of the mixing due to breaking internal waves must account for the generation, propagation and dissipation of wave energy. High resolution simulations can be used to examine the mechanisms of wave breaking, extending understanding gained from observations. Here I will describe different internal wave breaking mechanisms, including nonlinear wave-wave interactions, wave reflection from sloping and shoaling topography, and transient hydraulic jumps, as well as recent efforts to combine this understanding into a global model of the tidally-driven internal wave energy budget leading to an energetically consistent parameterisation of mixing. The impact of different geographical distributions of wave-breaking on global ocean circulation will be demonstrated using coupled climate models. 
Dr Sonya Legg, Princeton University, USA
Dr Sonya Legg, Princeton University, USASonya Legg received her PhD from Imperial College London in 1993, and a Climate and Global Change postdoctoral fellowship from NOAA in 1995. Legg has been a member of the Princeton University Atmospheric and Oceanic Sciences programme faculty for 10 years, following several years at Woods Hole Oceanographic Institution. Legg is currently the lead PI for MPOWIR (Mentoring Physical Oceanography Women to Increase Retention), a nation-wide mentoring effort. Legg’s research interests focus on turbulent mixing in the ocean, including tidal mixing and mixing in overflows, the representation of mixing processes in large-scale ocean models, and the impact of parameterised small-scale mixing on the large-scale ocean circulation and climate. Legg has participated in two climate process teams, multi-institutional collaborations bringing together observationalists, modellers, and climate model developers, to better parameterise ocean processes. |
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| 11:30 - 12:10 |
Mixing processes in the oil and gas industry
Oil wells are very long and skinny (with aspect ratios of the order 10^5) and in many operations a tube sits within the wellbore with fluids pumped down the centre of this pipe, and back up the annulus between the pipe and rock. Flow rates vary significantly leading to some operations being performed in laminar flows, whilst others are turbulent. The fluids can be Newtonian or non-Newtonian. When the tube is not concentric in the wellbore, it is possible that laminar, transitional and turbulent flow can coexist in the annular space at any particular depth. The simplest case of dispersion of a tracer in a single phase flow is already of interest as the time evolution of fluid properties of the outlet of a well can give an indication of earlier events near the bottom. Taylor dispersion calculations show how sensitive the outlet distribution can be to eccentricity of the inner tube, and how rotation of the inner tube can counteract this. In some cases it is also useful to understand how a tracer distribution approaches the Taylor limit. As many of the fluids used are non-Newtonian, even these relatively simple cases exhibit unusual behaviours. More complex cases involve pumping a sequence of fluids of varying densities and rheological properties down through the tube and up the annular space. In these cases mixing process are complex, with a variety of instabilities possible. An approximate model system can be derived for certain geometrical configurations leading to realistic prediction of mixing processes. Laminar flow problems are already challenging; adding the complexity of turbulent, or partially turbulent flows, leads to a range of problems which deserve greater study. This talk will lead from the single phase to the multi-fluid and from the laminar to the turbulent, to explain the broad range of rich mixing processes that can occur in an important practical application. 
Dr Simon Bittleston, Schlumberger Gould Research, UK
Dr Simon Bittleston, Schlumberger Gould Research, UKSimon Bittleston is currently Vice President of Research for Schlumberger, a position he assumed in 2012. He is responsible for research centres in Boston, Cambridge (UK), Moscow, Rio, Stavanger, Edmonton, Houston and Dhahran, covering all aspects of oil-field activities. Bittleston joined Schlumberger in 1985 and worked at Schlumberger Cambridge Research becoming a research programme manager. He moved to Norway in 1993 and became domain manager for the development of Marine Seismic systems where he was responsible for the development of Q-Marine. In 1999 he returned to the UK as a Research Director, and then in 2001 moved to Houston as VP Product Development which included all Product Development and Manufacturing for Schlumberger. In 2005 he moved to Paris and became VP of Mergers and Acquisitions – the team completed more than 40 investments. Bittleston holds a Bachelor’s degree in mathematics from Imperial College London, and a PhD in fluid mechanics from the University of Bristol, UK. He is also a By-Fellow of Churchill College, Cambridge and Fellow of Darwin College, Cambridge. |
Chair
Professor Richard Kerswell FRS, University of Bristol, UK
Professor Richard Kerswell FRS, University of Bristol, UK
Rich Kerswell is a professor of Applied Mathematics at the University of Bristol, UK. He received his PhD in Applied Mathematics from MIT in 1992, took up his first position in Mathematics at Newcastle University in the same year, and moved to Bristol in 1996. He has broad scientific interests ranging from astrophysical and geophysical fluid mechanics, through to granular media to transition, and turbulence.
| 13:10 - 13:50 |
Periodic orbits theory of turbulent flows
Partial differential equations are in principle infinite-dimensional dynamical systems. However, recent studies offer strong numerical evidence that the turbulent solutions of spatially extended dissipative systems evolve within a manifold spanned by a finite number of 'entangled' modes, dynamically isolated from the residual set of isolated, transient degrees of freedom. Initial studies, based on numerical simulations of long ergodic trajectories, yield no intuition about the geometry of such attractors. That is attained by studying the hierarchies of unstable periodic orbits, invariant solutions which, together with their Floquet vectors, provide an effective description of both the local hyperbolicity and the global geometry of an attractor embedded in a high-dimensional state space. Dynamical systems with translational or rotational symmetry arise frequently in studies of spatially extended physical systems, such as Navier-Stokes flows on periodic domains, with each fluid state having an infinite number of equivalent solutions obtained from it by a translation or a rotation. This multitude of equivalent solutions tends to obscure the dynamics of turbulence, and the crucial step in the analysis of such a system is symmetry reduction. We offer several implementations of 'method of slices' applicable to very high-dimensional problems and show that after application of the method, hitherto unseen global structures, for example to pipe flow, relative periodic orbits and their unstable manifolds are uncovered. Whether the periodic orbit theory of computing expectation values of measurable observables is applicable to such high-dimensional flows remains an open question. 
Professor Predrag Cvitanović, Georgia Institute of Technology, USA
Professor Predrag Cvitanović, Georgia Institute of Technology, USAPredrag Cvitanović is theoretical physicist at the Georgia Institute of Technology. He believes passionately in the unity of exact sciences, and in his ChaosBook.org he is developing theoretical tools that apply equally to classical chaos (turbulence, cardiac dynamics), stochastic dynamics and quantum theories. He has contributed to quantum field theory, the theory of exceptional Lie groups, and his nonlinear dynamics research spans a broad range of physical problems, from renormalisation in transitions to chaos, and periodic orbit theory of quantum systems to dynamical theory of hydrodynamical turbulence. Cvitanović is also known for his web books on Field Theory, Group Theory, and Chaos. |
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| 13:50 - 14:30 |
The zombie vortex instability – a new, fast, robust instability in rotating, horizontally-shearing, vertically-stratified flows
Without instabilities, gas around a forming protostar remains in orbit, and the final star cannot form; dust grains cannot accumulate to form planets; and the compositions of meteorites cannot be explained. Unfortunately, the Keplerian motion within a disk is assumed by most astrophysicists to be stable by Rayleigh’s theorem because the angular momentum of the disk increases with increasing radius. We show that there is a new purely hydrodynamic instability that is violent and destabilises the protoplanetary disk, filling it with turbulence. The essential ingredients of the new instability are rotation, shear, and vertical density stratification, so the instability can occur in stratified Boussinesq (or fully compressible) Couette flows. Our new instability occurs at critical layers where neutrally-stable eigenmodes are singular in the inviscid limit (but finite, with a width that scales as the Reynolds number Re to the -1/3 power when viscosity is present) and requires an initial finite-amplitude perturbation. In a flow initialised with weak Kolmogorov noise with initial Mach number Ma, when Ma > Re-1/2 (~10-7 in a protoplanetary disk) the instability will be triggered and create turbulence and large-volume and large-amplitude vortices that fill the disk. When the initial perturbation is an isolated vortex, the vortex triggers a new generation of vortices at the nearby critical layers. After this second generation of vortices grows large, it triggers a third generation. The triggering of subsequent generations continues ad infinitum in a self-similar manner creating a 3D lattice of turbulent 3D vortices. 
Professor Philip Marcus, University of California, Berkeley, USA
Professor Philip Marcus, University of California, Berkeley, USAPhilip Marcus is a Professor of Fluid Dynamics in the Department of Mechanical Engineering at the University of California at Berkeley. He is also Head Advisor for the UC Berkeley Graduate Program in Applied Science and Technology and a former associate editor of The Journal of Computational Physics and of The Journal of Fluid Dynamics. He is a Fellow of the American Physical Society and a former Chair of its Division of Fluid Dynamics. He is interested in a wide range of fluid flows: from Jupiter’s Great Red Spot to the formation of stars and planets, to the use of novel ways of carrying out three-dimensional morphing and using those ways to do ‘optimal design’ in aerodynamic and hydrodynamic applications. |
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| 15:00 - 15:40 |
The turbulent/non-turbulent interface in stably stratified fluids
The results of a study, employing direct numerical simulations, of the turbulent/nonturbulent interface of a wake in a stably-stratified fluid will be discussed. It is found that thresholds for both enstrophy and potential enstrophy are needed to identify the interface. Using conditional averaging relative to the location of the interface, various quantities of interest are examined. The thickness of the interface is found to scale with the Kolmogorov scale. From an examination of the Ozmidov and Kolmogorov length scales as well as the buoyancy Reynolds number, it is found that the buoyancy Reynolds number decreases and becomes of order 1 near the interface, indicating the suppression of the turbulence there by the stable stratification. Finally the overall rate of loss of energy due to internal wave radiation is found to be comparable to the overall rate of loss due to turbulent kinetic energy dissipation. 
Professor James Riley, University of Washington, USA
Professor James Riley, University of Washington, USAJim Riley, the PACCAR Professor of Engineering at the University of Washington, is a fluid dynamicist whose research and teaching emphasise transitioning and turbulent flows. He did his PhD studies with Stanley Corrsin at the Johns Hopkins University, and then was a post-doctoral fellow at the National Center for Atmospheric Research. Riley has worked extensively on a broad range of problems, among them turbulent dispersion, two-phase flows, boundary layer transition, free shear flows, chemically-reacting flows, and geophysical flows. His current research emphasises turbulent, chemically-reacting flows and also waves and turbulence in density-stratified flows and rotating flows. |
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| 15:40 - 16:20 |
Mixing and critical entrainment phenomena in stratified fluids
Density stratification can add a considerable layer of complexity to the dynamics of fluids: coherent structures, such as vortex rings, bodies or jets may move ambient fluids into regions where buoyancy forces can arise creating strong flows unless mitigated by mixing or viscosity. This can give rise to critical phenomena in which bodies and buoyant fluids may escape or become trapped as parameters (such as the propagation distance) are varied. This talk will present an overview of our theoretical, computational, and experimental studies on a class of these critical phenomena, focusing on the associated vertical transport and mixing. 
Professor Roberto Camassa, University of North Carolina, USA
Professor Roberto Camassa, University of North Carolina, USAAs professor in the Department of Mathematics of the University of North Carolina, Camassa’s research interest are in applied mathematics and fluid mechanics, particularly in modelling of wave propagation and mixing in stratified flows. Since 2007 he has been a University Kenan Distinguished Professor of Mathematics, and was the Director of the Carolina Center for Interdisciplinary and Applied Mathematics from 2008-2012. He holds a Laurea in Physics from the University of Milan, and an M.S. and a PhD from the California Institute of Technology in engineering science and applied mathematics. |
Chair
Dr John Taylor, University of Cambridge, UK
Dr John Taylor, University of Cambridge, UK
John Taylor is a University Lecturer in Oceanography in the Department of Applied Mathematics and Theoretical Physics and Fellow of St John’s College at the University of Cambridge. He received a PhD in Mechanical Engineering from the University of California, San Diego in 2008 where he was a National Defense Science and Engineering Graduate Fellow. He was awarded the Andreas Acrivos Dissertation Award from the American Physical Society in 2008. From 2008-2011, he was an NSF Mathematical Sciences Postdoctoral Fellow at MIT.
| 09:00 - 09:40 |
Experiments with mixing in stratified flow over a ridge
Interaction of geostrophic balanced flow with bottom topography is thought to generate lee waves that can carry energy into the overlying ocean and lead to turbulent mixing. Topography will also cause local mixing, particularly instabilities in the wake. Ocean models require parameterisation of these effects and currently assume 30% of the energy removed from the mean flow is consumed in local mixing and turbulent dissipation, the remainder being radiated and causing turbulent mixing elsewhere. I will discuss laboratory experiments with a ridge towed through uniform density stratification, or a mixed layer under a uniform gradient, in a long channel, creating a mean flow over the ridge. The total mixing rate is measured across three parameter regimes including linear lee waves, nonlinear flow and an evanescent regime in which wave radiation is weak. Measurements provide the depth-dependence of turbulent mixing, allowing separation of the local and remote contributions to mixing. Remote mixing is dominant only for a narrow band of Froude numbers; under other conditions local mixing is dominant. The results suggest that mixing by local nonlinear mechanisms close to abyssal ocean topography may be much greater than remote mixing by lee waves. 
Professor Ross Griffiths, Australian National University, Australia
Professor Ross Griffiths, Australian National University, AustraliaRoss's recent research interests include the dynamics of turbulent convection at very high Rayleigh numbers, the energetics of turbulent mixing in both stratified flows and convection, and the roles of convection, wind stress and mixing in the dynamics of basin scale and global circulation of the ocean. Past work has included laboratory modelling of 'double-diffusive convection', of the stability of ocean currents and density fronts, of upwelling plumes and sinking lithospheric slabs in the Earth's mantle, and of viscous gravity-driven flows with coupled cooling and solidification. |
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| 09:40 - 10:20 |
Rotating plane Couette flow – instabilities, structures and turbulence
Shear flows subjected to system rotation, where the rotation axis is parallel with the mean-flow vorticity, are influenced by a Coriolis force, which may have a strong effect on the flow field even at low rotation rates. For such flows, as pointed out by Bradshaw in 1969, there is an analogy with stratified flows. Here we will discuss plane Couette flow (PCF) under anticyclonic rotation both in the laminar and turbulent regimes. Without rotation, PCF is linearly stable for all Reynolds numbers, however, in experiments transition to turbulence is observed around Re=350. With anticyclonic rotation, the critical Reynolds number is as low as 20.6, at which point the flow bifurcates to a flow with streamwise-oriented roll cells. With increasing Reynolds number and/or rotation rate, the laminar roll cells develop various types of other complex instabilities and at higher Reynolds numbers the flow enters a turbulent regime, although it is still dominated by streamwise roll cells. We present experimental results where all three velocity components are measured with PIV, enabling determination of the mean flow and all four non-zero Reynolds stresses across the central parts of the channel. We discuss the resulting flow structures as well as an analysis of the Reynolds-stress equations and how they relate to the fact that the absolute vorticity, ie the sum of the averaged spanwise-flow vorticity and system rotation, tends to zero in the central region of the channel for high enough rotation rates. 
Professor Henrik Alfredsson, KTH, Sweden
Professor Henrik Alfredsson, KTH, SwedenHenrik Alfredsson has been a professor at KTH, Royal Institute of Technology, since 1986, and was one of the founders of the Fluid Physics Laboratory. His PhD research dealt with turbulent channel-flow experiments and he graduated in 1983. He has served in several academic positions at KTH, e.g. as the Dean of the Faculty and Chairman of AlbaNova University Center. He is a Fellow of the American Physical Society and the Royal Swedish Academy of Engineering Sciences and is also a Guest Professor at the University of Bologna. His research interests include both fundamental topics, such as stability, transition and turbulence in wall-bounded flows, and also applied areas, e.g. wind power, vehicle aerodynamics and the gas exchange processes in internal combustion engines. He has authored and co-authored more than 100 papers in peer-reviewed journals and supervised more than 60 masters and 20 PhD students. |
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| 10:50 - 11:30 |
Transition in unstratified pipe flow
Despite more than a century of research, the puzzle of why fluid motion along a pipe is observed to become turbulent as the flow rate is increased remains the outstanding challenge of hydrodynamic stability theory. The issue is both of deep scientific and engineering interest since most pipe flows are turbulent in practice, even at modest flow rates. All theoretical work indicates that the flow is linearly stable ie infinitesimal disturbances decay as they propagate along the pipe and the flow will remain laminar. In practice, finite amplitude perturbations are responsible for triggering turbulence and these become more important as the non-dimensional flow rate, the Reynolds number Re, increases. Transition is usually catastrophic and elucidating details of the processes involved is generally difficult. Here we show that the judicious choice of perturbation can be used to highlight important details and we also provide experimental evidence for long live edge states which are believed to exist on the boundary between laminar and turbulent flows. These new experimental results provide insights into the origins of the turbulent motion and suggest links can be made with recent theoretical work on the Navier Stokes equations. 
Professor Thomas Mullin, University of Manchester, UK
Professor Thomas Mullin, University of Manchester, UKTom Mullin is a Professor of Physics at the University of Manchester. He is also the Research Director of the Manchester Centre for Nonlinear Dynamics which is an interdisciplinary research centre based in the Schools of Physics and Mathematics. The centre was founded by TM in 2002 and currently involves eight academic members of staff and their post-docs and students. TM's research is focused on experimental investigations of transition to turbulence, instabilities in elastic materials, particle motion in viscous fluids and pattern formation in granular flows. |
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| 11:30 - 12:10 |
Stochastic parametrisation and inexact computing for weather and climate prediction
There are good reasons to suppose the closure schemes for weather and climate models should be formulated stochastically, rather than deterministically as has been traditional. This puts into sharp focus a question of both theoretical and practical importance: in a multi-scale system such as weather and climate (with scale-dependent Lyapunov exponents), how many bits of real information are carried by the prognostic variables as a function of scale. There are good reasons to suppose that for many small-scale variables, information can be represented using significantly fewer bits than 64 (the standard default for scientific computing). Assessing this quantitatively may be a route to making much more efficient use of supercomputing resources and hence to increasing model resolution. 
Professor Tim Palmer CBE FRS, University of Oxford, UK
Professor Tim Palmer CBE FRS, University of Oxford, UKTim Palmer is a Royal Society Research Professor in the Department of Physics at the University of Oxford. Prior to that he was Head of Division at the European Centre for Medium-Range Weather Forecasts where he pioneered the development of ensemble prediction techniques, allowing weather and climate predictions to be expressed in flow-dependent probabilistic terms. Such developments have included the reformulation of sub-grid parametrisations as stochastic rather than deterministic schemes. Over the last 10 years, Tim has been vocal in advocating for much greater dedicated computing capability for climate prediction than is currently available. He has won the top awards of the European and Meteorological Societies, the Dirac Gold Medal of the Institute of Physics, and is a Foreign or Honorary Member of a number of learned societies around the world. |
Chair
Dr Stuart Dalziel, University of Cambridge, UK
Dr Stuart Dalziel, University of Cambridge, UK
Stuart Dalziel is a Reader in Fluid Mechanics and the Director of the GK Batchelor Laboratory at the University of Cambridge. His research, combining experimental and theoretical studies, spans fluid flows in industrial and environmental problems including plumes, gravity currents, granular flows and mixing. A particular focus has been on turbulence in both statically stable and statically unstable stratified flows.
| 13:10 - 13:50 |
From topographic internal gravity waves to instabilities and turbulence
The substantial energy converted from the oscillating tide to internal waves at deep, rough topography is a key source of turbulence and mixing in the abyssal ocean. Some of this energy breaks down near the boundary to feed local turbulence and mixing while the remainder is radiated away to fuel remote turbulence. We have investigated the operative nonlinear processes through three-dimensional simulations that resolve the instabilities and ensuing turbulence. I will review local nonlinearities and their contribution to the baroclinic energy balance at a model triangular ridge and at a scaled-down model of realistic steep topography at Luzon Strait. The periodically stratified, oscillating boundary flow transitions to turbulence at sloping regions with near-critical angle where upslope bores form, at the upper portion of steep obstacles where downslope jets form and detach from the boundary, and through direct breaking of lee waves on or above the obstacle. Convective instability with high mixing efficiency occurs in the boundary layer as well as in breaking lee waves. High-mode internal wave beams launched from steep regions of the obstacle are turbulent in the near field. I will also touch upon the cascade of energy to waves with short vertical scales and eventually turbulence through parametric subharmonic instability (PSI) during refraction and after reflection. 
Professor Sutanu Sarkar, University of California, San Diego, USA
Professor Sutanu Sarkar, University of California, San Diego, USASutanu Sarkar received his B.Tech from IIT Bombay, M.S. from Ohio State University and PhD from Cornell University in 1988. After 4 years as a staff scientist at ICASE, NASA Langley Research Center, he joined UCSD where he is currently the Blasker Professor of Engineering. His current research interests are in the areas of simulation and modelling of turbulent flows, transport and mixing in the environment, and energy. He has received a NASA group achievement award (1994), the Bessel Award from the Humboldt Foundation (2001), and was elected Fellow, American Physical Society (2006), Associate Fellow, AIAA (2009) and Fellow, ASME (2010). |
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| 13:50 - 14:30 |
Flavours of stratified turbulence
The role of stratified turbulence in effecting the vertical flux of mass required to enable the deep water that forms in the polar oceans to upwell to the surface of the southern ocean, and thereby lead to closure of the overturning circulation, is well known. What is as yet insufficiently well understood, however, is how this small scale process might best be represented in large scale models of the ocean general circulation. This is a complex issue because of the variety of mechanisms through which the small scale turbulence is produced. These mechanisms include a variety of breaking wave related processes in which the hydrodynamic waves of interest include those generated through initial shear instabilities of either Kelvin-Helmholtz or Holmboe type. Equally relevant breaking wave related mechanisms include those in which internal waves launched by stratified flow over bottom topography thereafter ‘break’ either near to or distant from their source of excitation. In the latter case the forcing could be related either to the barotropic tide or to the action of larger scale baroclinic eddies. An important issue, insofar as the parameterisation problem is concerned, is whether there might be generic properties shared by high Reynolds number stratified turbulence irrespective of the mechanism through which it is produced. In the case of shear generated breaking waves involving either of the above mechanisms it has proven possible to demonstrate that the post transition characteristics of the turbulence are rather generic though dependent upon knowledge of three distinct turbulence characteristics, respectively the buoyancy Reynolds number Reb representative of turbulence intensity, a ‘bulk’ Richardson number Rib representative of the strength of the shear, and a turbulent Prandtl number Prt representing the ratio of turbulent momentum diffusivity to that for density. A summary of recently proposed parameterisation schemes will be presented. 
Professor W Richard Peltier, University of Toronto, Canada
Professor W Richard Peltier, University of Toronto, CanadaRichard Peltier received his doctoral degree in physics from the University of Toronto. His research is in the general area of geophysical fluid dynamics on processes that control the evolution of the atmosphere, the oceans and the solid Earth, and long timescale climate variability. In 2004 he shared the Vetlesen Prize with Nick Shackleton and in 2010 was the recipient of the Bower Award and Prize of the Franklin Institute for his research on 'Earth Systems'. In 2012, he won the Gerhard Hertzberg Canada Gold Medal in Science and Engineering, Canada’s highest scientific award, and in the following year the Killam Prize in Natural Science of the Canada Council for the Arts. His current position is as university Professor and Professor of Physics in Toronto where he is the Director of the Centre for Global Change Science and Scientific Director of the SciNet high performance computing facility. See atmosp.physics.utoronto.ca/~peltier. |
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| 15:00 - 15:40 |
Near-inertial energy propagation inside an anticyclone: a pathway to stratified turbulence
Understanding the manner by which wind-generated, near-inertial energy leaves the oceanic mixed layer continues to be a topic of interest since it provides an important pathway from a surface energy source to eventual dissipation at depth. Whether most of the dissipation occurs at the base of the mixed layer or in the stratified interior, at critical layers or through shear instability remains an open question. The role of mesoscale eddies in trapping near-inertial energy is, by now, well established. Here, the focus is on the vertical propagation of near-inertial energy trapped in an isolated eddy with a detailed examination of the energy budget and scales of generated inertia-gravity waves as a function of eddy vorticity and spatial extent. Waves with frequencies close to the inertial frequency break down primarily via shear instability, characterised by KH billows. Those with intermediate frequencies between inertial and buoyancy frequencies are subject to a hybrid shear/convective instability that gives rise to mushroom-like structures whereas high-frequency waves are prone to rapid convective instability. For near-inertial waves, the onset of instability occurs in the phase region of strongly stratified fluid in contrast to the scenario for convective instability where the density gradient is at its weakest. The energetics of breaking waves will be discussed as a function of their frequency and amplitude to establish whether the instability that leads to their breakdown is a factor in the resulting mixing efficiency. 
Dr Pascale Lelong, NorthWest Research Associates, USA
Dr Pascale Lelong, NorthWest Research Associates, USAM.-Pascale Lelong obtained her PhD in Applied Mathematics from the University of Washington, under the supervision of Professor James J Riley. Her thesis work, which resulted in the identification of a new resonant interaction between internal waves and vortical modes in stratified fluids, provided motivation for her continuing interest in stratified turbulence and internal-wave dynamics. Following a post-doc in the Advanced Study Program at the National Center for Atmospheric Research, she moved back to her native France for a second post-doc in Grenoble. She joined NorthWest Research Associates in 1994 as a Research Scientist and was promoted to Senior Research Scientist in 2004. Dr Lelong's research interests cover several aspects of stratified-flow dynamics, with an emphasis on oceanic applications. Recent contributions have focused on the production of stratified rotating turbulence following internal-wave breaking events, and the lateral dispersion of passive tracers in oceanic flows dominated by stratified turbulence or broadband internal wave fields on horizontal scales of 100 m to 10km. |
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| 15:40 - 16:20 |
The turbulent transition of a supercritical downslope flow: sensitivity to downstream conditions
Blocked, continuously stratified, crest controlled flows have hydraulically supercritical downslope flow in the lee of a ridge-like obstacle. The downslope flow separates from the obstacle and, depending on conditions further downstream, transitions to a subcritical state. A controlled, stratified overflow and its transition to a subcritical state are investigated here in a set of three-dimensional numerical experiments. The downslope flow is associated with an isopycnal and streamline bifurcation, which acts to form a nearly uniform density isolating layer and a sharp pycnocline that separates deeper blocked and stratified fluid between the ridges from the flow above. The height of the downstream obstacle is communicated upstream via gravity waves that propagate along the density interface and set the separation depth of the downslope flow. The penetration depth of the downslope flow, its susceptibility to shear instabilities, and the amount of energy dissipated in the turbulent outflow all increase as the height of a downstream ridge, which effectively sets the downstream boundary conditions, is reduced. 
Professor Kraig Winters, University of California San Diego, Scripps Institution of Oceanography, USA
Professor Kraig Winters, University of California San Diego, Scripps Institution of Oceanography, USADr Winters received his PhD in Applied Mathematics from the University of Washington in 1989. He has held academic positions at the University of Washington, the University of Western Australia, and the University of California San Diego, where he is currently Associate Director of Integrative Oceanography at the Scripps Institution of Oceanography. Kraig's research interests include rotating, stratified flows, topographic interactions, continuously stratified hydraulics and hydrodynamic stability. Dr Winters develops and applies high performance numerical techniques to problems in environmental fluid dynamics as a foundation for improving conceptual and theoretical understanding of fundamental processes in geophysical fluid dynamics. |