# Search Results

## You are looking at 1 - 8 of 8 items for

- Author or Editor: Ross Vennell x

- Refine by Access: All Content x

## Abstract

Intuitively, the transport of an oscillating flow in a short channel should be constrained to be approximately the same at all cross sections; that is, the transport is nondivergent. This intuitive constraint is quantified by developing a generalized definition of “shortness” given by the smallness of a nondimensional parameter *ε.* This parameter assesses the shortness of channels of variable cross-sectional area, with linear or nonlinear dynamical balances and, thus, is applicable to a wide range of channels, from tidal flow through the entrance to an estuary to subinertial flow through a strait. This analysis leads to a general result for a barotropic oscillating flow, which states that the variation in the amplitude of the transport along the channel is of order 2*ε* of the mean transport and the variation in the transport’s phase is of order 2 tan^{−1}
*ε.* A diagnostic model for tidal flow within a “short” narrow channel of variable depth is developed. The model shows that the phase of the cross-sectional average velocity is dependent only on the relative amplitude and phase of the surface oscillation at the ends of the channel. Tidal measurements presented in a companion paper provide observational support for both the general result and diagnostic model.

## Abstract

Intuitively, the transport of an oscillating flow in a short channel should be constrained to be approximately the same at all cross sections; that is, the transport is nondivergent. This intuitive constraint is quantified by developing a generalized definition of “shortness” given by the smallness of a nondimensional parameter *ε.* This parameter assesses the shortness of channels of variable cross-sectional area, with linear or nonlinear dynamical balances and, thus, is applicable to a wide range of channels, from tidal flow through the entrance to an estuary to subinertial flow through a strait. This analysis leads to a general result for a barotropic oscillating flow, which states that the variation in the amplitude of the transport along the channel is of order 2*ε* of the mean transport and the variation in the transport’s phase is of order 2 tan^{−1}
*ε.* A diagnostic model for tidal flow within a “short” narrow channel of variable depth is developed. The model shows that the phase of the cross-sectional average velocity is dependent only on the relative amplitude and phase of the surface oscillation at the ends of the channel. Tidal measurements presented in a companion paper provide observational support for both the general result and diagnostic model.

## Abstract

Storms crossing topography are shown to radiate long surface gravity waves. The waves are transients generated by changes in the depth-dependent amplitude of the atmospherically forced pressure wave beneath a storm. This generation mechanism for long waves, known as “meteorological tsunamis” or rissaga, does not appear to have been previously discussed. The transients have periods equal to the passage time of the storm, of order 30 min for small fast-moving storms. A 1D model is used to give the amplitudes of the transient waves generated by a small fast-moving storm crossing a topographic step on to a continental shelf and across a ridge. Large transients are generated by storms whose translation speed is subcritical in deep water and supercritical in shallow water, that is, faster than the shallow-water wave speed. Surprisingly, when the depth difference between the deep water and the continental shelf is large, a gentle transition from deep to shallow water over 10 storm widths only slightly reduces the amplitudes of the transients. The influence of a finite-width shelf on the enhancement of coastal storm surge is also discussed. A 2D numerical model illustrates the topographic transients generated by sub- and supercritical storms moving across a ridge. Topographic transients are suggested as a source of energy for seiches on shelves and within embayments. The energy may come from a storm crossing the adjacent continental slope and possibly from distant open-ocean storms crossing multiple ridges and seamounts.

## Abstract

Storms crossing topography are shown to radiate long surface gravity waves. The waves are transients generated by changes in the depth-dependent amplitude of the atmospherically forced pressure wave beneath a storm. This generation mechanism for long waves, known as “meteorological tsunamis” or rissaga, does not appear to have been previously discussed. The transients have periods equal to the passage time of the storm, of order 30 min for small fast-moving storms. A 1D model is used to give the amplitudes of the transient waves generated by a small fast-moving storm crossing a topographic step on to a continental shelf and across a ridge. Large transients are generated by storms whose translation speed is subcritical in deep water and supercritical in shallow water, that is, faster than the shallow-water wave speed. Surprisingly, when the depth difference between the deep water and the continental shelf is large, a gentle transition from deep to shallow water over 10 storm widths only slightly reduces the amplitudes of the transients. The influence of a finite-width shelf on the enhancement of coastal storm surge is also discussed. A 2D numerical model illustrates the topographic transients generated by sub- and supercritical storms moving across a ridge. Topographic transients are suggested as a source of energy for seiches on shelves and within embayments. The energy may come from a storm crossing the adjacent continental slope and possibly from distant open-ocean storms crossing multiple ridges and seamounts.

## Abstract

The dynamics of tidal flow through inlets are not fully understood; observations are scarce because of the small spatial scales over which the flow varies. This paper gives the first detailed measurements of the 2D structure of tidal currents and the dynamical terms of the momentum equation within a tidal inlet, leading to an improved understanding of the physics of tidal inlets. In the 180 cm s^{−1} peak flow the near-steady-state momentum balance is dominated by horizontal advection and the pressure gradient, with bottom friction playing a secondary role. At slack water, there is a balance between local acceleration and the pressure gradient. Numerical integration of the ADCP-measured terms in the momentum equation yields 60-m- resolution dynamic topography that shows a 7-cm variation at peak flood consistent with Bernoulli’s equation. The surface topography because of friction forms a linear ramp with a peak irreversible head loss of 2 cm over 600 m. Tidal velocities were extracted from the ADCP measurements by extending an existing spline analysis technique. This technique is known to be sensitive to the number and location of the nodes where weights are applied to the spline. Simulations with artificial data representative of the tidally varying ADCP measurements show that, provided there are sufficient nodes to resolve the smallest spatial scale of interest, velocities predicted by the spline technique are insensitive to the number or locations of the nodes.

## Abstract

The dynamics of tidal flow through inlets are not fully understood; observations are scarce because of the small spatial scales over which the flow varies. This paper gives the first detailed measurements of the 2D structure of tidal currents and the dynamical terms of the momentum equation within a tidal inlet, leading to an improved understanding of the physics of tidal inlets. In the 180 cm s^{−1} peak flow the near-steady-state momentum balance is dominated by horizontal advection and the pressure gradient, with bottom friction playing a secondary role. At slack water, there is a balance between local acceleration and the pressure gradient. Numerical integration of the ADCP-measured terms in the momentum equation yields 60-m- resolution dynamic topography that shows a 7-cm variation at peak flood consistent with Bernoulli’s equation. The surface topography because of friction forms a linear ramp with a peak irreversible head loss of 2 cm over 600 m. Tidal velocities were extracted from the ADCP measurements by extending an existing spline analysis technique. This technique is known to be sensitive to the number and location of the nodes where weights are applied to the spline. Simulations with artificial data representative of the tidally varying ADCP measurements show that, provided there are sufficient nodes to resolve the smallest spatial scale of interest, velocities predicted by the spline technique are insensitive to the number or locations of the nodes.

## Abstract

The phase of the *M*
_{2} surface elevation tide changes by 100° along a 40-km length of Cook Strait, New Zealand. Acoustic Doppler Current Profiler measurements are presented that show a change of only 12° in the phase of depth-averaged semidiurnal tidal currents along this same length. This phase change supports the general result developed by Vennell, which states that the phase of the cross-sectional average velocity is approximately constant along a “short” strait of variable cross-sectional area. Vennell also developed a relationship between the constant phase of tidal currents along the strait and the amplitude and phase of the surface elevation tide at the ends of a short strait. The velocity phase given by this relationship is shown to agree well with the observed tidal velocity phase in Cook Strait and one other strait.

## Abstract

The phase of the *M*
_{2} surface elevation tide changes by 100° along a 40-km length of Cook Strait, New Zealand. Acoustic Doppler Current Profiler measurements are presented that show a change of only 12° in the phase of depth-averaged semidiurnal tidal currents along this same length. This phase change supports the general result developed by Vennell, which states that the phase of the cross-sectional average velocity is approximately constant along a “short” strait of variable cross-sectional area. Vennell also developed a relationship between the constant phase of tidal currents along the strait and the amplitude and phase of the surface elevation tide at the ends of a short strait. The velocity phase given by this relationship is shown to agree well with the observed tidal velocity phase in Cook Strait and one other strait.

## Abstract

Wavelet and cross-wavelet power spectra of sea level records from tide gauges along the Atlantic coast of Canada showed a low-frequency barotropic response after Hurricane Florence crossed the Newfoundland shelf in September 2006. In comparison with two other storms, the results showed that Florence was the only one that excited a propagating sea level disturbance with a period range similar to the passage time of the storm over the shelf (26–30 h) and phase shifts consistent with a barotropic continental shelf wave (CSW). The high amplitude of the oscillations generated by Florence along the shore diminished from approximately 45 to 12 cm as the CSW propagated from the south coast of Newfoundland to the southern Nova Scotia seaboard. This paper presents the first direct measurement of a remarkably high alongshore group speed (11.4 ± 5.9 m s^{−1}), in the manner of free-barotropic CSW, by examination of sea level wavelet power spectra at different locations. Furthermore, using cross-wavelet analysis of pairs of stations, an exceptional phase speed of 16.0 ± 5.1 m s^{−1} has been found, greater than had been previously observed for a free CSW. The results were consistent with dispersion curves for the first-mode barotropic CSW.

## Abstract

Wavelet and cross-wavelet power spectra of sea level records from tide gauges along the Atlantic coast of Canada showed a low-frequency barotropic response after Hurricane Florence crossed the Newfoundland shelf in September 2006. In comparison with two other storms, the results showed that Florence was the only one that excited a propagating sea level disturbance with a period range similar to the passage time of the storm over the shelf (26–30 h) and phase shifts consistent with a barotropic continental shelf wave (CSW). The high amplitude of the oscillations generated by Florence along the shore diminished from approximately 45 to 12 cm as the CSW propagated from the south coast of Newfoundland to the southern Nova Scotia seaboard. This paper presents the first direct measurement of a remarkably high alongshore group speed (11.4 ± 5.9 m s^{−1}), in the manner of free-barotropic CSW, by examination of sea level wavelet power spectra at different locations. Furthermore, using cross-wavelet analysis of pairs of stations, an exceptional phase speed of 16.0 ± 5.1 m s^{−1} has been found, greater than had been previously observed for a free CSW. The results were consistent with dispersion curves for the first-mode barotropic CSW.

## Abstract

In this note we study the effect of an alongshore density gradient in driving the near-coastal circulation and determining the direction of the alongshore flow. We revisit and extend the results obtained by Malanotte-Rizzoli and Bergamasco (MRB) using the same simple analytical model but changing the longshore density distribution and examining the full solution, not only its far-field behavior as done by MRB. We find as a new result that the near-coastal flow is profoundly modified when passing from monotonic, northward increasing density profiles, the case studied by MRB, to double-ramp profiles with a density maximum. In particular, the reversal of the density gradient north of its maximum is a necessary condition for the creation of a strong southward flowing coastal cell. This cell does not exist when the density increases monotonically northward. The examples shown, even though idealized compare well both in flow direction and in order of magnitude with what is observed in winter in the northern Adriatic sea.

## Abstract

In this note we study the effect of an alongshore density gradient in driving the near-coastal circulation and determining the direction of the alongshore flow. We revisit and extend the results obtained by Malanotte-Rizzoli and Bergamasco (MRB) using the same simple analytical model but changing the longshore density distribution and examining the full solution, not only its far-field behavior as done by MRB. We find as a new result that the near-coastal flow is profoundly modified when passing from monotonic, northward increasing density profiles, the case studied by MRB, to double-ramp profiles with a density maximum. In particular, the reversal of the density gradient north of its maximum is a necessary condition for the creation of a strong southward flowing coastal cell. This cell does not exist when the density increases monotonically northward. The examples shown, even though idealized compare well both in flow direction and in order of magnitude with what is observed in winter in the northern Adriatic sea.

## Abstract

Many coastal regions in the world ocean are characterized by well-mixed conditions to shelf depth in the density field during the winter season. In these situations it is appropriate to construct a model based on the assumption that the shelf is vertically well mixed. Such a model has been constructed assuming that (i) vertical mixing of momentum is stronger than either horizontal mixing or inertial effects; (ii) the density field is also vertically well mixed, i.e., varies only in horizontal at zero order in the expansion in the vertical Peclet number, (iii) the cross-shelf scale is small compared to the alongshelf scale; (iv) depth varies only in cross-shelf direction. The transport streamfunction equation and the advective density equation can then be combined into a single model equation by noting that in the vertically well-mixed flow, density is conserved as it is advected along streamlines.

This model is used to study two different configurations quite common for shelf circulations in the world ocean. The first configuration considers the effect of a deep baroclinic ocean in driving the shelf circulation. Past studies show that a barotropic deep-ocean pressure gradient cannot drive significant shelf flow and that the continental slope effectively “insulates”the shelf from the deep ocean. Thus, the basic question we want to answer is: how does the baroclinic structure of a deep ocean flow affect its ability to penetrate the shelf and determine its circulation? The second configuration to which the model is applied is that of a coastal current driven by an alongshore buoyancy source, such as a river discharge or an alongshore jet.

In all model applications studied, the basic mechanism by which the flow is able to cross topography is bottom friction. In the first situation the flow is driven by prescribing the velocity and density at the outer edge of the shelf. Three types of shelf forcing by the deep ocean are studied: a wide inflow, a narrow inflow and forcing by a Gulf Stream ring. A specific application is made to the northern Adriatic coastal shelf forced by a dense water pool formed in wintertime in the Adriatic interior. In all cases, the main conclusion for the baroclinic deep-ocean inflow onto the well-mixed shelf is that, like in the barotropic case, the tendency for the flow to follow isobaths is much stronger than the degree to which bottom friction allows cross-isobath motion. The deep ocean inflow forces a horizontal boundary layer against the shelf edge. The width of this boundary layer, and therefore the shelf penetration, is larger if the drag coefficient is higher, the latitude lower or the bottom slope weaker. Also, surface-intensified deep ocean flows penetrate the shelf few strongly than bottom intensified flows.

In the two examples studied of flow entering the shelf region near shore, i.e. a coastal river outflow and a coastal jet, it is again shown that the vertical shear of the shore inflow again determines the overall flow pattern. Because of bottom friction, a light alongshore jet or a low density river, i.e., surface intensified flow, expands across the topography more slowly than a bottom intensified flow, such as a high density river or a heavy jet.

## Abstract

Many coastal regions in the world ocean are characterized by well-mixed conditions to shelf depth in the density field during the winter season. In these situations it is appropriate to construct a model based on the assumption that the shelf is vertically well mixed. Such a model has been constructed assuming that (i) vertical mixing of momentum is stronger than either horizontal mixing or inertial effects; (ii) the density field is also vertically well mixed, i.e., varies only in horizontal at zero order in the expansion in the vertical Peclet number, (iii) the cross-shelf scale is small compared to the alongshelf scale; (iv) depth varies only in cross-shelf direction. The transport streamfunction equation and the advective density equation can then be combined into a single model equation by noting that in the vertically well-mixed flow, density is conserved as it is advected along streamlines.

This model is used to study two different configurations quite common for shelf circulations in the world ocean. The first configuration considers the effect of a deep baroclinic ocean in driving the shelf circulation. Past studies show that a barotropic deep-ocean pressure gradient cannot drive significant shelf flow and that the continental slope effectively “insulates”the shelf from the deep ocean. Thus, the basic question we want to answer is: how does the baroclinic structure of a deep ocean flow affect its ability to penetrate the shelf and determine its circulation? The second configuration to which the model is applied is that of a coastal current driven by an alongshore buoyancy source, such as a river discharge or an alongshore jet.

In all model applications studied, the basic mechanism by which the flow is able to cross topography is bottom friction. In the first situation the flow is driven by prescribing the velocity and density at the outer edge of the shelf. Three types of shelf forcing by the deep ocean are studied: a wide inflow, a narrow inflow and forcing by a Gulf Stream ring. A specific application is made to the northern Adriatic coastal shelf forced by a dense water pool formed in wintertime in the Adriatic interior. In all cases, the main conclusion for the baroclinic deep-ocean inflow onto the well-mixed shelf is that, like in the barotropic case, the tendency for the flow to follow isobaths is much stronger than the degree to which bottom friction allows cross-isobath motion. The deep ocean inflow forces a horizontal boundary layer against the shelf edge. The width of this boundary layer, and therefore the shelf penetration, is larger if the drag coefficient is higher, the latitude lower or the bottom slope weaker. Also, surface-intensified deep ocean flows penetrate the shelf few strongly than bottom intensified flows.

In the two examples studied of flow entering the shelf region near shore, i.e. a coastal river outflow and a coastal jet, it is again shown that the vertical shear of the shore inflow again determines the overall flow pattern. Because of bottom friction, a light alongshore jet or a low density river, i.e., surface intensified flow, expands across the topography more slowly than a bottom intensified flow, such as a high density river or a heavy jet.

## Abstract

Applying a two-dimensional (2D) divergence-free (DF) interpolation to a one-person deployable unmanned underwater vehicle’s (UUV) noisy moving-vessel acoustic Doppler current profiler (MV-ADCP) measurements improves the results and increases the utility of the UUV in tidal environments. For a 3.5-h MV-ACDP simulation that spatially and temporally varies with the *M*
_{2} tide, the 2D DF-estimated velocity magnitude and orientation improves by approximately 85%. Next the 2D DF method was applied to velocity data obtained from two UUVs that repeatedly performed seven 1-h survey tracks in Bear Cut Inlet, Miami, Florida. The DF method provides a more realistic and consistent representation of the ADCP measured flow field, improving magnitude and orientation estimates by approximately 25%. The improvement increases for lower flow velocities, when the ADCP measurements have low environmental signal-to-noise ratio. However, near slack tide when flow reversal occurs, the DF estimates are invalid because the flows are not steady state within the survey circuit.

## Abstract

Applying a two-dimensional (2D) divergence-free (DF) interpolation to a one-person deployable unmanned underwater vehicle’s (UUV) noisy moving-vessel acoustic Doppler current profiler (MV-ADCP) measurements improves the results and increases the utility of the UUV in tidal environments. For a 3.5-h MV-ACDP simulation that spatially and temporally varies with the *M*
_{2} tide, the 2D DF-estimated velocity magnitude and orientation improves by approximately 85%. Next the 2D DF method was applied to velocity data obtained from two UUVs that repeatedly performed seven 1-h survey tracks in Bear Cut Inlet, Miami, Florida. The DF method provides a more realistic and consistent representation of the ADCP measured flow field, improving magnitude and orientation estimates by approximately 25%. The improvement increases for lower flow velocities, when the ADCP measurements have low environmental signal-to-noise ratio. However, near slack tide when flow reversal occurs, the DF estimates are invalid because the flows are not steady state within the survey circuit.