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## Abstract

Hamon *et al.*(1975) analyzed two years of surface current data from ships' set along two tracks parallel to 560 km of the east Australian shelf and found a phase lag of 10 days between long (120 day) period current fluctuations 19 km offshore and 6.5 km offshore. This is explained in terms of the propagation characteristics of topographic waves on the continental shelf. It is shown that these current fluctuations can lead to a significant amount of coastal upwelling as they are damped out by bottom friction. The average circulation on the east Australian shelf is discussed. The simplest response to the known longshore pressure gradient would be a steady longshore current and upwelling circulation, but it is shown that this is incompatible with a heat budget for the water on the shelf. Hence something other than bottom friction is required to balance most of the longshore pressure gradient; the onshore momentum flux of the topographic waves identified in the current data is shown to be a likely candidate. The implications of this interpretation for the circulation in deeper water off the shelf are discussed.

## Abstract

Hamon *et al.*(1975) analyzed two years of surface current data from ships' set along two tracks parallel to 560 km of the east Australian shelf and found a phase lag of 10 days between long (120 day) period current fluctuations 19 km offshore and 6.5 km offshore. This is explained in terms of the propagation characteristics of topographic waves on the continental shelf. It is shown that these current fluctuations can lead to a significant amount of coastal upwelling as they are damped out by bottom friction. The average circulation on the east Australian shelf is discussed. The simplest response to the known longshore pressure gradient would be a steady longshore current and upwelling circulation, but it is shown that this is incompatible with a heat budget for the water on the shelf. Hence something other than bottom friction is required to balance most of the longshore pressure gradient; the onshore momentum flux of the topographic waves identified in the current data is shown to be a likely candidate. The implications of this interpretation for the circulation in deeper water off the shelf are discussed.

## Abstract

An attempt is made to Parameterized the large-Scale average diapycnal (cross-isopycnal) mixing that presumably occurs in the thermohaline fronts that develop when large-scale epipycnal (along-isopycnal) gradients of *T* and *S* are stirred along isopycnals by mesoscale eddies. It is assumed that double-diffusive intrusions develop at the fronts and that their thickness is given by the formula of Ruddick and Turner (1979). This, combined with a crude estimate of the frontal width and a very over-simplified model of the eddy field, leads to a formula for the average diapycnal diffusivity for salt or some neutral tracer, and suggests that the mechanism is important in weakly stratified water with a large epipycnal gradient of salinity. The diapycnal eddy diffusivities for temperature is negative for a stably stratified temperature field. However, the opposite signs of the diapycnal diffusivities for salt and heat are unlikely to lead to observable consequences on account of the dominance, in duxes across isopleths of *T* or *S*, of down-gradient epipycnal transports.

## Abstract

An attempt is made to Parameterized the large-Scale average diapycnal (cross-isopycnal) mixing that presumably occurs in the thermohaline fronts that develop when large-scale epipycnal (along-isopycnal) gradients of *T* and *S* are stirred along isopycnals by mesoscale eddies. It is assumed that double-diffusive intrusions develop at the fronts and that their thickness is given by the formula of Ruddick and Turner (1979). This, combined with a crude estimate of the frontal width and a very over-simplified model of the eddy field, leads to a formula for the average diapycnal diffusivity for salt or some neutral tracer, and suggests that the mechanism is important in weakly stratified water with a large epipycnal gradient of salinity. The diapycnal eddy diffusivities for temperature is negative for a stably stratified temperature field. However, the opposite signs of the diapycnal diffusivities for salt and heat are unlikely to lead to observable consequences on account of the dominance, in duxes across isopleths of *T* or *S*, of down-gradient epipycnal transports.

## Abstract

Vertical spectra of temperature perturbations are due to (i) internal wave displacement in the mean profile and (ii) fine-structure that would still be measured in the absence of internal waves. The former is probably confined to low wavenumbers, but at a lower energy level could be responsible for some of the reported fine-structure. The latter is distorted by the internal waves and differs from the true fine-structure spectrum by an amount proportional to the mean-square strain of internal waves.

## Abstract

Vertical spectra of temperature perturbations are due to (i) internal wave displacement in the mean profile and (ii) fine-structure that would still be measured in the absence of internal waves. The former is probably confined to low wavenumbers, but at a lower energy level could be responsible for some of the reported fine-structure. The latter is distorted by the internal waves and differs from the true fine-structure spectrum by an amount proportional to the mean-square strain of internal waves.

## Abstract

In a rotating gratified fluid, with small Ekman number E and Rossby number Ro, vertical diffusion of momentum is balanced by local deceleration for large values of the Burger number S, and hence leads to an increase in S. For small values of S a feature spreads laterally and S decreases; in this case a transformation to density coordinates leads to a horizontal-diffusion equation, which can be generalized to allow for arbitrary values of S and Ro. If Ro ≪ S, as well as Ro ≪ 1, the potential-vorticity equation can be linearized and the relative effect of vertical and horizontal diffusion of either momentum or mass can be examined.

## Abstract

In a rotating gratified fluid, with small Ekman number E and Rossby number Ro, vertical diffusion of momentum is balanced by local deceleration for large values of the Burger number S, and hence leads to an increase in S. For small values of S a feature spreads laterally and S decreases; in this case a transformation to density coordinates leads to a horizontal-diffusion equation, which can be generalized to allow for arbitrary values of S and Ro. If Ro ≪ S, as well as Ro ≪ 1, the potential-vorticity equation can be linearized and the relative effect of vertical and horizontal diffusion of either momentum or mass can be examined.

## Abstract

Attempts to predict the impact on a tidal regime of large engineering structures are generally based on the use of a numerical model which is calibrated to reproduce the natural tidal regime and then rerun with the structures in place. It is usually assumed that the “input” tide at the open boundary is unchanged by the structures, though this is clearly wrong in principle.

We show how errors in this procedure can be corrected for, or at least estimated, using output from the numerical model and estimates of the impedance of the exterior ocean. The ocean impedance can be expressed as an infinite series in terms of the normal modes of the ocean, with some terms allowing for near-resonant enhancement of particular modes, and the infinite tail corresponding to a local source-like behavior which can be estimated independently.

Application of the technique to the problem of predicting the impact of Fundy tidal power suggests that any predicted change may be uncertain to about ±25% of the change in mass flux across the open boundary. This uncertainty could amount to ±4% of the tidal range for a large tidal power development.

It is clear that numerical models used in this type of problem should generally extend to the edge of the continental shelf. The role of side boundaries from the coast to the edge of the shelf is uncertain, although in the Fundy problem there is little mass flux across them so that they appear not to be important.

We also estimate that the impact of Fundy tidal power development on global ocean tides would be a change of a few millimeters in M_{2}.

## Abstract

Attempts to predict the impact on a tidal regime of large engineering structures are generally based on the use of a numerical model which is calibrated to reproduce the natural tidal regime and then rerun with the structures in place. It is usually assumed that the “input” tide at the open boundary is unchanged by the structures, though this is clearly wrong in principle.

We show how errors in this procedure can be corrected for, or at least estimated, using output from the numerical model and estimates of the impedance of the exterior ocean. The ocean impedance can be expressed as an infinite series in terms of the normal modes of the ocean, with some terms allowing for near-resonant enhancement of particular modes, and the infinite tail corresponding to a local source-like behavior which can be estimated independently.

Application of the technique to the problem of predicting the impact of Fundy tidal power suggests that any predicted change may be uncertain to about ±25% of the change in mass flux across the open boundary. This uncertainty could amount to ±4% of the tidal range for a large tidal power development.

It is clear that numerical models used in this type of problem should generally extend to the edge of the continental shelf. The role of side boundaries from the coast to the edge of the shelf is uncertain, although in the Fundy problem there is little mass flux across them so that they appear not to be important.

We also estimate that the impact of Fundy tidal power development on global ocean tides would be a change of a few millimeters in M_{2}.

## Abstract

A simple model in which the cross-strait sea surface slope is geostrophically balanced and the along-strait slope is balanced by acceleration and friction, is shown to be supported by the results of Buchwald and Miles for fluctuating flow through a gap between two semi-infinite oceans. For a narrow gap (compared with the Rossby radius and the scale of the motion in the far field), the transport through it is exactly the same as that predicted by the model, provided that the gap is regarded as having an elective length as determined in this paper. The importance of the models is that they demonstrate that, at low frequency, the flow may be “geostrophically controlled” and the transport limited to a value much less than that which would arise in a nonrotating system. The neglect of nonlinear advective terms in the models is justified by a comparison or the Bernoulli set-down in the strait with the driving head and the mean water depth. The formula for the flux through a strait may be applied in studies of the forced of ocean basins connected by straits. In particular, we draw attention to the existence of damped low-frequency normal modes for two connected (but frictionless) ocean basins.

## Abstract

A simple model in which the cross-strait sea surface slope is geostrophically balanced and the along-strait slope is balanced by acceleration and friction, is shown to be supported by the results of Buchwald and Miles for fluctuating flow through a gap between two semi-infinite oceans. For a narrow gap (compared with the Rossby radius and the scale of the motion in the far field), the transport through it is exactly the same as that predicted by the model, provided that the gap is regarded as having an elective length as determined in this paper. The importance of the models is that they demonstrate that, at low frequency, the flow may be “geostrophically controlled” and the transport limited to a value much less than that which would arise in a nonrotating system. The neglect of nonlinear advective terms in the models is justified by a comparison or the Bernoulli set-down in the strait with the driving head and the mean water depth. The formula for the flux through a strait may be applied in studies of the forced of ocean basins connected by straits. In particular, we draw attention to the existence of damped low-frequency normal modes for two connected (but frictionless) ocean basins.

## Abstract

During the initial stages of the deepening of the surface mixed layer, the rate of increase of potential energy is proportional to the input of energy to the mixed layer by the wind. In an attempt to reconcile an apparent discrepancy between the rate of deepening in laboratory experiments (Kato and Phillips,1969) and in the ocean (Denman and Miyake, 1973), a simple model for the momentum and energy transfer by the wind to surface waves and the mixed layer is suggested. The net transfer of momentum τ_{ml} is the wind stress τ less the local growth of surface wave momentum and the divergence of the surface wave momentum flux, and the net energy transfer Ė_{ml} is the work Ė done on the waves by the wind less the local growth of surface wave energy, the divergence of the surface wave energy flux and the viscous dissipation of the waves. Using the JONSWAP wave observations, the net momentum transfer is 0.97τ (Hasselmann *et al*., 1973). Using a. simple momentum transfer function, allowing direct generation of long gravity waves and capillary-gravity waves, to estimate work done on the waves, the energy actually transferred to the mixed layer is a few percent of _{τ}
*U*
_{0}, where *U*
_{10} is the 10 m wind speed. The oceanic and laboratory rates of deepening of the mixed layer appear roughly consistent. In addition, the flow in the mixed layer apparently adjusts itself so that the surface flow is Ė_{ml}/τ_{ml}.

## Abstract

During the initial stages of the deepening of the surface mixed layer, the rate of increase of potential energy is proportional to the input of energy to the mixed layer by the wind. In an attempt to reconcile an apparent discrepancy between the rate of deepening in laboratory experiments (Kato and Phillips,1969) and in the ocean (Denman and Miyake, 1973), a simple model for the momentum and energy transfer by the wind to surface waves and the mixed layer is suggested. The net transfer of momentum τ_{ml} is the wind stress τ less the local growth of surface wave momentum and the divergence of the surface wave momentum flux, and the net energy transfer Ė_{ml} is the work Ė done on the waves by the wind less the local growth of surface wave energy, the divergence of the surface wave energy flux and the viscous dissipation of the waves. Using the JONSWAP wave observations, the net momentum transfer is 0.97τ (Hasselmann *et al*., 1973). Using a. simple momentum transfer function, allowing direct generation of long gravity waves and capillary-gravity waves, to estimate work done on the waves, the energy actually transferred to the mixed layer is a few percent of _{τ}
*U*
_{0}, where *U*
_{10} is the 10 m wind speed. The oceanic and laboratory rates of deepening of the mixed layer appear roughly consistent. In addition, the flow in the mixed layer apparently adjusts itself so that the surface flow is Ė_{ml}/τ_{ml}.

## Abstract

Earlier work has suggested that internal wave reflection off sloping bottoms may cause significant diapycnal mixing in the deep ocean, and may also represent an important sink of internal wave energy. Most theories have been limited, however, by the representation of the bottom as an infinite plane slope. In this paper, the scattering of internal waves off irregular topography is studied for a few idealized bottom shapes. We pay special attention to the critical case, which occurs when the bottom slope *dh*/*dx* locally matches the wave ray slope *s*. Analytical solutions for bottom shapes such that *dh*/*dx* = *s* at a single point are discussed for both locally convex and concave topography, and are compared with the results of specular reflection theory. They lead to the important conclusion that one is more likely to observe energy enhancement at the critical frequency above locally convex rather than concave topography. This suggests that energy dissipation rates associated with the breaking of internal waves may also be higher above locally convex topography. We also note that, for locally convex topography, rapid variations of the reflected wavefield with height above the bottom can be explained by purely geometric effects, and need not be a consequence of nonlinear interactions.

## Abstract

Earlier work has suggested that internal wave reflection off sloping bottoms may cause significant diapycnal mixing in the deep ocean, and may also represent an important sink of internal wave energy. Most theories have been limited, however, by the representation of the bottom as an infinite plane slope. In this paper, the scattering of internal waves off irregular topography is studied for a few idealized bottom shapes. We pay special attention to the critical case, which occurs when the bottom slope *dh*/*dx* locally matches the wave ray slope *s*. Analytical solutions for bottom shapes such that *dh*/*dx* = *s* at a single point are discussed for both locally convex and concave topography, and are compared with the results of specular reflection theory. They lead to the important conclusion that one is more likely to observe energy enhancement at the critical frequency above locally convex rather than concave topography. This suggests that energy dissipation rates associated with the breaking of internal waves may also be higher above locally convex topography. We also note that, for locally convex topography, rapid variations of the reflected wavefield with height above the bottom can be explained by purely geometric effects, and need not be a consequence of nonlinear interactions.

## Abstract

The Green's function for a semi-infinite ocean with depth a function of distance from the boundary is developed numerically for the M_{2} frequency and with Coriolis frequency and depth profile appropriate to the continental slope off the Gulf of Maine. This involves numerical integration of the linearized shallow water equations for all longshore wavenumbers, followed by numerical Fourier transformation. This variable-depth Green's function is approximately equal to Buchwald's (1971) constant-depth Green's function for distances along the boundary greater than the width of the slope, and at very short range tends to limiting values which can be approximated analytically.

The Green's function, when combined with currents from Greenberg's (1979) numerical model of the Bay of Fundy and Gulf of Maine, is used to explain substantial observed variations in M_{2} amplitude and phase along the edge of the shelf off the Gulf of Maine; the variable-depth Green's function produces significantly better results than the constant-depth Green's function. The results support the basic premise that the M_{2} elevation at the shelf edge in the absence of the Gulf of Maine would be fairly constant, and suggest ways of deriving open boundary input for tidal models of coastal seas with a minimum of offshore gaging.

## Abstract

The Green's function for a semi-infinite ocean with depth a function of distance from the boundary is developed numerically for the M_{2} frequency and with Coriolis frequency and depth profile appropriate to the continental slope off the Gulf of Maine. This involves numerical integration of the linearized shallow water equations for all longshore wavenumbers, followed by numerical Fourier transformation. This variable-depth Green's function is approximately equal to Buchwald's (1971) constant-depth Green's function for distances along the boundary greater than the width of the slope, and at very short range tends to limiting values which can be approximated analytically.

The Green's function, when combined with currents from Greenberg's (1979) numerical model of the Bay of Fundy and Gulf of Maine, is used to explain substantial observed variations in M_{2} amplitude and phase along the edge of the shelf off the Gulf of Maine; the variable-depth Green's function produces significantly better results than the constant-depth Green's function. The results support the basic premise that the M_{2} elevation at the shelf edge in the absence of the Gulf of Maine would be fairly constant, and suggest ways of deriving open boundary input for tidal models of coastal seas with a minimum of offshore gaging.

## Abstract

We present an analysis of 50 days of current meter and sea Revel data collected in a long narrow strait connecting the Gulf of St. Lawrence to the Atlantic Ocean. The dynamical balances implied by a scale analysis of the equation of motion are compared with the data for semidiurnal and diurnal tides and for low-frequency flows, the main result being that the near-surface currents along the strait are, as expected, in geostrophic balance with the sea level slope across the strait. The flow appears to be driven by the sea level difference between opposite ends of the strait produced by large-scale meteorological forcing, and a regression model involving acceleration and friction suggests a spindown time of 1.1 days. The near-bottom currents are significantly less than those new the surface. At both levels the currants are reasonably uniform across the channel, apart from the possibility of nearshore intensification at the lower level. The vertical and horizontal structure of the low-frequency current fluctuations, and the spindown time, are reasonably consistent with the predictions of a dynamical model in which a stratified fluid in a strait of rectangular cross section is driven by an oscillatory pressure gradient along the strait.

Sea level data from an island at the eastern end of the strait of Belle Isle suggest that the flow fluctuations are confined to the south side of the Strait for both incoming and outgoing flows. The moan baroclinic flow appears to be close to critical and so may be hydraulically controlled. Cross-channel geostrophy permits the surface flow through the Strait to be monitored by sea level gages located on opposite sides of the channel, and eight years of data on the monthly mean sea level difference across the Strait suggest substantial winter inflow into the Gulf of St. Lawrence. There is considerable interannual variability for all seasons.

## Abstract

We present an analysis of 50 days of current meter and sea Revel data collected in a long narrow strait connecting the Gulf of St. Lawrence to the Atlantic Ocean. The dynamical balances implied by a scale analysis of the equation of motion are compared with the data for semidiurnal and diurnal tides and for low-frequency flows, the main result being that the near-surface currents along the strait are, as expected, in geostrophic balance with the sea level slope across the strait. The flow appears to be driven by the sea level difference between opposite ends of the strait produced by large-scale meteorological forcing, and a regression model involving acceleration and friction suggests a spindown time of 1.1 days. The near-bottom currents are significantly less than those new the surface. At both levels the currants are reasonably uniform across the channel, apart from the possibility of nearshore intensification at the lower level. The vertical and horizontal structure of the low-frequency current fluctuations, and the spindown time, are reasonably consistent with the predictions of a dynamical model in which a stratified fluid in a strait of rectangular cross section is driven by an oscillatory pressure gradient along the strait.

Sea level data from an island at the eastern end of the strait of Belle Isle suggest that the flow fluctuations are confined to the south side of the Strait for both incoming and outgoing flows. The moan baroclinic flow appears to be close to critical and so may be hydraulically controlled. Cross-channel geostrophy permits the surface flow through the Strait to be monitored by sea level gages located on opposite sides of the channel, and eight years of data on the monthly mean sea level difference across the Strait suggest substantial winter inflow into the Gulf of St. Lawrence. There is considerable interannual variability for all seasons.