Horizontal Mixing Coefficients Research Articles

Evaluation of a Stochastic Mixing Scheme in the Deep Convective Gray Zone Using a Tropical Oceanic Deep Convection Case Study

AbstractA stochastic horizontal subgrid‐scale mixing scheme is evaluated in ensemble simulations of a tropical oceanic deep convection case using a horizontal grid spacing (Δh) of 3 km. The stochastic scheme, which perturbs the horizontal mixing coefficient according to a prescribed spatiotemporal autocorrelation scale, is found to generally increase mesoscale organization and convective intensity relative to a non‐stochastic control simulation. Perturbations applied at relatively short autocorrelation scales induce differences relative to the control that are more systematic than those from perturbations applied at relatively long scales that yield more variable outcomes. A simulation with mixing enhanced by a constant factor of 4 significantly increases mesoscale organization and convective intensity, while turning off horizontal subgrid‐scale mixing decreases both. Total rainfall is modulated by a combination of mesoscale organization, areal coverage of convection, and convective intensity. The stochastic simulations tend to behave more similarly to the constant enhanced mixing simulation owing to greater impacts from enhanced mixing as compared to reduced mixing. The impacts of stochastic mixing are robust, ascertained by comparing the stochastic mixing ensembles with a non‐stochastic mixing ensemble that has grid‐scale noise added to the initial thermodynamic field. Compared to radar observations and a higher resolution Δh = 1 km simulation, stochastic mixing seemingly degrades the simulation performance. These results imply that stochastic mixing produces non‐negligible impacts on convective system properties and evolution but does not lead to an improved representation of convective cloud characteristics in the case studied here.

Freshwater transport by eddies within the Bay of Bengal's central axis

The excess of freshwater from rivers and precipitation delivered to the Bay of Bengal (BoB) must be exported to the neighboring ocean in order to establish a quasi-steady state salinity field. The BoB's sea surface salinity is approximately 3 PSU less than that of the Arabian Sea, which experiences net evaporation, a difference reflecting the efficiency of exchange between the two embayments (Gordon et al., 2019). Using Argo salinity profiles from 2003 to 2018 along the BoB's central axis, we investigate the significance of eddies in the removal of excess freshwater injected into the northern BoB by rivers. Southwestward freshwater volume flux is estimated by combining horizontal freshwater (salinity) gradients, as a function of latitude, depth, and season, with a realistic estimate of the horizontal mixing coefficient. The ratio of these fluxes for 0–50 m: 50–100 m: 100–300 m depth slabs is 5.68 : 1.75: 1 in the 15 ± 2° N (northern) study box and 4.61 : 2.24: 1 in the 10 ± 2° N (southern) study box, highlighting the importance of the upper 50 m in the removal of river runoff. In the northern BoB, boreal winter experiences the highest freshwater eddy flux, a consequence of the accumulated freshwater from the previous summer monsoon season. Lower latitudes reach their peak freshwater flux in the summer, a delayed response due to the time required to transport the freshwater southward. Southwestward eddy freshwater flux in the top 300 m can account for almost all of the export of the 0.094 Sv (Sv = 106 m3/s) river runoff into the northern BoB.

Sensitivity of Global Ocean Deoxygenation to Vertical and Isopycnal Mixing in an Ocean Biogeochemistry Model

AbstractLarge‐scale loss of oxygen under global warming is termed “ocean deoxygenation” and is caused by the imbalance between physical supply and biological consumption of oxygen in the ocean interior. Significant progress has been made in the theoretical understanding of ocean deoxygenation; however, many questions remain unresolved. The oxygen change in the tropical thermocline is poorly understood, with diverging projections among different models. Physical oxygen supply is controlled by a suite of processes that transport oxygen‐rich surface waters into the interior ocean, which is expected to weaken due to increasing stratification under global warming. Using a numerical model and a series of sensitivity experiments, the role of ocean mixing is examined in terms of effects on the mean state and the response to a transient warming. Both vertical and horizontal (isopycnal) mixing coefficients are systematically varied over a wide range, and the resulting oxygen distributions in equilibrated and transient simulations are examined. The spatial patterns of oxygen loss are sensitive to both vertical and isopycnal mixing, and the sign of tropical oxygen trend under climate warming can reverse depending on the choice of mixing parameters. An elevated level of isopycnal mixing disrupts the vertical advective‐diffusive balance of the tropical thermocline, increasing the mean state oxygen as well as the magnitude of the transient oxygen decline. These results provide first‐order explanations for the diverging behaviors of simulated tropical oxygen with respect to ocean mixing parameters.

3D1D hydro-nucleosynthesis simulations – I. Advective–reactive post-processing method and its application to H ingestion into He-shell flash convection in rapidly accreting white dwarfs

ABSTRACT We present two mixing models for post-processing of 3D hydrodynamic simulations applied to convective–reactive i-process nucleosynthesis in a rapidly accreting white dwarf (RAWD) with [Fe/H] = −2.6, in which H is ingested into a convective He shell. A 1D advective two-stream model adopts physically motivated radial and horizontal mixing coefficients constrained by 3D hydrodynamic simulations. A simpler approach uses diffusion coefficients calculated from the same simulations. All 3D simulations include the energy feedback of the 12C(p, γ)13N reaction from the H entrainment. Global oscillations of shell H ingestion in two of the RAWD simulations cause bursts of entrainment of H and non-radial hydrodynamic feedback. With the same nuclear network as in the 3D simulations, the 1D advective two-stream model reproduces the rate and location of the H burning within the He shell closely matching the 3D simulation predictions, as well as qualitatively displaying the asymmetry of the XH profiles between the upstream and downstream. With a full i-process network the advective mixing model captures the difference in the n-capture nucleosynthesis in the upstream and downstream. For example, 89Kr and 90Kr with half-lives of $3.18\,\,\mathrm{\mathrm{min}}$ and $32.3\,\,\mathrm{\mathrm{s}}$ differ by a factor 2–10 in the two streams. In this particular application the diffusion approach provides globally the same abundance distribution as the advective two-stream mixing model. The resulting i-process yields are in excellent agreement with observations of the exemplary CEMP-r/s star CS31062-050.

Impacts of Stochastic Mixing in Idealized Convection-Permitting Simulations of Squall Lines

AbstractThis study investigates impacts of altering subgrid-scale mixing in “convection-permitting” kilometer-scale horizontal-grid-spacing (Δh) simulations by applying either constant or stochastic multiplicative factors to the horizontal mixing coefficients within the Weather Research and Forecasting Model. In quasi-idealized 1-km Δh simulations of two observationally based squall-line cases, constant enhanced mixing produces larger updraft cores that are more dilute at upper levels, weakens the cold pool, rear-inflow jet, and front-to-rear flow of the squall line, and degrades the model’s effective resolution. Reducing mixing by a constant multiplicative factor has the opposite effect on all metrics. Completely turning off parameterized horizontal mixing produces bulk updraft statistics and squall-line mesoscale structure closest to an LES “benchmark” among all 1-km simulations, although the updraft cores are too undilute. The stochastic mixing scheme, which applies a multiplicative factor to the mixing coefficients that varies stochastically in time and space, is employed at 0.5-, 1-, and 2-km Δh. It generally reduces midlevel vertical velocities and enhances upper-level vertical velocities compared to simulations using the standard mixing scheme, with more substantial impacts at 1- and 2-km Δh compared to 0.5-km Δh. The stochastic scheme also increases updraft dilution to better agree with the LES for one case, but has less impact on the other case. Stochastic mixing acts to weaken the cold pool but without a significant impact on squall-line propagation. It also does not affect the model’s overall effective resolution unlike applying constant multiplicative factors to the mixing coefficients.

Estimation of apparent water age and mixing process of water in the creek ecosystem of Mumbai Harbour Bay

Short-lived Ra isotopes (224Ra and 223Ra) were used to estimate the apparent water age and mixing process, in the creek ecosystem of Mumbai Harbour Bay. The apparent water age was estimated using the Radium Age Model and the Radium Balance Approach. The apparent water age for three different sampling trips in the creek varies from 3.65 ± 1.22 to 4.51 ± 1.51 days using the Radium age model. Whereas using the Radium Balance Approach in the creek, the apparent water age was estimated to be 6.51 ± 1.67 days. Similar apparent water age from both approaches was found for the creek ecosystem under steady state. The longitudinal variation of the 224Ra and 223Ra activity ratio from the middle of the creek indicated net water mass movement towards the open sea. The flushing rate of the creek water towards the open sea was estimated to be 6.67 ± 0.89 km day−1. The horizontal mixing coefficient (Kh) of the creek water was estimated to be 800 ± 107 m2s−1 indicating rapid dispersion of the tracer.

A Physically Based Horizontal Subgrid-Scale Turbulent Mixing Parameterization for the Convective Boundary Layer

Abstract Compared to the representation of vertical turbulent mixing through various planetary boundary layer (PBL) schemes, the treatment of horizontal turbulent mixing in the boundary layer has received much less attention. In mesoscale and convective-scale models, subgrid-scale horizontal turbulent mixing has traditionally been associated with mesoscale circulations or eddies. Its parameterization most often adopts the gradient-diffusion model, where the horizontal mixing coefficients are usually set constant, or through the 2D Smagorinsky formulation, or in some cases based on the 1.5-order turbulence kinetic energy (TKE) closure. For horizontal turbulent mixing associated with boundary layer eddies, the traditional schemes are shown to perform poorly. This work investigates the characteristic turbulence velocity and length scales based on analysis of a well-resolved, wide-domain large-eddy simulation of a convective boundary layer (CBL). To improve the representation of horizontal turbulent mixing by CBL eddies, a class of schemes is proposed with different levels of sophistication. The first two schemes can be used together with first-order PBL schemes, while the third uses TKE to define its characteristic velocity scale and can be used together with TKE-based higher-order PBL schemes. The proposed parameterizations are tested a posteriori in idealized simulations of turbulent dispersion of a passive scalar. Comparisons show improved horizontal dispersion by the proposed schemes and further demonstrate the weakness of the existing schemes.

Simulating the thermal behavior in Lake Ontario using EFDC

The thermal behavior of Lake Ontario (spring warming, thermal bar formation, and summer stratification) is simulated using the three-dimensional thermo-hydrodynamic model, Environmental Fluid Dynamics Code (EFDC). The model is forced with hourly meteorological data from weather stations around the lake and flow data from Niagara and St. Lawrence Rivers. The simulation is performed from April to July 2011 on a curvilinear grid, with cells approximately 2 × 2 km2 and bathymetry interpolated onto the grid. We implement model improvements by (a) updating the evaporation algorithm to ensure accurate simulation of evaporation rates and latent heat fluxes and (b) specifying appropriate solar radiation attenuation coefficients to ensure sufficient absorption of incoming solar radiation by the water column. The study also calibrated horizontal and vertical mixing coefficients. Results show that the model accurately simulated the overall surface temperature profiles with RMSEs between 1 and 2 °C and the vertical temperature profiles during the lake mixed phase with RMSEs < 0.5 °C. Overall, the modified EFDC model successfully replicated thermal bar evolution.

Inappropriate attempts to use distributions of 228Ra and 226Ra in coastal waters to model mixing and advection rates

Numerous investigators have used the advection–diffusion equation and the distributions of the four isotopes of radium to model coastal mixing rates. However, there is a dichotomy in approach. Some models use the short-lived 224Ra (T1/2=3.7 days) and 223Ra (T1/2=11 days) to determine horizontal mixing coefficients and the long-lived 226Ra (T1/2=1600 years) and 228Ra (T1/2=5.75 years) to test for the effects of advection. Because the timescales of mixing in most coastal systems (10–80km offshore) are on the order of months or less, radioactive decay and particle removal of the long-lived isotopes are neglected in these models. If the long-lived isotopes display a linear gradient with distance offshore, this is taken as evidence that conservative mixing rather than advection controls the radium distribution. In this case it is appropriate to neglect the advection term and calculate mixing rates based on the exponential decay of the short-lived isotopes. Other models assume that radioactive decay of all of the isotopes impacts their distribution offshore. These models set up equations that separate the effects of mixing from advection and attempt to force mixing rates derived from all of the Ra isotopes to match. There are several reasons these models are doomed to fail. First, 224Ra and 223Ra look at different scales of mixing-there is no reason they must give the same rate. Secondly, on the timescale of coastal mixing decay of 226Ra and 228Ra is essentially zero. Equations that include decay terms for 226Ra and 228Ra become unrealistic when we consider that the measurement error is considerably greater than decay. In fact particle removal of 226Ra is more important than radioactive decay. Finally, these models require steady-state conditions on the timescales of the decay terms. In order to use such models, the source functions and distributions of 228Ra and 226Ra would have to be constant for several times their half lives, approximately 25 and 4000 years, respectively. Seasonal and annual variability in supply and mixing rearranges the distributions, violating the steady-state assumption. Thus, models utilizing 226Ra and 228Ra radioactive decay are useless in the coastal zone.

Short-lived radium isotopes on the Scotian Shelf: Unique distribution and tracers of cross-shelf CO2 and nutrient transport

Radium (Ra) isotopes have become an established tool for investigating mixing rates on continental shelves, and more recently have been used to quantify the release of dissolved compounds enriched in pore-waters into the water column. We present results from Ra sampling of the Scotian Shelf region of the Canadian northwestern Atlantic Ocean, which reveal cross-shelf Ra distributions that are unique compared to other coastal regions. We explain the observations of lower 224Ra activities near the coast, relatively high activities at large distances offshore (>100km), and gradients in both offshore and onshore directions by referring to regional geomorphology, as well as shelf bathymetry and circulation patterns. Vertical mixing above shallow offshore banks allows for Ra enrichments in offshore surface waters, while horizontal dispersion of this bottom-generated signal can transport Ra off the shelf break in surface waters, and towards the shore beneath the surface mixed layer. On the Scotian Shelf, estimating horizontal diffusivity (KX) using a 1-D Ra diffusion model is limited by the presence of two distinct Ra sources (land and sediment), by three dimensional shelf topography, as well as by complex hydrodynamic conditions. Here, a numerical 2-D diffusion model reproduces Ra distributions on the shelf using both coastal and benthic sources. Horizontal and vertical mixing coefficients are then calculated by minimizing deviations between model output and observations. Onshore gradients in CO2 and nutrient species combined with model-derived KX values can yield onshore carbon and nutrient fluxes in subsurface waters, which in turn supply the CO2 outgassing from the Scotian Shelf. Our results thus provide constraints for cross-shelf transports of carbon and nutrients on the Scotian Shelf in order to guide mass balance or model based budget approaches in future studies.

Interannual similarity and variation in seasonal circulation of Mars' atmospheric Ar as seen by the Gamma Ray Spectrometer on Mars Odyssey

More than 3 Mars' years (MY) of atmospheric argon (Ar) measurements are used to study annual and seasonal variations in atmospheric transport and mixing. Data are obtained over the period 20 May 2002 to 4 May 2008 by the Gamma Subsystem (GS) of the Gamma Ray Spectrometer (GRS) on the Mars Odyssey spacecraft in orbit around Mars. Here we augment previous studies of Mars' Ar in which strong seasonal variations were observed and horizontal meridional mixing coefficients for the southern hemisphere were computed. Comparison of year‐to‐year seasonal abundance shows strong similarity but also some short‐period (∼15°–30° Ls) and interannual variations. Evidence for short periods of strong eddy transport is exhibited during autumn and winter. The seasonal change in Ar concentration for southern latitudes is relatively gradual and well defined, but seasonal changes at high northern latitudes are chaotic and indicate that atmospheric disturbance is ubiquitous. Major topographic landforms (Elysium, Tharsis, Noachis Terra, Hellas) apparently have little control over seasonal Ar concentration at the spatial resolution of the GRS data set. Some indication of local enhanced Ar concentration is present from 30°N to 60°N for the Hellas and Tharsis sectors in late winter and early spring. The data show some significant (3σ) differences between MY 26 and MY 27 in geographical sectors that are likely produced by local weather. The GS data do not show seasonal variation of Ar at equatorial and low‐latitude zones, in contrast to those from the Alpha Particle X‐ray Spectrometer (APXS) measurements from the Mars Exploration Rovers.

Establishment, validation and discussions of a three dimensional wave-induced current model

A three-dimensional numerical model was established to simulate the wave-induced currents. The depth-varying residual momentum, surface roller, wave horizontal and vertical turbulent mixing effects were incorporated as major driving forces. A surface roller evolution model considering the energy transfer, roller density and bottom slope dissipation was developed. The expression of the wave-induced horizontal turbulent mixing coefficient proposed by Larson and Kraus (1991) was extended to three-dimensional form. Plenty of experimental cases were used to validate the established model covering the wave setup, undertow, longshore currents and rip currents. Validation results showed the model could reasonably describe the main characteristics of different wave-induced current phenomena. The incorporation of surface roller for breaking waves should not be neglected in the modeling of surfzone hydrodynamics. The wave-induced turbulent mixing affects the structures of wave-induced current either in horizontal or in vertical directions. Sensitivity analysis of the major calibration parameters in the established model was made and their ranges were evaluated.

ITF and Poleward Heat Transport of Indian Ocean

A sigma coordinate model is used to study the heat transport variability and the influence of Indonesian Throughflow (ITF) heat transport on the Indian Ocean. The vertical mixing coefficients were provided by the turbulence scheme. The horizontal mixing coefficients for momentum (viscosity) and tracers (diffusivity) were calculated by a Smagorinsky-type formulation. The model is initialized with the Levitus94 climatological data set for annual mean temperature and salinity fields and is forced by seasonal and yearly varying da Silva SMD 1994 and Hellerman and Rosenstein (1983) wind data set. The spin-up of the model has been carried out separately for open and closed. The ITF transport is found around 10 Sv (Svedrup) (1 Sv = 106 m3/s), and the heat transport across the equator is found at its maximum amplitude 1.3 PW (Peta Watt) (1 PW = 1015 Watts) in March and −1.6 PW in July. It is found that the overall effect of the ITF heat transport on the Indian Ocean is dominant on the south of 10°S, and this has a small effect between equator and 10°S.

Assessment of groundwater discharges into West Neck Bay, New York, via natural tracers

A field experiment to compare methods of assessing submarine groundwater discharge (SGD) was held on Shelter Island, NY, in May 2002. We evaluated the use of radon, radium isotopes, and methane to assess SGD rates and dynamics from a glacial aquifer in the coastal zone. Fluxes of radon across the sediment-water interface were calculated from changes in measured surface water inventories following evaluation and correction for tidal effects, atmospheric evasion, and mixing with offshore waters. These fluxes were then converted to SGD rates using the measured radon concentration in the groundwater. We used the short-lived radium isotopes to calculate a horizontal mixing coefficient to assess radon loss by mixing between nearshore and offshore waters. We also made an independent calculation of SGD using the Ra-derived mixing coefficient and the long-lived 226Ra concentration gradient in the bay. Seepage rates were calculated to range between 0 and 34 cm day −1 using the radon measurements and 15 cm day −1 as indicated by the radium isotopes. The radiotracer results were consistent and comparable to SGD rates measured directly with vented benthic chambers (seepage meters) deployed during this experiment. These meters indicated rates between 2 and 200 cm day −1 depending on their location. Both the calculated radon fluxes and rates measured directly by the automated seepage meters revealed a clear reproducible pattern of higher fluxes during low tides. Considering that the two techniques are completely independent, the agreement in the SGD dynamics is significant. Methane concentration in groundwater was very low (∼30 nM) and not suitable as SGD tracer at this study site.

Adjusting Internal Model Errors through Ocean State Estimation

Abstract Oceanic state estimation is a powerful tool to estimate internal model parameters simultaneously with the model’s initial conditions and surface forcing field that jointly would bring a model into consistency with time-varying large-scale ocean observations. Here an attempt to estimate geographically varying fields of horizontal and vertical viscosity and diffusivity within a 9-yr-long estimation procedure is presented. The estimated coefficients are highly efficient in preserving watermass characteristics and frontal structures by reducing the model temperature and salinity drift, especially around the Southern Ocean. The estimated mean circulation results in stronger transports of western boundary currents and of the Antarctic Circumpolar Current. Moreover, an increase of about 10% in the strength of the meridional overturning circulation and in the poleward heat transport can be found. Estimated changes in the horizontal mixing coefficients seem to agree with the notion that diapycnal mixing is superfically high with Laplacian mixing formulations, especially close to frontal structures in the ocean. In comparison with adjustments in tracer diffusivities (vertically and horizontally), adjustments of viscosity coefficients are fairly minor outside lateral boundary regions, suggesting that state estimation attempts might be most successful in providing enhanced insight into tracer mixing.

Instability of the Thermohaline Ocean Circulation on Interdecadal Timescales

The stability of three-dimensional thermally driven ocean flows in a single hemispheric sector basin is investigated using techniques of numerical bifurcation theory. Under restoring conditions for the temperature, the flow is stable. However, when forced with the associated heat flux, an interdecadal oscillatory timescale instability appears. This occurs as a Hopf bifurcation when the horizontal mixing coefficient of heat is decreased. The physical mechanism of the oscillation is described by analyzing the potential energy changes of the perturbation flow near the Hopf bifurcation. In the relatively slow phase of the oscillation, a temperature anomaly propagates westward near the northern boundary on a background temperature gradient, thereby changing the perturbation zonal temperature gradient, with corresponding changes in meridional overturning. This is followed by a relatively fast phase in which the zonal overturning reacts to a change in sign of the perturbation meridional temperature gradient. The different responses of zonal and meridional overturning cause a phase difference between the effect of temperature and vertical velocity anomalies on the buoyancy work anomaly, the latter dominating the changes in potential energy. This phase difference eventually controls the timescale of the oscillation.

On the Robustness of the Interdecadal Modes of the Thermohaline Circulation

Ocean models in box geometry forced by constant surface fluxes of density have been found to spontaneously generate interdecadal oscillations of the thermohaline circulation. This paper analyzes the sensitivity of these oscillations to various physical effects, including the presence of mesoscale turbulence, various thermal surface boundary conditions, and the presence of wind forcing or bottom topography. The role of unstable long baroclinic waves is also reexamined in an attempt to understand the oscillation period. In idealized geometry, it is found that the low-frequency variability of the thermohaline circulation under quasi-constant surface fluxes is a robust feature of the large-scale circulation. It is not strongly affected by energetic mesoscale turbulence; the oscillation period is relatively invariant with respect to varying resolution and momentum and tracer horizontal mixing coefficients, although it loses some regularity as shorter and longer periods of variability emerge when the mesoscale activity increases in strength with smaller mixing coefficients. The oscillations are also retained as the ocean model is coupled to an interactive atmospheric energy balance model; the thermohaline modes are robust to a range of exchange coefficients that widens with the amplitude of the mean circulation. The presence of an additional wind-forced component generally weakens the oscillation, and depending on the relative strength of thermodynamic and dynamic forcings, the oscillation may be completely killed. A simple interpretation is given, highlighting the role of upward Ekman pumping in damping density anomalies. Finally, the interaction of these baroclinic modes with bottom topography depends strongly on the relative directions of the mean topographic features and the mean currents and baroclinic waves, but usually results in a damping influence.

Dispersion Experiments in U.K. Coastal Waters

Over the period 1968 to 1999, Brixham Environmental laboratory carried out dye tracing experiments to determine local mixing conditions at coastal and estuarine sites around the United Kingdom. Results from 25 different locations, and from five non-U.K. sites, have been analysed to estimate horizontal and vertical mixing coefficients. Analysis of the data from the 19 sites which had the most complete data sets showed that the minimum lateral dispersion coefficient ranged from 0·003 to 0·42m2s−1with a median value of 0·05m2s−1. Typical vertical diffusion coefficients ranged between 2·0×10−4to 110·0×10−4m2s−1and had a median value of 20·0×10−4m2s−1. Comparisons of the values obtained have been made with mixing coefficients derived from earlier dye tracer studies in the North Sea, the Irish Sea and off the eastern seaboard of the U.S.A.A plot of minimum lateral dispersion coefficients against the corresponding vertical diffusion coefficients showed that the results fell into two distinct bands, broadly represented by shallow or deep water. Within each band, the lateral mixing coefficients appeared to vary in inverse proportion to the vertical coefficients, as would be expected in shear dispersion in which mixing is restricted by the surface and seabed or pycnocline. Curves representing this variation had different constants of proportionality for the shallow and deep waters. This was ascribed to a reduction in the curvature of the velocity profiles in the deep water areas, where stronger currents may have reduced the degree of stratification.Analysis of the full data set has not identified any generally applicable relationship between the mixing coefficients and tidal currents or wind, however, relationships between these parameters could be found within specific survey areas. For example, lateral diffusion coefficients in the Solent appeared to be correlated with the tidal current amplitude.

Influences of Topography on the Modeling of Abyssal Water Masses. Part II: Spurious Extrema

Abstract Unphysical extrema are found in ocean simulations employing space-centered advection even when horizontal mixing coefficients are sufficient to suppress checkerboard behavior. They are mostly found as isolated spurious temperature minima (density maxima) occurring in close association with topography and in places of concentrated upwelling or overflowing adjacent to the margins of deep basins, where velocities considerably exceed the vertical, or sometimes horizontal, grid Peclet condition. Temperature depressions may be as large as the expected temperature difference between levels and are capable of contaminating upstream water mass properties through horizontal diffusion and convective adjustment. Examples are discussed with reference to the finite difference solution for a stream of variable speed and diffusivity. Increased vertical resolution disproportionately reduces the magnitude but not necessarily the incidence of depressions. Flux correction eliminates the extrema and the contamination...

Tidal Circulation and Residence Time in a Macrotidal Estuary: Cobscook Bay, Maine

Cobscook Bay is a macrotidal estuary situated near the entrance to the Bay of Fundy, where the mean semi-diurnal tidal range is 5·7m. Vigorous tidal currents in the bay maintain cold water temperatures year-round and effectively exchange nutrients and other dissolved matter with offshore waters. Partly because of the cold water and tidal exchange, a net-pen salmon aquaculture industry has rapidly expanded in the last decade, raising questions about sustainable levels of production in the environmentally pristine bay. The present study addresses the question of dispersion and flushing of materials in the bay, using a three-dimensional numerical model to simulate the circulation driven by the semi-diurnal tide and runoff from principal rivers. With initialization based on May 1995 cruise data, the results show that the tidal-mean flushing times for neutral surface particles vary from less than one day in the main channel near the entrance to more than a week in the extremities of the inner arms of the bay. A bay-wide average flushing time is about two days, or four tidal cycles, but the detailed distribution is strongly influenced by a pair of counter-rotating eddies that forms in the central bay during each flooding tide. The eddy pattern preferentially directs the initial flood into a southern arm of the bay, where particles and dissolved materials are sequestered. The effective horizontal mixing coefficient in the main channel of the central bay is 300–400m2s−1, leading to rapid dispersal of particles and pollutants in the along-channel direction and into the shallow inner arms of the bay where they tend to accumulate. A map of tidal-mean residence time indicates that most current aquaculture sites are located in reasonably well flushed regions.