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SCIENTIFIC PROGRAMS AND ACTIVITIES |
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Invited Speaker AbstractsLeon Boegman Flow separation and resuspension beneath shoaling nonlinear internal waves Laboratory observations are presented showing the structure and
dynamics of the turbulent bottom boundary layer beneath nonlinear
internal waves (NLIWs) of depression shoaling upon sloping topography.
The adverse pressure gradient beneath the shoaling waves causes
the rear face to steepen, flow separation to occur, and wave-induced
near-bottom vortices to suspend bed material. The resuspension is
directly attributed to the near-bed viscous stress and to near-bed
patches of elevated positive Reynolds stress generated by the vortical
structures. These results are consistent with published field observations
of resuspension events beneath shoaling NLIWs. Elevated near-bed
viscous stresses are found throughout the domain at locations that
are not correlated to the resuspension events. Near-bed viscous
stress is thus required for incipient sediment motion but is not
necessarily a precursor for resuspension. Resuspension is dependent
on the vertical velocity field associated with positive Reynolds
stress and is also found to occur where the mean (wave-averaged)
vertical velocity is directed away from the bed. The results are
interpreted by analogy to the eddy-stress and turbulent bursting *************************************************************************************************** Lydia Bourouiba Role of nonlocal interactions in the two-dimensionalization
of forced rotating turbulence Coauthors: D. Straub (McGill University) *************************************************************************************************** Magda Carr Benthic boundary layer flow induced by large amplitude internal solitary waves (ISWs) is investigated. Experimental measurements of the velocity fields close to the bottom boundary are presented to illustrate the generation of an unsteady boundary jet along the bed beneath an ISW of depression. The formation of the jet, the structural characteristics of which show striking similarities with those predicted by numerical model studies by Diamessis & Redekopp (2006), is attributed to boundary layer separation in the adverse pressure gradient region of the wave-induced flow. Moreover, experimental evidence is presented in support of the theoretical prediction of Diamessis & Redekopp (2006) for wave-induced vortex shedding at the lower solid boundary as a result of global instability. Measurements of the velocity field close to the bottom boundary illustrate coherent periodic shedding of vortex structures at the lower boundary in the adverse pressure gradient region aft of the wave. The vortical structures ascend high into the water column and cause significant benthic turbulence. It is shown that global instability has a critical threshold dependent upon the Reynolds number of the flow and the amplitude of the wave. The critical amplitudes observed are approximately half that predicted by Diamessis & Redekopp (2006) indicating internal wave-induced benthic mixing may be even more prominent than previously thought. The benthic boundary layer flow induced by an ISW of elevation is less clearly understood. There is debate in the current literature as to whether ISWs of elevation can induce vortical structures and re suspend sedimentary material in a similar fashion to ISWs of depression (see Statsna & Lamb 2002 and Diamessis & Redekopp 2006). Recent experimental findings will be presented and discussed in the context of this debate. *************************************************************************************************** Melissa Coman Horizontal convection forced by two spatially-separated regions of destabilising flux We present horizontal convection experiments in which the thermal forcing is such that there is one region of stabilising buoyancy flux but two regions of destabilising buoyancy flux. We focus on the steady state circulation owing to the two plumes that form as a consequence of the destabilising fluxes. This arrangement of buoyancy fluxes is motivated by the high latitude sinking in the Northern and Southern Hemispheres of the current ocean. The experiments broadly outline the interaction of two deep sinking plumes and describes how the circulation and interior stratification changes when the ratio of the destabilising ‘surface’ buoyancy fluxes change. We classify the flow into three regimes of overturning, according to the pattern of interior circulation and depending on the relative strengths of the two plumes. We find that unequal plumes increase the interior stratification above that of two equal plumes, and when one plume is stronger than the other by more than 10%, the interior stratification is set by the stronger plume. We also introduce a sill into the horizontal convection experiment. The gap above the sill must accommodate a mass exchange in the thermal boundary layer and the return flow over the sill. We find that for a sill to have a significant effect on the circulation and heat transport the gap above the sill must be less than 25% of the depth of the domain. *************************************************************************************************** Georges Djoumna The advection process strongly affects the evolution of temperature, salinity, and passive tracers in the ocean interior. It is related to the stability, accuracy, and efficiency of the numerical methods that are used in the ocean models. Here, the finite-element, semi-implicit, and semi-Lagrangian methods are used on unstructured meshes to solve the nonlinear shallow water system. A new semi-Lagrangian scheme is developed by tracking back a particle located at a quadrature node. It is shown that standard interpolation schemes such as linear and quadratic perform quite well with this alternative semi-Lagrangian method. A class of high order C1 interpolating schemes based on the Hsieh-Clough-Tocher finite-element is also developed for an accurate treatment of the advection terms. By tracking the characteristics backward from both the interpolation and quadrature nodes and using C1 interpolating schemes, an accurate treatment of the nonlinear advection terms and hence, of Rossby waves, is obtained. Numerical results of the test problems to simulate, the linear advection of a cosine hill and the slowly propagating Rossby modes are presented that demonstrate the performance of the proposed approach on more realistic problems. *************************************************************************************************** David DritschelUniversity of St Andrews Jet sharpening Jets - narrow currents of streaming fluid - are found widely in planetary atmospheres and in the oceans. They are a product of fluid dynamical nonlinearity, whereby gradients of a nearly conservative dynamical tracer, potential vorticity, are steepened in places by Rossby wave breaking and homogenised in others by turbulent mixing. This talk illustrates, in a simple model, how jets intensify or sharpen as a result of basic barotropic and baroclinic instabilities. *************************************************************************************************** Jerome Fontane Two-dimensional forced turbulence Two-dimensional turbulence has been extensively studied as it represents the simplest model for geophysical flows and it also exhibits one of the most remarkable features of fluid dynamics, namely the dual cascade of energy and enstrophy. When the flow is fed with an energy input at some given wavenumber kf , energy cascades upscale partly through the growing of vortices and enstrophy cascades downscale through vorticity filamentation. Since the pioneering theoretical work of Kraichnan (1967) and Batchelor (1969), it is well recognised that the energy spectrum takes the form E(k) = C.2/3k.5/3 for k < kf and E(k) = CƒÅ2/3k.3 for k > kf where . and ƒÅ are respectively constant energy and enstrophy fluxes. However, Scott (2007) has recently pointed out the nonrobustness of this spectral form especially when the forcing wavenumber is well separated from the dissipation range and the Reynolds number is large. In that case, the energy-cascading range steepens from k.5/3 to k.2. High resolution numerical simulations using two different algorithms (spectral methods and contour advection) confirm the departure from Kraichnanfs spectral prediction of the k.5/3 energy-cascading range. The spectra are seen to converge very rapidly to a fixed form, then only evolving in time at large scales. We propose an analytical form for the enstrophy spectrum whose parameters are determined from the total energy and enstrophy evolution. The front of the enstrophy spectrum evolving towards low wavenumbers is consistent with the linear growth of energy. Finally, we discuss the spectrum shape by investigating the role played by filaments and coherent structures, the latest being responsible for the departure from Kraichnanfs theory. *************************************************************************************************** Stephen D Griffiths Modelling internal tides in the ocean Internal tides are generated as the surface (barotropic) tide flows
over topography. The implied vertical motion at the sea-floor can
force large amplitude internal waves in the stratified ocean interior,
with vertical displacements of 50m or more. At sufficiently low
latitudes, this internal tide propagates away from the generation
region, leading to an important energy transfer from the barotropic
tide to the ocean interior. *************************************************************************************************** S. G. Gopalakrishnan Recent Developments in Hurricane Structure and Intensity Forecasting Research at NOAA Forecasting intensity changes in Tropical Cyclones (TCs) is a complex and challenging multi-scale problem because the factors that are known to influence these changes may vary in scales ranging between several hundreds of kilometers (example: environmental shear and upper ocean structure) to a few kilometers (example: vortex scale interactions and ocean waves) and, perhaps sometime, even down to a few hundred meters (example: individual cloud and turbulent scale motions). The hurricane forecast improvement project (HFIP) is a unified NOAA approach to guide and accelerate improvements in hurricane track, intensity and structure forecasts, with an emphasis on rapid intensity change. An integral component of the HFIP will be the development of improved coupled atmosphere-ocean-land surface, high-resolution non-hydrostatic regional models.A general introduction of the NOAAs high-resolution version of the hurricane prediction system, called the HWRFX, will be presented. The prediction system appears to produce some of the salient features observed in the inner core at about 3 km resolution. Within the context of this system some of the basic mechanisms leading to modeled intensity changes as a function of horizontal grid resolution will also be discussed. Our initial finding indicates that better resolution may be important to improve forecast of vortex scale motions but the hurricane intensity change forecasting problem is simply beyond a model grid resolution or a multi-processor problem. Better representation of physical processes in numerical models and improved initial conditions may lead to improved intensity forecasting. *************************************************************************************************** Jets in planetary-scale turbulent flows This present work focuses on one key feature of large-scale flows in planetary atmospheres: high speed currents of fluid or 'jets'. We present the results from a series of freely-decaying quasigeostrophic turbulence simulations conducted to investigate the emergence of jets and their characteristic spacing. These numerical experiments have been carried out using a very accurate 'contour-advective semi-Lagrangian' (CASL) algorithm in order to simulate these complex flows, the evolution of which are controlled by two basic parameters, namely the Rossby deformation length and the planetary vorticity gradient. We discuss the problem of defining jets and determining their characteristic spacing and present evidence of persistent vortices co-existing with jets at long times, a result which few past studies have observed without forcing. Coauthors: David G. Dritschel *************************************************************************************************** Paul Kushner Climatic influences on mixing in small lakes This talk will present some ideas on the question of how climate
variability and change influences the process of mixing in small
lakes. In particular, we are interested in the thermal- and wind-forced
vertical flux of heat and nutrients by eddying motions in small
lakes that are capable of developing seasonal stable thermal stratification.
Lake mixing depends nonlinearly on meteorological fields like the
surface wind and temperature; because of this nonlinearity, the
average meteorology does not necessarily reflect the average lake
mixing. Because meteorological variability relevant to lake mixing
often results from continental or even planetary scale atmospheric
teleconnections like the PDO and AO/NAM, lake mixing is also a process
whose control is highly nonlocal. We discuss these issues in the
context of a recent study of summertime lake mixing dynamics at
Toolik Lake in Northern Alaska. At this site summertime mixing is
strongly controlled by the frequency and intensity of the rapid
temperature drops and extreme wind events associated with passing
cold fronts. Because of the nonlinear relationship between meteorological
forcing and surface winds and temperatures, these subseasonal timescale
(less than two week timescale) events are able to dominate the lake
mixing, more than variability of the mean climate. Control of subseasonal
variability is, in turn, linked to large-scale patterns of circulation.
We will discuss how the lessons learned in this case study might
apply to other studies of mixing in small lakes, and hope to generate
a discussion on how research in this area might be further pursued
collaboratively between climate scientists and limnologists. *************************************************************************************************** Kevin Lamb Energetics of Solitary-like Internal Waves in the Ocean Large amplitude, internal solitary-like (ISWs) waves are highly
energetic phenomena common to the coastal ocean. They can contain
a *************************************************************************************************** Dan Lucas Vortices are ubiquitous phenomena in the atmosphere and oceans and our understanding of geophysical flows relies on a thorough knowledge of the dynamics of such structures. To such an end vortex equilibria have proved an invaluable tool in helping to develop fast and accurate mathematical models of a wide variety of fluid regimes. In this work we present a new class of vortex equilibria possessing helical symmetry. Such helical vortices are observed in a number of environmental applications, most notably in rotor wakes (e.g. wind turbines, propellors). Coherent columnar vortices (e.g. tornados) can also be observed to evolve with a twisting structure. We define our steadily rotating equilibrium states by contours bounding a region of uniform axial vorticity in an incompressible inviscid irrotational unbounded fluid. We consider single and multiple vortex equilibria, parameterised by mean radius and centroid position, and examine stability properties using a helical CASL algorithm. *************************************************************************************************** Rebekah Martin The Storm Studies in the Arctic (STAR) is a four-year research Network (2007-2010) involving a wide range of activities on the part of researchers from five Canadian universities and Environment Canada. The project is concerned with the documentation, better understanding and improved prediction of meteorological and related hazards in the Canadian Arctic. As part of the project, a major meteorological field campaign took place from October 10 –November 30, 2007 and in February 2008 and was focused on southern Baffin Island, Nunavut, Canada. During the fall study period of the campaign, a major storm event occurred over the southern Baffin Island region from 16-19 November, 2007. During the system’s passage, over the Hudson Strait, several drop sondes and microwave measurements of its warm front were taken. This talk will provide an overview of the structure of this Arctic system as revealed by these measurements. As well, we will discuss a comparison of the archived forecast model output to the measurements. *************************************************************************************************** David J Muraki The evolution of weather systems in the midlatitude atmosphere are well-explained by the theory of quasigeostrophy (QG), in which slow, synoptic-scale airflows are described through the advection of potential vorticity (PV). The mathematics of QG is often justified by a limit of small Rossby number. However, this assumed limit is made invalid across the equator by the vanishing of the Coriolis effects. A model based upon the dynamics of PV is developed for rotating shallow water on the sphere. Specifically, a PV-streamfunction relationship is defined which determines the flow velocities for the entire sphere. At midlatitudes, the fluid dynamics are equivalent to the beta-plane theory of QG, in the usual small Rossby number sense. In the equatorial regions, wave propagation at short-scales mimics the dispersion relation for equatorial beta waves. These dynamics compare favorably with computations of the equatorial crossing of topographic waves by Grose & Hoskins (1979). Despite that this PV model is not obtained in the usual manner of small Rossby number asymptotic analysis, the propagation of mesoscale waves across the equatorial region retains QG-like accuracy. The PV dynamics are contrasted with the shallow water primitive equations from the perspectives of ray theory and baroclinic instabilities. *************************************************************************************************** Julie Pietrzak Stratified flows and their role in controlling the exchange between rivers and ocean basins Estuaries, with their associated coastal river plumes, are the interface between fresh river waters and saline coastal waters. Much of the exchange between the two systems is controlled by stratified flows within the estuary and along the coastal zone. These Regions of Freshwater Influence (ROFI's) dominate the transport of freshwater and matter in coastal oceans. They control the exchange of freshwater, sediment, contaminants and nutrients between inland rivers and ocean basins. Consequently they have a huge impact on the health and biological productivity of coastal seas. They also control the ultimate fate of increased river runoff due to climate change, as it makes it way to the oceans. Yet they are poorly resolved in large scale models. We present a new upwelling mechanism; as detected in a unique sequence of sea surface temperature satellite images. These are the first images to show coastal upwelling induced by tidal straining. We also use a numerical model to show how this tidally driven upwelling mechanism comes into being. We discuss the implications of tidal straining induced upwelling on coastal dynamics and its impact on the fluxes of sediment and nutrients in the coastal zone. We also examine the role of wind driven upwelling and straining on stratification and mixing. Having shown the importance of this narrow coastal zone, we then explain why it should be resolved in ocean models and briefly introduce our unstructured grid model developments. We show that coastal and estuarine models based on unstructured meshes have distinct advantages over traditional Cartesian based models. *************************************************************************************************** Francis Poulin The Instability of Time-Dependent Baroclinic Shear Flows Geophysical shear flows in nature are often idealized to be steady.
This approach has proven useful in predicting the stability characteristics
of many flows such as the Gulf Stream, but it is not without limitations.
As time variations are ubiquitous in nature, it is of great interest
to understand how they can alter the stability of a system. Here,
I present examples of aperiodic systems in order to better understand
what effect irregularity (stochasticity) has on the stability characteristics
of a basic state. In particular, I discuss the Mathieu's equation
and the linearized Phillips model. *************************************************************************************************** Marek Stastna Two examples of multiscale simulations in stratified flow over topography In this talk I will discuss the simulation of two different problems in stratified flow over topography that span widely disparate length scales. In the first problem, I consider the effects of rotation on supercritical flow over isolated topography. For appropriately tuned inflows, with rotation turned off, the simulations yield large disturbances that are trapped over the topography. Rotation allows a tail of long long, hydrostatic Poincare waves to form behind the initial disturbance. In certain cases a secondary non-hydrostatic disturbance can form well behind the topography (50 kilometers in some cases). In the second problem, I consider the effects of boundary layer separation on the generation of internal wave beams by subcritical flow such as a seiche over short topography. Throughout I will discuss the computational hurdles that needed to be overcome and will speculate on the sort of model improvements that would allow the greatest gains. *************************************************************************************************** G E Swaters The role of dissipation in the transition to instability in baroclinic
quasi-geostrophic flow can be counter-intuitive (Klein and Pedlosky,
JPO, 1992). It is natural to assume that dissipation acts to reduce
the growth rates of baroclinic flows that are inertially (i.e.,
in the absence of dissipation) unstable and for flows that are inertially
stable, dissipation will lead to the decay in the perturbation amplitudes
over time. However, it has been known since Holopainen (Tellus,
1961) and, within the context of the Phillips model, Romea (JAS,
1977) that sub-critical baroclinic shears in the linear inertial
stability theory can be destabilized by the presence of an Ekman
boundary layer and that this destabilization occurs even in the
zero dissipation limit of the frictional theory. That is, there
is a range of sub-critical baroclinic shears (in the linear inviscid
theory) which are destabilized by the presence of an Ekman boundary
layer no matter how small the Ekman number is. Recent work by Kretchetnikov
and Marsden (Rev. Mod. Phys., 2007 and Arch. Rat. Mech. Anal., 2009)
has described this counter-intuitive dissipative destabilization
within the context of the underlying Hamiltonian structure of the
(inviscid) model equations. In particular, Kretchetnikov and Marsden
(2009) have extended Romea's (1977) work and showed that Ekman destabilization
within the Phillips model can occur for baroclinic shears that are
inertially nonlinearly stable in the sense of Liapunov. *************************************************************************************************** Chuong Tran The number of degrees of freedom of three-dimensional Navier-Stokes
turbulence In Kolmogorov's phenomenological theory of turbulence, the energy inertial range scales with the wave number k as k-5/3 and extends up to a dissipation wave number kn, which is given in terms of the energy dissipation rate e and viscosity n by kn ? (e/n3)1/4. This result leads to Landau's heuristic estimate for the number of degrees of freedom that scales as R9/4, where R is the Reynolds number. Here we consider the possibility of establishing a quantitative basis for these results from first principles. In particular, we examine the extent to which they can be derived from the three-dimensional Navier-Stokes system, making use of Kolmogorov's hypothesis of finite and viscosity-independent energy dissipation only. It is found that the Taylor microscale wave number kT (a close cousin of kn) can be expressed in the form kT ? CU/n = (CU/\norm)1/2(e/n3)1/4. Here U and \norm are, respectively, a "microscale" velocity and the root mean square velocity and C ? 1 is a dynamical parameter. This result can be seen to be in line with Kolmogorov's prediction for kn. Furthermore, it is shown that the minimum number of greatest Lyapunov exponents whose sum becomes negative does not exceed R9/4, where R is defined in terms of an average energy dissipation rate, the system length scale, and n. This result is in a remarkable agreement with the Landau estimate, up to a presumably slight discrepancy between the conventional and the present energy dissipation rates used in the definition of R. *************************************************************************************************** Michael Waite Buoyancy scale dynamics in stratified turbulence Much of the research in stratified turbulence over the last two
decades has been motivated by the kinetic energy spectrum of the
atmospheric mesoscale, which is observed to have a -5/3 spectral
slope. It has been shown recently that such a spectrum can result
*************************************************************************************************** Matthew Wells A theory to explain the entrainment ratio of gravity currents The dynamics of both density and turbidity currents are determined by mixing and drag due to turbulence at the upper and lower interface. The magnitude the mixing and interfacial drag is often parameterized in terms of a dimensionless entrainment ratio E in gravity currents, but there has not previously been any unifying theory to predict either the magnitude of E or to determine how E depends upon the stability of the flow. Such a theory would then predict when the bottom drag co-efficient CD would be greater of less than the interfacial drag E, for different Reynolds and Froude numbers. We present an explanation of the functional dependence of E upon the Froude number and Reynolds number of a gravity current. Our theory is based upon the observed variation of the flux coefficient G (sometimes known as the mixing efficiency). Our main theoretical result is that E= 0.25 G Fr2 cos(?), where ? is the angle of the slope over which the gravity current flows, and Fr the Froude number. In the case of high Froude numbers we find that E ~ 0.1, consistent with observations of a constant entrainment ratio in unstratified jets and weakly stratified plumes. For Froude numbers close to one, G is constant and has a value in the range of 0.1 - 0.3, which means that E ~ Fr2, again in agreement with observations, and previous experiments. For Froude numbers less than one, G decreases rapidly with Froude number, explaining the sudden decrease in entrainment ratios that has been observed in all field and experimental observations. We also show that the functional form of the stratified turbulent diffusivity K? has the same dependence upon the Froude number as the entrainment ratio. *************************************************************************************************** Ram Yerubandi The Laurentian Great Lakes have horizontal scales of hundreds of
kilometers and depth scales of hundreds of meters. These lakes are
subjected to many of the same forcing as coastal oceans and serve
as model basins for understanding the complex coastal ocean dynamics.
An understanding of the hydrodynamic processes is essential to develop
science based integrated management of the Great Lakes. With this
broad objective in mind systematic monitoring and modeling studies
of the North American Great Lakes have been carried out for well
over three decades at Environment Canada's National Water Research
Institute. In the first part of the talk I will briefly describe
some historical modeling activities in the Great Lakes. ***************************************************************************************************
Contributed Talks AbstractsPayam Aghsaee Breaking of Shoaling Internal Solitary Waves The breaking of fully nonlinear internal solitary waves shoaling upon a uniformly sloping boundary was investigated using two-dimensional direct numerical simulations. Our simulations were limited to narrow-crested waves, which are shown to be more common in geophysical flows. The simulations were performed for a wide range of boundary and wave slopes (0.01 < S < 0.3) extending the parameter range considered in previous laboratory and numerical studies. Over steep slopes (S > 0.1), three distinct breaking processes were observed; surging, plunging and collapsing breakers which are associated with reflection, convective instability and boundary layer separation, respectively. Over mild slopes S < 0.05 nonlinearity varies gradually and fission results from dispersion. The dynamics of each breaker type were investigated and the predominance of a particular mechanism was associated with a relatively rapid developmental timescale. The breaking location was modelled as a function of wave amplitude (a), characteristic wave length (Lw) and the isopycnal length along the slope (Li). The breaker type was characterized in wave slope (a/Lw) versus S space and the reflection coefficient (R), modelled as a function of the internal Iribarren number, was in agreement with other studies. The effects of grid resolution and Reynolds number R on (R), boundary layer separation and the evolution of global instability were considered. High Reynolds numbers (R > 104) were found to trigger a global instability, which modifies the breaking process, relative to the lower Re case, but not necessarily the breaking location and results in an increase in the reflection coefficient by approximately 10%. Co-authors: Leon Boegman (Queens University), Kevin Lamb (University of Waterloo)*************************************************************************************************** Abbas Dorostkar Three Dimensional Modeling of Internal Waves in a Medium Sized
Lake Co-authors: Andrew Pollard (Queen's University), Peter Diamessis (Cornell University) *************************************************************************************************** Michael Dunphy The Influence of Mesoscale Eddies on the Internal Tide The barotropic tide dissipates a well established estimate of 2.5
TW of energy at the M2 frequency. Bottom topography is responsible
for a lot of this dissipation, and the generation of the internal
tide is also a substantial sink of this energy. The fate of this
energy is largely described by a cascade from large scales to smaller
scales by non-linear wave-wave interactions until the energy is
dissipated at turbulent length scales. *************************************************************************************************** V. Gerasik Complex group velocity in absorbing media Complex group velocity is common in absorbing and active media.
From the physical point of view the concept of the complex group
velocity is obscure. Unlike purely real group velocities in conservative
dynamical systems, complex group velocity cannot *************************************************************************************************** D. Godlovitch Monte Carlo Modelling of the Evolution of the Sea Ice Thickness Distribution A Markov Chain Monte Carlo (MCMC) method for simulating the dynamic evolution of the thickness distribution of sea ice is introduced. It has been observed that the sea ice thickness distribution has a relatively invariant negative exponential form over data from a wide range of geographic locations and as yet, no model directly examines the physical mechanisms behind this property. The thickness distribution of sea ice results from a combination of thermodynamic growth and ice-ice interactions caused by forcing from winds and currents. The ice-ice interactions are complex and difficult to describe due to the material properties of sea ice. By simplifying the dynamics, a MCMC model is developed in order to explore the relative importance of the physical processes contributing to the observed thickness distribution. *************************************************************************************************** Wentao Liu Lake Erie Modeling with ELCOM Hydrodynamic and thermodynamic modeling of Lake Erie from April to October 2002 with ELCOM (Estuary, Lake and Coastal Ocean Model) is discussed in this talk. Observation data of inflows, outflows, winds, solar radiation, air temperature, and humidity are input hourly to the model. Three sizes of equally-spaced horizontal grids are implemented in the model, which range from 2 km, 1 km, to 600m. By comparing different grids, the preliminary results of the temperature and the velocities in the surface and vertical curtains crossing each basin are presented. Given the continuous mooring observation data for the temperature in one station in the eastern basin from May to October 2002, the simulation matches the observation quite well. There are also data available in several sampling stations in each basin, which contains the temperature profiles for four different days. A comparison of the observation and simulation using different sizes of grids is investigated as well. *************************************************************************************************** K. Mitchell Fourier Spectral Computing on the Sphere Co-authors: David Muraki (Simon Fraser University), Andrea Blazenko *************************************************************************************************** M. Nica Faraday waves in the Shallow Water Model Faraday waves appear on the free surface of a fluid that is subject to sinusoidal vertical forcing. In this presentation, we study the generation of these waves in the context of the rotating reduced gravity shallow water model. By solving the linear stability problem we compute the regime of unstable wave numbers as well as their corresponding growth rates. Furthermore, we study the nonlinear evolution of these unstable modes to determine the effects of nonlinear equilibration. The effects of viscosity, Coriollis force, and stochastic forcing will all be considered. *************************************************************************************************** P. Pernica Does the variability in wind driven turbulence drive variation in plankton patchiness? Previous observations of the patchiness of zooplankton in the South Arm basin of Lake Opeongo (Ontario, Canada) have been linked to wind speed, with heterogeneous distributions occurring at wind speeds of 3 m/s - 7 m/s (Blukacz et al. 2009). The variations in wind velocity are thought to directly affect the structure of the mixed layer of the lake. In July 2008, velocity profiles of the water column of the epilimnion were measured over a one week duration. The effect of the wind on the mixed layer of the lake is quantified using the dimensionless Froude number (Fr) and the turbulent kinetic energy (TKE). Fr compares inertial forces to the strength of the stratification of the surface layer. Results indicate that the wind speed correlates with Fr. Wind speeds of 3 m/s to 7 m/s for which zooplankton patchiness was observed (Blukacz et al. 2009) correspond to Fr~1 indicating that basin is in a weakly mixed state. Average TKE in the epilimnion is shown to correlate with Fr and also displays spatial heterogeneity corresponding with Bluckacz (2007) observed change points of zooplankton variance. Co-author: M.G.Wells *************************************************************************************************** Modeling ice algae in the Canadian Arctic Archipelago *************************************************************************************************** T. Rees Simulating Forced Waves In Continuously Stratified Fluids In this talk I will discuss some of the problems that arise in numerical simulations where forcing the momentum equations is used to generate internal waves. In particular, I will show that when forcing waves in a fluid of nonconstant buoyancy frequency the expected waves in the resulting flow do not necessarily possess the most energy. I will explain this result using Sturm-Liouville theory, and present a method that forces the intended waves resonantly while avoiding resonance in undesired waves. This will be demonstrated in the context of a fully nonlinear pseudo-spectral model but the analysis naturally extends to any numerical method. *************************************************************************************************** Results from numerical experiments of a stratified Boussinesq fluid with background current are presented. The iterative numerical model includes a sheared background current and valley-like topography. Trapped waves of different amplitudes are produced for different types of background currents. A hysteresis loop is observed by changing the shear of the background currrent: significant differences in the amplitude of the wave develop if the shear is increased as opposed to decreased. Extensions to stratified non-Boussinesq fluids have been made. *************************************************************************************************** A high-order numerical study of western boundary current separation along a curved coastline Western boundary currents, such as the Gulf Stream and the Kuroshio,
are of great interest because they contribute significantly to the
pole-ward transportation of heat, chemistry and biology in the world's
oceans. The dynamics of these currents are highly nonlinear and
thus numerical simulations are perhaps the best tool available to
study them. Recent advances in understanding the separation process
of western boundary currents are due to simulations that integrated
the barotropic Quasi-Geostrophic model using low-order numerical
methods such as finite differences or the finite element method
as in [1]. Co-authors: Francis Poulin (University of Waterloo), Serge d'Alessio
(University of Waterloo) *************************************************************************************************** A Pseudospectral Method for the Direct Simulation of the Incompressible Navier-Stokes Equations Direct simulation of fluid flow in three dimensions is possible with modern computing resources. Demands on system memory scale as O(N^3), and this can be easily prohibitive. A pseudospectral method for these simulations has optimal memory characteristics, and even with a mixed Forurier/Chebyshev polynomial expansion allows single-timestep solution times with O(N^3 log(N)) complexity. This talk introduces such a model and presents preliminary results on the three-dimensionalization of a dipole/no-slip wall interaction. *************************************************************************************************** Paul Ullrich Riemann-Solver Based Shallow-Water FV Models on the Sphere In this work we present a set of well-balanced second-, third- and fourth-order finite volume (FV) methods for solving the shallow water equations on the sphere using the MUSCL scheme of van Leer (1979), where edge fluxes are obtained via solving Riemann problems at Gaussian quadrature points along each edge. We compare three types of Riemann solver, including the basic solver of Rusanov, the scheme of Roe (1981) and the new AUSM+-up solver of Liou (2006). We also make use of the cubed sphere grid of Ronchi et al. (1996), which provides almost uniform resolution in all areas of the sphere using six identical grid patches obtained from "inflating" a cube that has been placed inside of a sphere. The resulting numerical methods are compared using several standard shallow water test cases, including the test suite of Williamson et al. (1992) and the unstable barotropic instability of Galewsky et al. (2004). As expected, we observe high-order accuracy from each of the finite volume schemes.
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