Stratified Interior Research Articles

Ageostrophic instability in a rotating stratified interior jet

AbstractOceanic large- and meso-scale flows are nearly balanced in forces between Earth’s rotation and density stratification effects (i.e. geostrophic, hydrostatic balance associated with small Rossby and Froude numbers). In this regime advective cross-scale interactions mostly drive energy toward larger scales (i.e. inverse cascade). However, viscous energy dissipation occurs at small scales. So how does the energy reservoir at larger scales leak toward small-scale dissipation to arrive at climate equilibrium? Here we solve the linear instability problem of a balanced flow in a rotating and continuously stratified fluid far away from any boundaries (i.e. an interior jet). The basic flow is unstable not only to geostrophic baroclinic and barotropic instabilities, but also to ageostrophic instabilities, leading to the growth of small-scale motions that we hypothesize are less constrained by geostrophic cascade behaviours in a nonlinear regime and thus could escape from the inverse energy cascade. This instability is investigated in the parameter regime of moderate Rossby and Froude numbers, below the well-known regimes of gravitational, centrifugal, and Kelvin–Helmholtz instability. The ageostrophic instability modes arise with increasing Rossby number through a near-degeneracy of two unstable modes with coincident phase speeds. The near-degeneracy occurs in the neighbourhood of an identified criterion for the non-integrability of the ‘isentropic balance equations’ (namely $A\ensuremath{-} S= 0$ with $A$ the absolute vertical vorticity and $S$ the horizontal strain rate associated with the basic flow), beyond which development of an unbalanced component of the flow is expected. These modes extract energy from the basic state with large vertical Reynolds stress work (unlike geostrophic instabilities) and act locally to modify the basic flow by reducing the isopycnal Ertel potential vorticity gradient near both its zero surface and its critical surface (phase speed equal to basic flow speed).

Nearshore internal bores and turbulent mixing in southern Monterey Bay

We observed transient stratification and mixing events associated with nearshore internal bores in southern Monterey Bay using an array of instruments with high spatial and temporal resolution. The arrival of the bores is characterized by surging masses of dense (cold) water that tend to stratify the water column. The bore is followed by a gradual drop in the temperature throughout the water column over several hours (defined here as the bore period) until a sharp warm‐front relaxation, followed by high frequency temperature fluctuations, returns the column back to nearly its original state (defined here as the mixing period). Mixing periods revealed increased temperature variance at high frequencies (ω > ), as well as a greater percentage of events where dynamic instabilities may be present (Ri< 0.25), suggesting active mixing of the stratified water column. Turbulent dissipation rates in the stratified interior during the mixing period, estimated using the technique of isopycnal slope spectra, revealed mean values the same order of magnitude as near‐bed bottom‐generated turbulence. Observations indicate that local shear‐produced turbulent kinetic energy by the warm front relaxations dominates mixing in the stratified interior. The non‐canonical nature of these bore and relaxation events is also investigated with a numerical model, and the dynamics are shown to depend on the internal Iribarren number. Our results suggest that nearshore internal bores interacting with local bathymetry dramatically alter local dynamics and mixing in the nearshore with important ecological implications.

On the boundary-layer structure of high-Prandtl-number horizontal convection

This paper describes the boundary-layer structure of the steady flow of an infinite Prandtl number fluid in a two-dimensional rectangular cavity driven by differential heating of the upper surface. The lower surface and sidewalls of the cavity are thermally insulated and the upper surface is assumed to be either shear-free or rigid. In the limit of large Rayleigh number (R → ∞), the solution involves a horizontal boundary layer at the upper surface of depth of order R−1/5 where the main variation in the temperature field occurs. For a monotonic temperature distribution at the upper surface, fluid is driven to the colder end of the cavity where it descends within a narrow convection-dominated vertical layer before returning to the horizontal layer. A numerical solution of the horizontal boundary-layer problem is found for the case of a linear temperature distribution at the upper surface. At greater depths, of order R−2/15 for a shear-free surface and order R−9/65 for a rigid upper surface, a descending plume near the cold sidewall, together with a vertically stratified interior flow, allow the temperature to attain an approximately constant value throughout the remainder of the cavity. For a shear-free upper surface, this constant temperature is predicted to be of order R−1/15 higher than the minimum temperature of the upper surface, whereas for a rigid upper surface it is predicted to be of order R−2/65 higher.

THERMAL TIDES IN FLUID EXTRASOLAR PLANETS

Asynchronous rotation and orbital eccentricity lead to time-dependent irradiation of the close-in gas giant exoplanets -- the hot Jupiters. This time-dependent surface heating gives rise to fluid motions which propagate throughout the planet. We investigate the ability of this "thermal tide" to produce a quadrupole moment which can couple to the stellar gravitational tidal force. While previous investigations discussed planets with solid surfaces, here we focus on entirely fluid planets in order to understand gas giants with small cores. The Coriolis force, thermal diffusion and self-gravity of the perturbations are ignored for simplicity. First, we examine the response to thermal forcing through analytic solutions of the fluid equations which treat the forcing frequency as a small parameter. In the "equilibrium tide" limit of zero frequency, fluid motion is present but does not induce a quadrupole moment. In the next approximation, finite frequency corrections to the equilibrium tide do lead to a nonzero quadrupole moment, the sign of which torques the planet {\it away} from synchronous spin. We then numerically solve the boundary value problem for the thermally forced, linear response of a planet with neutrally stratified interior and stably stratified envelope. The numerical results find quadrupole moments in agreement with the analytic non-resonant result at sufficiently long forcing period. Surprisingly, in the range of forcing periods of 1-30 days, the induced quadrupole moments can be far larger than the analytic result due to response of internal gravity waves which propagate in the radiative envelope. We discuss the relevance of our results for the spin, eccentricity and thermal evolution of hot Jupiters.

Dynamics of Winds and Currents Coupled to Surface Waves

We discuss the coupling processes between surface gravity waves and adjacent winds and currents in turbulent boundary layers. These processes mediate exchanges of momentum, heat, and gases between the atmosphere and ocean and thus are of global significance for climate. Surface waves grow primarily by pressure-form stress from airflow over the waveforms, and they dissipate in the open sea by wave breaking that injects and stirs momentum, energy, and bubbles into the ocean. Wave motions pump wind eddies that control fluxes across the lower atmosphere. Flow separation occurs behind steep wave crests, and at high winds the crests flatten into spume, which diminishes the drag coefficient. In the ocean the Lagrangian-mean wave velocity, Stokes drift, induces a vortex force and material transport. These generate Langmuir circulations penetrating throughout the boundary layer and enhancing entrainment at the stratified interior interface in combination with other turbulent eddies and inertial-shear instability.

The effect of floor heat source area on the induced airflow in a room

We examine the role of heat source geometry in determining rates of airflow and thermal stratification in natural displacement ventilation flows. We modify existing models to account for heat sources of finite (non-zero) area, such as formed by a sun patch warming the floor of a room. Our model allows for predictions of the steady stratification and ventilation flow rates that develop in a room due to a circular heat source at floor level. We compare our theoretical predictions with predictions for the limiting cases of a point source of heat (yielding a stratified interior), and a uniformly heated floor (yielding a mixed interior). Our theory shows a smooth transition between these two limits, which themselves result in extremes of ventilation, as the ratio of the heat source radius to the room height increases. Our model for the transition from displacement to mixing ventilation is compared to previous work and demonstrates that the transition can occur for smaller sources than previously thought, particularly for rooms with large floor area compared to ceiling height.

Observations of turbulent mixing in a phytoplankton thin layer: Implications for formation, maintenance, and breakdown

Coincident measurements of chlorophyll a (Chl a) and temperature microstructure from Monterey Bay, California, U.S.A., are used to investigate the dynamics of a phytoplankton thin layer in the context of vertical turbulent mixing. The thin layer was situated in the thermocline of a 20.5‐m water column, between a strongly turbulent surface mixed layer and a weakly turbulent stratified interior. The differential mixing established an asymmetric layer with a stronger Chl a gradient at the base of the layer than at the top. Sinking by Akashiwo sanguinea could have balanced turbulent mixing above the layer, but cannot explain the mid‐column convergence needed to maintain the thin layer. Swimming by A. sanguinea directed towards a mid‐column nitracline could have balanced turbulent mixing on both sides of the layer and supported the observed Chl a gradients. Results from a Eulerian advection‐diffusion model suggest that cell swimming may have varied over the lifetime of the layer, with stronger or more directed swimming required for layer formation and weaker or less directed swimming needed to maintain the layer. In‐layer growth is unlikely to have played a primary role in supporting the observed Chl a gradients. From the one‐dimensional (vertical) observations, the role of shear‐induced straining cannot be evaluated, but shear instabilities appear important to forcing elevated rates of turbulent diffusion within the layer. Finally, a Lagrangian particle‐tracking model is used to explore the implications of a balance of vertical velocity and turbulent diffusion on the vertical motions of individual cells that constitute the thin layer.

The structure of dissipation in the western Irish Sea front

We report on an intensive campaign in the summer of 2006 to observe turbulent energy dissipation in the vicinity of a tidal mixing front which separates well mixed and seasonally stratified regimes in the western Irish Sea. The rate of turbulent dissipation ε was observed on a section across the front by a combination of vertical profiles with the FLY dissipation profiler and horizontal profiles by shear sensors mounted on an AUV (Autosub). Mean flow conditions and stratification were obtained from a bed mounted ADCP and a vertical chain of thermistors on a mooring. During an Autosub mission of 60 h, the vehicle, moving at a speed of ~ 1.2 m s − 1 , completed 10 useable frontal crossings between end points which were allowed to move with the mean flow. The results were combined with parallel measurements of the vertical profile of ε which were made using FLY for periods of up to 13 h at positions along the Autosub track. The two data sets, which show a satisfactory degree of consistency, were combined to elucidate the space–time variation of dissipation in the frontal zone. Using harmonic analysis, the spatial structure of dissipation was separated from the strong time dependent signal at the M 4 tidal frequency to yield a picture of the cross-frontal distribution of energy dissipation. A complementary picture of the frontal velocity field was obtained from a moored ADCP and estimates of the mean velocity derived from the thermal wind using the observed density distribution. which indicated the presence of a strong (0.2 m s − 1 ) jet-like flow in the high gradient region of the front. Under neap tidal conditions, mean dissipation varied across the section by 3 orders of magnitude exceeding 10 − 2 W m − 3 near the seabed in the mixed regime and decreasing to 10 − 5 W m − 3 . in the strongly stratified interior regime. The spatial pattern of dissipation is consistent in general form with the predictions of models of tidal mixing and does not reflect any strong influence by the frontal jet.

Parameterization of Eddy Fluxes near Oceanic Boundaries

Abstract In the stably stratified interior of the ocean, mesoscale eddies transport materials by quasi-adiabatic isopycnal stirring. Resolving or parameterizing these effects is important for modeling the oceanic general circulation and climate. Near the bottom and near the surface, however, microscale boundary layer turbulence overcomes the adiabatic, isopycnal constraints for the mesoscale transport. In this paper a formalism is presented for representing this transition from adiabatic, isopycnally oriented mesoscale fluxes in the interior to the diabatic, along-boundary mesoscale fluxes near the boundaries. A simple parameterization form is proposed that illustrates its consequences in an idealized flow. The transition is not confined to the turbulent boundary layers, but extends into the partially diabatic transition layers on their interiorward edge. A transition layer occurs because of the mesoscale variability in the boundary layer and the associated mesoscale–microscale dynamical coupling.

A theoretical model for horizontal convection at high Rayleigh number

We present a simple flow model and solution to describe ‘horizontal convection’ driven by a gradient of temperature or heat flux along one horizontal boundary of a rectangular box. Following laboratory observations of the steady-state convection, the model is based on a localized vertical turbulent plume from a line or point source that is located anywhere within the area of the box and that maintains a stably stratified interior. In contrast to the ‘filling box’ process, the convective circulation involves vertical diffusion in the interior and a stabilizing buoyancy flux distributed over the horizontal boundary. The stabilizing flux forces the density distribution to reach a steady state. The model predictions compare well with previous laboratory data and numerical solutions. In the case of a point source for the plume (the case which best mimics the localized sinking in the large-scale ocean overturning) the thermal boundary layer is much thicker than that given by the two-dimensional boundary layer scaling of H. T. Rossby (Tellus, vol. 50, 1965, p. 242).

Microstructure measurements in natural waters: Methodology and applications

Modern approaches to microstructure data processing, including wavelet denoising, are discussed. The wavelet procedure is applied to small-scale shear signals before estimating the dissipation rate ε and to the temperature/density profiles used to calculate Thorpe scales. Microstructure data obtained on the Mediterranean shelf of Catalonia are used to illustrate various approaches to the Thorpe displacement calculations. It is suggested that the Weibull probability function is an appropriate model for the Thorpe scale distribution. Microstructure measurements from the upper layer of the Boadella reservoir (Catalonia, Spain) support this finding. A new analytical approximation for the 1D Panchev–Kesich spectrum is deduced and the results of ε computation are compared with spectral fitting by the widely used Nasmyth spectrum. Applying the Kraichnan spectral model to compute ε from temperature spectra in the convective-viscous sub-range is examined as an alternative to the Batchelor spectrum. Microstructure measurements taken in Lake Banyoles (Catalonia, Spain) and in the North Atlantic were used for spectral calculations. Statistical analysis of eddy K b and thermal K θ diffusivities measured on a shallow shelf of the Black Sea shows the importance of process-orientated domain averaging of the diffusivities in obtaining good correspondence between K b and K θ in active turbulent regions. In weakly turbulent, stratified interior layers, the averaged K b and K θ differ significantly, which may point to the inapplicability of isotropic formulae used for ε and temperature dissipation χ θ estimates, as well as to a dependence of the mixing efficiency γ on the Richardson number or in some cases on regions of fossil turbulence.

Sub-inertial modulation of semi-diurnal currents over the continental slope in the Faeroe-Shetland Channel

Observations were made over the continental slope in the Faeroe-Shetland Channel with the purpose of studying motions in the semidiurnal tidal frequency band and their interaction with background conditions. Specifically, the study focused on internal (baroclinic) tidal motions associated with internal gravity waves. In the internal tide (IT) source region, kinetic energy spectra reveal a fall-off rate with frequency of σ −2 which is associated with the passage of strongly non-linear fronts at the sea-bed. At a distance of 10 km off shore from the source region spectra from both the permanent pycnocline and weakly stratified interior exhibit a fall-off rate of σ −3, indicative of a regime in which internal waves are dominated by higher harmonics of the M 2 semidiurnal tidal frequency as a result of non-linear advection. The bandwidth, Δ σ = 0.23 – 0.3 cycles per day (cpd) of the semidiurnal band determined from the distribution of baroclinic energy outside the deterministic tidal frequencies, implies a modulation period of 3.3–4.3 days and which is observed as pulses of semidiurnal energy that are not related to the spring–neap cycle. The period of modulation is related to changes in the background stratification and the low-frequency vorticity. Variations in stratification are sufficient to modify the IT path by>150 m in the vertical over a horizontal distance of 10 km.The cross-slope gradient of the low-frequency ( σ < 0.75 cpd ) long-slope velocity, ∂ V / ∂ x , which represents one component of the vorticity varies with a periodicity of 3–4 days and has a magnitude sufficient to increase the effective Coriolis frequency to a value larger than M 2 so that the IT is unable to propagate as a free internal gravity wave. The source of the subinertial variability in the background conditions is attributed to meteorologically forced continental shelf waves which respond in two ways to prevailing winds and which perturb the pre-existing geostrophic balance that exists over the slope; oscillatory, clockwise rotating currents with a frequency of 0.7× f, where f is the Coriolis frequency, result from short impulsive winds whilst a quasi-steady long-slope flow persists as long as stronger winds of longer duration prevail. The impact of the observed subinertial variability in low-frequency vorticity and stratification raises doubts as to whether an ‘attractor’, along which internal wave energy is found following repeated reflections within a confined basin, may be observed in such a dynamic environment.

Dissipation in the Baltic proper during winter stratification

Profiles of dissipation rates and stratification between 10 and 120 m depth were measured with a loosely tethered profiler over a 9‐day winter period in the Gotland Basin of the Baltic Sea. Supplementary measurements of current profiles were made with moored ADCPs. Temporal and spatial patterns of the stratification were observed by means of towed CTD. Shallow freshwater lenses in the surface mixed layer, mesoscale eddies, inertial oscillations, and inertial waves as part of the internal wave spectrum provided the marine physical environment for the small‐scale turbulence. Two well‐separated turbulence regimes were detected. The turbulence in the surface mixed layer was well correlated with the wind. The majority of the energy flux from the wind to the turbulent kinetic energy was dissipated within the surface mixed layer. A minor part of this flux was consumed by changes of the potential energy of the fresh water lenses. The penetration depth Hpen of the wind‐driven turbulence into the weakly stratified surface mixed layer depended on the local wind speed (W10) as Hpen = cW103/2 Active erosion of the Baltic halocline by wind‐driven turbulence is expected for wind speeds greater than 14 m/s. The turbulence in the strongly stratified interior of the water column was quite independent of the meteorological forcing at the sea surface. The integrated production of turbulent kinetic energy exceeded the energy loss of inertial oscillations in the surface layer suggesting additional energy sources which might have been provided by inertial wave radiation during geostrophic adjustment of coastal jets and mesoscale eddies. The averaged dissipation rate profile in the stratified part of the water column, best fitted by ε ∝ EN, was different from the scaling of the dissipation in the thermocline of the ocean [Henyey et al., 1986]. The diapycnical mixing coefficient (Kv) was best fit by Kv = a0/N according to Stigebrandt [1987] with a0 ≈ 0.87 × 10−7 m2/s2. The diapycnal diffusivity estimated from the dissipation rate was lower than those estimated by the bulk method.

Spin-up from rest in a stratified fluid: boundary flows

We present the results of an integrated experimental, numerical and theoretical examination of spin-up from rest of a stratified fluid. A vertical cylindrical container of radius R and height 2H containing fluid of viscosity ν and characterized by a constant buoyancy frequency N is set impulsively to rotate about its symmetry axis with angular speed Ω = f/2. The characteristic Ekman number E = ν/ΩR2 is small and the Schmidt number S = ν/Ds (where Ds is the diffusivity of salt) is large. The investigation is focused on elucidating the initial stage of spin-up, which is characterized by an axisymmetric circulation driven by nonlinear Ekman layers adjoining the horizontal boundaries. Fluid is drawn by the boundary layers from the stationary, stratified interior and transported into corner regions. It is shown that the corner regions are restricted to a height of approximately 0.3Rf/N from the horizontal boundaries, above which the fluid remains unperturbed apart from that spun up by diffusion of momentum from the sidewall boundary. Two distinct regions thus emerge: rotating corner regions, and a quiescent stratified core. After a time 1.3/(E1/2N), the corner regions cover the bulk of the horizontal boundaries and the boundary layer suction is suppressed. Our study provides a framework for understanding the subsequent evolution of the spin-up process, which may be characterized by axisymmetry-breaking instabilities of the stratified core.

Stability and transition of stratified natural convection flow in open cavities

In this study we have investigated the behaviour of natural convection flow in open cavities, with both homogeneous and thermally stratified ambient, using direct numerical simulation. The cavity is insulated at the top and bottom boundaries, heated from the left-hand side boundary and open at the right-hand side. A wide range of Rayleigh numbers were considered (5 × 106 to 1 × 1010) with Pr = 0.7 for all cases. It was found that the homogeneous flow is steady for all Rayleigh numbers considered, whereas the stratified flow with a high enough Rayleigh number exhibits low- and high-frequency signals of the same type as are observed for closed cavity flow. The thermal boundary layer is examined in detail and it is shown that both low- and high-frequency signals are located predominantly in the upper region of the heated plate and are associated with a reverse-S-flow formed by the boundary layer exit jet interacting with the stratified interior. The low-frequency signal is associated with standing waves in the boundary layer, whereas the high-frequency signal is associated with travelling waves. The high-frequency signal occurs initially as a harmonic of the base low-frequency signal. A corner jet with the same inlet characteristics as the natural convection boundary layer exit jet is also examined and shown to exhibit a similar bifurcation, but with the low frequency always dominant. It is suggested that the generation mechanism for the bifurcation of the natural convection flow is the same as that for the corner jet.

Thermal stratification produced by plumes and jets in enclosed spaces

The airflow and thermal stratification produced by a localised heat source located at floor level in a closed room is of considerable practical interest and is commonly referred to as a ‘filling box’. In rooms with low aspect ratios H/ R≲1 (room height H to characteristic horizontal dimension R) the thermal plume spreads laterally on reaching the ceiling and a descending horizontal ‘front’ forms separating a stably stratified, warm upper region from cooler air below. The stratification is well predicted for H/ R≲1 by the original filling box model of Baines and Turner (J. Fluid. Mech. 37 (1968) 51). This model represents a somewhat idealised situation of a plume rising from a point source of buoyancy alone—in particular the momentum flux at the source is zero. In practical situations, real sources of heating and cooling in a ventilation system often include initial fluxes of both buoyancy and momentum, e.g. where a heating system vents warm air into a space. This paper describes laboratory experiments to determine the dependence of the ‘front’ formation and stratification on the source momentum and buoyancy fluxes of a single source, and on the location and relative strengths of two sources from which momentum and buoyancy fluxes were supplied separately. For a single source with a non-zero input of momentum, the rate of descent of the front is more rapid than for the case of zero source momentum flux and increases with increasing momentum input. Increasing the source momentum flux effectively increases the height of the enclosure, and leads to enhanced overturning motions and finally to complete mixing for highly momentum-driven flows. Stratified flows may be maintained by reducing the aspect ratio of the enclosure. At these low aspect ratios different long-time behaviour is observed depending on the nature of the heat input. A constant heat flux always produces a stratified interior at large times. On the other hand, a constant temperature supply ultimately produces a well-mixed space at the supply temperature. For separate sources of momentum and buoyancy, the developing stratification is shown to be strongly dependent on the separation of the sources and their relative strengths. Even at small separation distances the stratification initially exhibits horizontal inhomogeneity with localised regions of warm fluid (from the buoyancy source) and cool fluid. This inhomogeneity is less pronounced as the strength of one source is increased relative to the other. Regardless of the strengths of the sources, a constant buoyancy flux source dominates after sufficiently large times, although the strength of the momentum source determines whether the enclosure is initially well mixed (strong momentum source) or stably stratified (weak momentum source).

The X‐Ray Iron Emission from Tycho's Supernova Remnant

We present the results of broadband spectral model fits to the X-ray spectrum of Tycho's supernova remnant obtained by the Solid-State Imaging Spectrometers on the ASCA Observatory. We use single temperature, single ionization age, nonequilibrium ionization models to characterize the ejecta and the blast-shocked interstellar medium. Previous spectral studies have suggested that the Fe ejecta in this Type Ia remnant are stratified interior to the other ejecta. These studies, however, have generally restricted their attention to the Fe K blend at 6.5 keV. ASCA provides data over a broad energy range that allow the placement of important constraints simultaneously from the Fe L emission near 1 keV, as well as the Fe K emission. We find that the simplest models, with emission from the ejecta and blast wave each at a single temperature and ionization age, severely underestimate the flux in the Fe K blend. These models also show that there is little Fe emission associated with the Si and S ejecta shell, which has an average temperature kT ~ 0.86 keV and ionization age net ~ 1011 cm-3 s. The blast-shocked interstellar medium has abundances roughly 0.3 times the solar value, while the ejecta—with the exception of Fe—have relative abundances that are typical of Type Ia supernovae. The addition of another component of Fe emission—which we associate with ejecta—at a temperature at least 2 times higher and an ionization age ~100 times lower than the Si ejecta does provide a good fit to the spectrum. This model is consistent with imaging results. Although fluorescent emission from dust in the remnant may contribute to the Fe K flux, we conclude that it is unlikely to be the dominant component.

Biogeochemical cycling in the global ocean: 1. A new, analytical model with continuous vertical resolution and high‐latitude dynamics

A new, simple analytical model of ocean chemistry is presented which includes continuous vertical resolution, high‐latitude dynamics, air‐sea exchange and sea ice cover. In this high‐latitude exchange/interior diffusion‐advection (HILDA) model, ocean physics are represented by four parameters: k and w, an eddy diffusion coefficient and a deep upwelling velocity in the stratified interior; q, a rate of lateral exchange between the interior and a well‐mixed, deep polar ocean; and u, an exchange velocity between surface and deep layers in the polar ocean. First, estimates are made of ice‐free and ice‐covered areas at high latitudes, surface temperatures, and air‐sea exchange velocities from available data. Then values of the physical parameters are estimated from simultaneous, least mean square fits of model solutions for temperature (T) and “abiotic” carbon 14 (Δ14C) to interior profiles of T and Δ14C and surface layer Δ14C values all derived from available data. Best fit values for k, w, q, and u are 3.2×10−5 m2 s−1, 2.0×10−8 m s−1, 7.5×10−11 s−1 and 1.9×10−6 m s−1 respectively. These results are interpreted in terms of modes of ocean circulation and mixing and compared with results from other simplier and more complex models. In parts 2 and 3 of this series, these values for k, w, q and u are taken as inputs for studying phosphorus, oxygen, and carbon cycling in the global ocean with the HILDA model.

The Effect of Current-Induced Stress Perturbation On Baroclinic Rossby Waves in a Continuously Stratified Model

Abstract A shear stress at the air–sea interface is induced by the presence of surface currents. In the case of isotropic wind, a quadratic stress law leads to a stress curl proportional to and opposing the surface current vorticity. This causes a spindown effect on the surface vorticity field at a rate proportional to the characteristic wind speed. This effect of surface vorticity spindown or friction on propagating baroclinic Rossby waves is analyzed in a continuously stratified system with well-mixed boundary layers above and below it. In this system, both bottom friction and surface friction modulate the baroclinic Rossby waves in the stratified interior each time a wave group is reflected at the lower and the upper interfaces. The reflection coefficient and the corresponding spatial attenuation rate are calculated for various values of wave frequency, wind speed, and interior stratification. Both bottom friction and surface friction are important dissipation mechanisms for the baroclinic Rossby waves...

Managing Hydrocarbon Injectionat At Judy Creek

Abstract Tile Judy Creek Beaverhill Lake ‘A’ and ‘B’ Pools have been undergoing pattern hydrocarbon miscible flood (HCMF) since 1985 and 1987 respectively. This paper describes the evolution of the hydrocarbon injection strategy for the Judy Creek Pools from 1985 to today. The original HCMF design for each pattern was a water-alternating- gas (WAG) ratio of 1.0. minimum solvent bank of 15% of the continuous hydrocarbon pore volume (CHCPV), and a minimum chase gas bank of 20% of the CHCPV. Analysis of performance data has resulted in an evolution of HCMF design parameters and operating strategy, injection strategy is now specific to each pattern and zone. Downhole isolation equipment has been used extensively to improve zonal control leading to better reservoir sweep: examples of this are presented. Both ofthese changes have significantly improved tertiary recovery, but also have greatly increased the data management required. Imperial Oil's current method of designing, scheduling, and reporting hydrocarbon injection banks and WAG ratios by pattern and geologic zone is discussed. This includes a computer program that has been developed to calculate pattern and zonal hydrocarbon banks and WAG ratios. Approximately 1,400 103m3/d (50 mmcf/d) of hydrocarbon is injected into the Judy Creek HCMF3. Optimal use of injectant is a key lever in maximizing profitability of these hydrocarbon miscible floods. Introduction The Judy Creek "A" and "B" Pools are located about 200 km northwest of Edunonton. Alberta, and were both discovered in 1959. Figure 1 is a gross thickness of 70m (230 ft). The "B" pool is geologically similar but smaller its original oil in place is estimated at 39.8x 106 m3 (250 MMSTB) and it covers an area of 4.915 ha (12,000 acres). Examples from both pools have been included, but the paper will focus on the "A" pool. Geologically, the "A" Pool is an atoll-like reefal limestone. It can be generally described as a highly porous organic reel margin surrounding a more stratified interior lagoon. Figure 2 shows a cross-section through the reef. Pore volume and continuity vary widely. The reef margin geology exhibits high porosity and permeability and good lateral and vertical continuity. In contrast, the ref interior is characterized by varying porosity and permeability, with thin pay zones separated by thicker tight streaks. There is poor lateral and vertical community. Core studies have defined five cycles of reef growth (denoted as the R1 and R5 zone). Except in the reef margin, there is no vertical flow between these boundaries. The "A" pool was originally developed on 64 and 160 acre) well spacing, under solution gas drive. A peripheral waterflood scheme was implemented in 1964. In 1974, a pattern waterflood scheme was implemented, as he penpheral waterflood injections were unable to support production wells in the red interior In 1975 and 1978, extensive infill drilling occurred., reducing the well spacing to 32 ha (80 acre) in many areas off the pool.