The maximum power that can be obtained from a confined array of turbines in steady or tidal flows is considered using the two-dimensional shallow-water equations and representing the turbine farm by a uniform local increase in friction within a circle. Analytical results supported by dimensional reasoning and numerical solutions show that the maximum power depends on the dominant term in the momentum equation for flows perturbed on the scale of the farm. If friction dominates in the basic flow, the maximum power is a fraction (half for linear friction and 0.75 for quadratic friction) of the dissipation within the circle in the undisturbed state; if the advective terms dominate, the maximum power is a fraction of the undisturbed kinetic energy flux into the front of the turbine farm; if the acceleration dominates, the maximum power is similar to that for the linear frictional case, but with the friction coefficient replaced by twice the tidal frequency.

In an earlier study, we defined an “unexpected wave” as, for example, a wave twice as high as any of the preceding 30 waves. Here we extend earlier deep water simulations to allow for the greater crest enhancement in water of finite depth and find that the predicted frequency of unexpected waves increases significantly. We also analyze data obtained by wave buoys off the east and west coasts of Canada. In both deep and intermediate depth water, the occurrence of unexpected waves is in reasonable accord with our simulations, supporting our assumption of random superposition of waves though with local crest enhancement by the non-resonant second harmonic.

“Extreme” waves are commonly defined as extremely large waves compared to the background wave field and are often called “rogue” waves. Wave buoy records off Canada’s west coast reveal strong spatial and temporal variability in the occurrence rate of rogue waves with differences up to a factor three over distances less than 100 km. Strong tidal currents interact with the wave field. On the continental shelf rogue waves occur, on average, twice as frequently during strong currents compared to slack tide. In Dixon Entrance rogue wave occurrence peaks during the weakest currents. The significant wave height, characterizing the background wave field, is also strongly affected by currents. Modulations of up to 2m within one tidal cycle are observed. In coastal locations the wave field is modulated at the tidal semi-diurnal period, in deep water modulations occur at the inertial period. An important aspect, in addition to the large wave height, is the surprise effect of extreme waves. So-called “unexpected waves” are waves which are twice as large as any wave during a quiescent period of at least a few minutes duration. Their occurrence rate has been modelled based on random linear superposition and extracted from surface elevation records from waverider buoys at about 50 locations along Canada’s east and west coast. Simulations are in reasonable agreement with the observations.

The generation of internal tides can be ascribed to the action of a buoyancy force caused by the flow of the barotropic tide over topographic features. It is commonly assumed that the barotropic flow can be taken as hydrostatic, but it is shown here that this leads to a linearized governing equation for the baroclinic tide that is only valid if the baroclinic tide is also hydrostatic. A governing equation for the baroclinic tide, valid for any situation, is derived here and is shown to be exactly equivalent to a simple transformation of the governing equation for the combined barotropic and baroclinic tides.

An overflow of magnitude 0.25 Sv ( Sv equivalent to 106 m(-3) s(-1)) has been predicted to enter the Makarov Basin ( part of the Canadian Basin in the Arctic Ocean) from the Eurasian Basin via a deep gap in the dividing Lomonosov ridge. The authors argue that this overflow does not ventilate the deep Makarov Basin ( below 2400 m) where the water is too warm and salty to be compatible with such a large cold fresh inflow. However, complete isolation of the homogeneous bottom layer of the Makarov Basin must be ruled out because changes there are too small to arise from more than a small fraction of the measured geothermal heat flux into the basin. A small cold fresh inflow of about 0.01 Sv from the Amundsen Basin seems to be required. This could occur if the gap in the dividing Lomonosov Ridge is shallower than previously thought. It could also occur if there is active mixing and dilution of the predicted overflow in the gap, leaving only a small fraction to descend into the deep Makarov Basin. Hydraulic theory and hydrographic observations are used to rule out any significant flow of dense water from the Makarov Basin into the deep Canada Basin, confirming previous hypotheses of isolation of the deep water in the Canada Basin.

Power generation by tidal currents requires the establishment of a pressure difference across a turbine. This limits the power output to a fraction of the undisturbed energy flux through the same cross-sectional area, though the maximum possible value of this fraction is not well established. It is further shown that an array of turbines in the entrance to a bay is most effective if it is uniformly distributed across the entrance. The maximum power available for a quadratic drag law occurs when the tidal range inside the bay is reduced to 0.74 of the original amplitude, suggesting that power generation is compatible with the maintenance of good flushing and with use of the bay for other purposes. Moreover, this exploitation of tidal power through continuous operation of current turbines in the entrance is not much less productive than more conventional schemes that rely on trapping the water at high tide and releasing it during a small part of the tidal cycle.

Estuarine flow in Juan de Fuca Strait is highly seasonal in nature and an appreciable along‐channel surface pressure gradient is coincident with the peak Fraser River discharge. An upper layer momentum balance requires the vertical eddy viscosity Av to be of the order of 0.02 m2 s−1, slightly larger than implied by conventional empirical formulae and used in current models. Mixing in an estuarine channel and a large vertical eddy viscosity should lead to significant cross‐channel flows. This secondary circulation, which may resemble internal Ekman layers and intrusions of water mixed at the sloping sides of the strait, is much less understood than the basic along‐channel estuarine exchange. Unfortunately, historical current meter data in Juan de Fuca Strait are of insufficient spatial resolution to show the predicted patterns.

An air-sea buoyancy flux out of the ocean between the surface outcroppings of different isopycnals must be balanced by a convergence of advective and diffusive fluxes of buoyancy across those isopycnals (Walin, 1982; Tziperman, 1986; Garrett et al., 1995). For steady conditions, the diapycnal diffusive flux due to vertical mixing in the surface mixed layer is very small, so that the advective buoyancy flux dominates (Speer, 1993; Garrett et al., 1995). The associated advective buoyancy flux can then be used to estimate the volume fur of water out of the base of the surface mixed layer. The resulting thermodynamic algorithm provides a valuable estimate of water mass formation in the ocean.In contrast, for the time-dependent real ocean with horizontal and vertical gradients of the horizontal buoyancy gradient, diurnal and seasonal mixed layer deepening and entrainment in the presence of a buoyancy jump at the base of the mixed layer contributes to the annual volume flux out of the base of the deepest (wintertime) mixed layer. The mismatch between the predictions of the ideal algorithm and measured rates of water mass formation (Speer, 1997) may thus be partly due to mixed layer processes lather than diapycnal mixing in the thermocline. (C) 1998 Published by Elsevier Science Ltd. All rights reserved.

Mathematical models based on our understanding of oceanic processes are frequently used in the assessment and control of marine pollution. Although no general model is available, it is usually possible to provide some quantitative estimate of the impact of a practice. Reducing the inevitable uncertainty of the estimate requires the identification of key processes, through sensitivity analysis of the model output, followed by focused experimental or modelling work. Continued basic research is also required in order to improve the chances of discovering unforeseen factors that could lead to major revisions of present assessments.

Eriksen (1982, 1985) has drawn attention to the increased vertical shear due to internal wave reflection off a sloping bottom. For a typical incident spectrum we calculate a cut-off wavenumber for the reflected spectrum such that the shear from all lower wavenumbers gives a Richardson number of order 1, and we assume that the energy flux associated with higher wavenumbers is lost to dissipation and mixing. Our results appear to be significant for deep ocean mixing rates and the energy balance of the internal wave field in the ocean but the theory is presently limited by weak assumptions.

We report the details and some extensions of a three-dimensional model, developed by GESAMP (1983), relevant to the oceanic dispersion of low-level radioactive waste escaping from a deep-sea dump site. The model includes simple parameterizations of physical dispersal, geochemical scavenging at the sea floor and in the water column, and decay. A closed-form solution may be approximated asymptotically for various physical regions to give simple formulae for the concentration. The results are of some operational value but are particularly useful for increasing intuition about the behaviour that may be expected from more realistic models. In particular, radionuclides may be located in a parameter space defined by two dimensionless numbers that show the importance of scavenging and decay. Four different regions of this parameter space correspond to the radionuclides (or other pollutants) being primarily widespread or confined near the source, and principally in the water column or on the sea-floor sediments. We also show the relationship of the three-dimensional model to a horizontally averaged one-dimensional model, and discuss the nature of the concentration field very near the source where a constant. Fickian, diffusivity is an incorrect parameterization of turbulent dispersion processes.

The unpredictability of low frequency currents in the ocean reduces the practicality of iceberg trajectory prediction using deterministic models. However, an optimum statistical model may be developed in which the future velocity of an iceberg (other than the predictable part due to wind, mean flow or tides) is a weighted sum of previous (measured) velocities. The weights are related to the Lagrangian velocity autocorrelation function. The scheme may be used to predict error bars as well as future positions. The theory is outlined in this paper and extended to allow for noise and inertial waves. For appropriate parameter values it is found that there is little value in using more than a one-term predictor, i.e. one based solely on the most recently measured velocity. It is shown how the scheme could also be used to predict, approximately, the probability that a given iceberg will enter a circle of specified radius around a wellsite within a specified time.

An axisymmetric model of the evolution of temperature over central Georges Bank in spring, summer, and early fall is used to estimate bounds on the horizontal dispersion coefficient, KH, consistent with the observed development of a "hot spot" in this region. We find that KH is in the range of 150–380 m2∙s−1, in agreement with estimates based on drogue dispersion (EG&G 1979). The effect of such a dispersion rate on passive scalars is considered for a variety of initial distributions. Although, in the absence of air–sea transfer, any initial salinity difference across the central portion of the Bank would be essentially eliminated in a few weeks, local precipitation appears to be sufficient to maintain the observed distribution. Our results indicate that maintenance of primary production at 2 g C∙m−2∙d−1 over the central portion of the Bank requires that greater than 50% of the nitrogen demand be supplied by local regeneration, assuming the Redfield ratio to be appropriate. Because exchange with off-the-Bank waters is slowest for the very center of the Bank, the supply of new nitrogen to this area should be particularly low. On the other hand, fish larvae in this area may benefit from a relatively long residence time.Key words: horizontal exchange, Georges Bank, heat budget, nitrogen budget, residence time

In an attempt to understand the causes of low frequency flow through the Strait of Belle Isle, we relate sea level data from four stations in the northeast Gulf of St. Lawrence to meteorological forcing. Our main tool is a multiple regression, at each frequency, of sea level on local atmospheric pressure and two orthogonal large scale pressure gradients which represent geostrophic winds. The results show an inverted barometer response to atmospheric pressure and a frequency‐dependent response to wind which can be tentatively interpreted in terms of coastal setup due to wind driven longshore currents, or barotropic setup of semi‐enclosed regions (such as the northeast Gulf or the whole Gulf). A simple model for barotropic flow through the Strait is developed in order to provide an estimate, from data at the western end of the Strait, of sea level changes on the Labrador shelf.