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Jason H. Middleton

Abstract

The properties of low-frequency waves, trapped on a wide, reef-fringed continental shelf are predicted theoretically and compared with limited observations from the northeast coast of Australia. A theoretical model of free topographically trapped waves is developed for a simple step-shaped shelf geometry with a shallow reef on the outer shelf. Dimensional arguments show that the flow across the reef obeys a balance between pressure gradient, Coriolis and frictional effects. Relative to the results for a shelf having no reef, the theoretical dispersion relation for a reef-fringed shelf predicts some modification of the baroclinic and Kelvin modes, a more substantial increase in phase speed of the equatorward propagating shelf-wave mode for shorter wavelengths and the existence of an additional poleward propagating mode, trapped on the continental shelf by the reef. Rotary transfer functions, relating the wind stress vectors to the current vectors, are used to remove the wind-driven contribution from the currents leaving wind-reduced current vector time series. Spectral estimates of the wind-reduced data show features consistent with free wave theory and, in addition, wavenumber-frequency points calculated from the wind-reduced current vectors by rotary coherence techniques show good support for modes with properties consistent with the presence of the reef.

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Jason H. Middleton

Abstract

A depth-averaged barotropic model is used to investigate the steady response of the coastal ocean to alongshore pressure gradients imposed by the deep ocean. Solution indicate that the dimensionless continental margin width δ is the appropriate parameter determining the effectiveness of the transmission of the alongshore pressure field from ocean to coast. For linear depth profiles having depth h = h 0 + h 1 x the abyssal plane at x=lδ=(fk/r)½(h 1 l 2/2)½ where f is the Coriolis parameter, r is the linear friction coefficient for alongshore flow and k is the wavenumber of the alongshore pressure perturbation. For parabolic depth profiles having h=h 0+h 2 x 2 to x=l, δ=(3fk/2r)(h2 l 3/3). On narrow continental margins with δ≪1, oceanic pressure fields are almost completely transmitted to the coast causing substantial near-coastal currents, while on wide continental margins with δ≫1 the near coastal ocean is unaffected by the oceanic pressure field. In general, the oceanic pressure field drives a strong circulation at the outer slope, and this circulation weakens toward the coast. This contrasts with the coastal circulation resulting from an alongshore wind stress, which is strongest at the coast and weakens with distance offshore.

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Richard Manasseh and Jason H. Middleton

Abstract

Analyses of wind velocity and air pressure data, acquired by a set of low-level anemometers at Sydney Airport, Australia, indicate the passage of a set of three remarkably smooth atmospheric boundary layer oscillations that traveled ahead of a thunderstorm on 27 December 1991. The oscillations were probably generated by a nearby thunderstorm outflow, propagating into a stably stratified atmospheric layer. It is likely that the phenomenon was initiated by the degenerating of an outflow gravity current into a family of amplitude-ordered solitary waves. Although reasonable agreement can be obtained on the propagation speed using a linear theory, the weakness of the trapping mechanism for this solution and an overestimation of the weakly nonlinear wave half-width leads to a conclusion that the waves fully nonlinear.

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Doron Nof and Jason H. Middleton

Abstract

The communication between shallow and deep oceans via gaps in the separating barrier reefs is examined using a simplified two-layer analytical model. Attention is focused on the flow resulting from a sea-level difference between the ocean and the lagoon. Such a difference imposes a pressure gradient along the gap which, in turn, forces a flow into the lagoon. The coral reefs, which extend all the way to the surface and are exposed to the atmosphere at low tide, are presented by two portions of an infinitely long wall. A group of passages, whose combined width is not very small compared to the Rossby radius, is represented by a single gap separating the two portions of the wall.

The fully nonlinear model is inviscid, hydrostatic and nondiffusive. Nonlinearity is essential because (i) the flow in the passages is rather fast, and (ii) the depth variations are of order unity. Steady solutions for the upstream and downstream fields are constructed analytically using the momentum equation in an integrated form, the Bernoulli integral and conservation of potential vorticity.

It is found that, surprisingly, the transport through the gap is independent of the gap's width. Upstream, the oceanic water approaches the gap only from one direction; upon reaching the gap, the approaching current splits into two branches. One continues to flow in the oceanic basin and never enters the gap whereas the other passes through the gap and penetrates into the lagoon. When the sea-level difference between the ocean and the lagoon exceeds a critical value, water below the oceanic thermocline is pulled up and forced into the lagoon. This nutrient-rich upwelled water forms a boundary current that hugs the barrier reef on the right hand side in the Northern Hemisphere. We term this new type of upwelling and suction “geostrophic pumping” because it is a result of the geostrophic flow away from the gap.

A possible application of this geostrophic pumping to the upwelling and inflow in the Great Barrier Reef is briefly discussed. The model provides a plausible explanation for the health of the coral on the lagoon side where, without such an inflow, the nutrients would have been depleted.

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Patrick Marchesiello and Jason H. Middleton

Abstract

The East Australian Current (EAC) is a western boundary current flowing southward off the east coast of Australia. Its eddy variability has been shown to be vigorous, a typical feature being the formation of a large warm core eddy in the western Tasman Sea. The dynamics controlling the development of such an eddy are the subject of this paper. The Princeton Ocean Model was tuned for conditions that prevail in the western Tasman Sea, and initialized with features based on the Royal Australian Navy weekly temperature charts. A 70-day simulation initialized with summer conditions captures the formation of a large warm core eddy that matches fairly well the observations. Analyses of the results demonstrate that the formation of these eddies is associated with a wide range of dynamical aspects observed in the region, such as oscillation and propagation of the Tasman Front, EAC separation from the coast, formation of cold-core frontal eddies, and nutrient enrichment of coastal waters.

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Pritha Das and Jason H. Middleton

Abstract

An analytical theory of barotropic tides propagating onto a sloping continental shelf from the deep ocean is developed. The plane Poincaré waves incident from the deep ocean are obliquely angled, and a full matching of shelf and ocean solutions is implemented. Allowance for a nonzero water depth at the coast requires an additional term, the Bessel function of second kind, in the solution. The full solution is examined for response characteristics for both frictionless tides and for tides affected by a linear bottom friction, and energy dissipation rates are evaluated. Results for narrow continental shelves indicate that a small but nonzero coastal wall depth, in conjunction with the angle of incidence, can play a significant role in modifying the response, while for wider continental shelves both of these features greatly modify the response at resonance.

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Jason H. Middleton and Richard E. Thomson

Abstract

In tropical regions, and for applications where the alongshore scale k −1 of the forcing is large, the assumption of constant Coriolis parameters f in Csanady's Arrested Topographic Wave (ATW) model is invalid. Here we generalize the ATW model for study wind-driven coastal circulation by allowing f to vary according to the β-plane approximation f = 0 + βy, and by deriving solutions for finite width shelves. Bottom friction is assumed to be linear in the depth-averaged velocity with coefficient r and the depth h(x) = sx is assumed to increase linearly with distance x offshore. The generalization includes the ATW solutions as a subset; however, theoretical and numerical calculations show that the dimensionless parameter β/f 0 k plays a key role in the flow structure. In particular, for infinitely wide shelves and nonzero values of β/f 0 k, enhanced trapping occurs for coastal circulation off an east cost while trapped solutions cease to exist for circulation off a west coast. For finite width shelves, specification of zero sea level anomaly at the shelf break allows solutions for wind-driven circulation on both eat and west costs. Inclusion of the β effect results in a smaller trapping scale for coastal flows on east coasts (western ocean boundaries) and a larger trapping scale for coastal flows on west coasts. Asymptotic solutions for geographically varying wind stress with oscillatory form are presented as examples.

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David A. Griffin and Jason H. Middleton

Abstract

The salient features of subinertial frequency fluctuations of current, sea level, temperature and wind stress observed within the Capricornia section of the Great Barrier Reef are interpreted by comparison with coastal-trapped wave (CTW) theories Near-coastal currents and sea levels are modeled with some success by a theory of first-mode wind-forced barotropic continental shelf waves with geographical origin at Fraser Island, the southern across-shelf boundary of the study region. However, current and temperature variations of period 8–10 days on the continental slope are observed to have energy far in excess of that generated by the local wind. Decomposition of the observed alongshore velocity field in terms of baroclinic CTW modes indicates the signal is predominantly a second- or third-mode wave propagating equatorward at 0.4–0.6 m s−1. These modes have most of their energy flux propagating along the continental slope, and the energy levels indicate that the source region lies to the south of Fraser Island. The possible biological and geological relevance of CTW activity within the study region is briefly discussed.

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Madeleine L. Cahill and Jason H. Middleton

Abstract

Observations of current, bottom pressure, and wind from the shelf of the Northern Great Barrier Reefare interpreted using a two-layer, frictional, step-shelf model forced by propagating wind stress. Distinguishing features of the region are the many reefs on the shallow shelf, the well-mixed nature of the shelf waters, and the steep continental slope.

The instrument army was deployed from April to October 1982 and comprised 14 current meters, nine pressure gauges, and two weather stations. Low-pass [<0,6 cycles per day (cpd)] filtered velocity and pressure data are analyzed separately using a time domain empirical orthogonal function (EOF) analysis. The first EOFs of both velocity and pressure data are found to account for most of the observed variance on the shelf. Time series of these two EOFs are both highly coherent, with the local longshore wind stress at “weatherband” frequencies(<0.3cpd);however, the frequency transfer functions of the wind to the current and of the wind to the pressure are very different. The observed velocity transfer function (evaluated from data) is frequency independent and has almost zero phase whereas the observed pressure transfer function decreases with frequency and lags the wind by about 60°. Theoretical response functions of the step-shelf model (with a high coefficient of friction on the shelf) have these same characteristics. The difference in the response functions for velocity and pressure is due to the large contribution that the sea level response over the slope makes to the sea level over the shelf while having very little effect on shelf velocities. Thus, the observed pressure response over the shelf reflects the dynamic balance over the slope, which is that of an internal Kelvin wave, while the longshore velocity response on the shelf is determined simply by the balance between wind stress and bottom friction on the shelf.

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Andrew J. Weaver and Jason H. Middleton

Abstract

Two models, one numerical and one analytical, are used to investigate mechanisms for the generation and flow of the Leeuwin Current observed off the west coast of Australia. Three numerical experiments are conducted using the Bryan–Cox Ocean General Circulation Model. In the first experiment an alongshore density gradient is imposed, while in the latter two experiments the additional effects of warm, fresh North West Shelf waters are considered. The alongshore density gradient in the Indian Ocean produces an onshore geostrophic flow which turn southward and intensifies as it flows along the coast of Western Australia and into the Great Australian Bight. Maximum alongshore surface velocities occur just off the shelf break and below this poleward current is a weak equatorward flow. The magnitudes of the velocity vectors and associated advection of temperature and salinity, and the width, structure and geographical location of the current all agree well with field observations. The effects of the warm, fresh North West Shelf waters are to enhance the alongshore barotropic current on the shelf. This response is mainly local and diminishes with alongshore distance. Model results suggest that the Leeuwin Current a baroclinic current driven by an alongshore density gradient in the Indian Ocean, maintained by equatorward surface heating and poleward surface cooling. The numerical results further predict the existence of a cyclonic circulation off Northwest Cape in the top 120 m of water. It is deduced that the seasonal modification of the Leeuwin Current is due to local winds and seasonal variation in the north–south density gradient.

A linear analytical model of the continental shelf cicculation coupled to a two layer open ocean confirms the conclusions drawn from the numerical model, and shows that the shelf circulation obeys a simple balance between alongshore pressure gradient forces (due to steric height gradients), and bottom friction. It is shown that in the absence of vertical mixing, the presence of a sloping shelf is necessary for the existence of the trapped eastern boundary current. Without the sloping shelf the current radiates offshore through baroclinic Rossby wave propagation. For parameters applicable to the Leeuwin Current, the analytic model predicts realistic alongshore transports.

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