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## 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

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

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

We analyze 5 months of sea-level data from Katakolon, Greece, in terms of local atmospheric pressure and the two components of geostrophic wind. The response to pressure is isostatic at low and high frequencies, but significantly nonisostatic for intermediate frequencies centered on about 0.01 cycles per hour. The response is consistent with a simple theory in which the fluctuating barotropic flow through the Straits of Gibraltar and Sicily is geostrophically controlled at low frequency. The local geostrophic wind contributes very little to the sea level variance; the response coefficients, while not well determined, are qualitatively as expected and quantitatively correspond to a very narrow near-shore region of shallow water.

## Abstract

We analyze 5 months of sea-level data from Katakolon, Greece, in terms of local atmospheric pressure and the two components of geostrophic wind. The response to pressure is isostatic at low and high frequencies, but significantly nonisostatic for intermediate frequencies centered on about 0.01 cycles per hour. The response is consistent with a simple theory in which the fluctuating barotropic flow through the Straits of Gibraltar and Sicily is geostrophically controlled at low frequency. The local geostrophic wind contributes very little to the sea level variance; the response coefficients, while not well determined, are qualitatively as expected and quantitatively correspond to a very narrow near-shore region of shallow water.

## 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.

## Abstract

Phillips has shown that an undulating motion of a layered medium relative to a measuring instrument will result in a σ^{−2} spectrum (frequency or wavenumber) over a bandwidth determined by the thickness of the layers and of the sheets separating them. We show, for *any* (temperature) fine-structure statisteally stationary in depth with covariance *r*
_{θ}(*y*
_{1}−*y*
_{2})=<θ(*y*
_{1})θ(*y*
_{2})>, that the covariance of the observed time ceries can be expressed in terms of *r*
_{θ} and the covariance in the vertical displacement ζ, assuming ζ to he josintly normal. An explicit expression for the spectrum is given for the case that the rms value of ζ is large compared to the vertical coherence scale of the fine-structure. We tentatively conclude that the fine-structure dominates in the upper few octaves of the internal wave spectra, and then extends the spectra beyond the cutoff frequency (wavenumber). The loss of vertical coherence due to fine-structure occurs over a distance inversely proportional to frequency, in general agreement with an empirical rule proposed by Webster.

## Abstract

Phillips has shown that an undulating motion of a layered medium relative to a measuring instrument will result in a σ^{−2} spectrum (frequency or wavenumber) over a bandwidth determined by the thickness of the layers and of the sheets separating them. We show, for *any* (temperature) fine-structure statisteally stationary in depth with covariance *r*
_{θ}(*y*
_{1}−*y*
_{2})=<θ(*y*
_{1})θ(*y*
_{2})>, that the covariance of the observed time ceries can be expressed in terms of *r*
_{θ} and the covariance in the vertical displacement ζ, assuming ζ to he josintly normal. An explicit expression for the spectrum is given for the case that the rms value of ζ is large compared to the vertical coherence scale of the fine-structure. We tentatively conclude that the fine-structure dominates in the upper few octaves of the internal wave spectra, and then extends the spectra beyond the cutoff frequency (wavenumber). The loss of vertical coherence due to fine-structure occurs over a distance inversely proportional to frequency, in general agreement with an empirical rule proposed by Webster.

## 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

Short, dissipative, surface waves superposed on longer waves cause a growth of the long wave momentum *M _{l}
* at a ratewhere

*k*,

_{l}*a*are the amplitude and wavenumber of the long waves, so that

_{l}*k*

_{l}*a*is their steepness;

_{l}*S*is the radiation stress of the short waves and τ

_{a}*, the rate of transfer of momentum to the short waves by the wind; and the angle braces denote an average over the long-wave phase θ =*

_{s}*k*

_{l}*x*−ω

*.*

_{l}tThe first term in the above equation is the radiation stress interaction (Phillips, 1963; Hasselmann, 1971) and is generally negligible compared with the second term, neglected by Hasselmann (1971), which shows that long waves can grow if short wave generation (rather than dissipation) is correlated with the long wave orbital velocity.

Even if the modulation of τ*
_{s}
* is only O(

*k*

_{l}*a*) times 〈τ

_{l}*〉, this mechanism can contribute a significant fraction of long wave momentum. However, even a substantially greater modulation of τ*

_{s}*, perhaps due to varying exposure of short waves to the wind, is unlikely to account for all the alleged momentum input to long waves, due to the upper bound*

_{s}*k*

_{l}*a*on the efficiency of the process.

_{l}## Abstract

Short, dissipative, surface waves superposed on longer waves cause a growth of the long wave momentum *M _{l}
* at a ratewhere

*k*,

_{l}*a*are the amplitude and wavenumber of the long waves, so that

_{l}*k*

_{l}*a*is their steepness;

_{l}*S*is the radiation stress of the short waves and τ

_{a}*, the rate of transfer of momentum to the short waves by the wind; and the angle braces denote an average over the long-wave phase θ =*

_{s}*k*

_{l}*x*−ω

*.*

_{l}tThe first term in the above equation is the radiation stress interaction (Phillips, 1963; Hasselmann, 1971) and is generally negligible compared with the second term, neglected by Hasselmann (1971), which shows that long waves can grow if short wave generation (rather than dissipation) is correlated with the long wave orbital velocity.

Even if the modulation of τ*
_{s}
* is only O(

*k*

_{l}*a*) times 〈τ

_{l}*〉, this mechanism can contribute a significant fraction of long wave momentum. However, even a substantially greater modulation of τ*

_{s}*, perhaps due to varying exposure of short waves to the wind, is unlikely to account for all the alleged momentum input to long waves, due to the upper bound*

_{s}*k*

_{l}*a*on the efficiency of the process.

_{l}## 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}.