Propagation of coastal‐trapped waves under an ice cover in Hudson Bay*

Abstract

Three arrays of current‐meter moorings were deployed under landfast sea ice in southeast Hudson Bay for eight weeks in spring 1986. Spectral analysis shows low‐frequency signals with periods of 3 to 11 days. These signals are interpreted as being due to coastal‐trapped waves propagating cyclonically in Hudson Bay; their theoretical dispersion relations and corresponding modal structures are presented for winter stratification and are compared with observations. At a period of 3 days both the modified external Kelvin wave and higher mode continental shelf waves may be important in describing the observed low‐frequency variability, whereas at a period of 10 days the Kelvin wave appears to be the dominant mode. The generation mechanisms for these coastal trapped waves are also investigated. Two sources have been studied: the longshore atmospheric pressure gradient and the average atmospheric pressure over the ice cover in Hudson Bay. Coherence and phase analyses performed with time series of longshore current and atmospheric forcing data reveal that both the average atmospheric pressure and the longshore atmospheric pressure gradient are important in explaining the observed low‐frequency variability, without indicating which one is the most important.     

Impacts of the MJO in the Indian Ocean and on the Western Australian coast

The large sea surface temperature variations induced by the Madden-Julian Oscillation (MJO) on the northwest shelf of Australia and the remote influence of the MJO on the subtropical Western Australian coast are explored using the POAMA Ensemble Ocean Data Assimilation System reanalyses (PEODAS) for the period 1980–2010. The focus here is during the November–April extended summer season when the impacts of the MJO on and along the west coast of Australia are greatest. The MJO is well known to force equatorial Kelvin and Rossby waves in the Indian Ocean, and these are well depicted in the PEODAS reanalyses. When the downwelling Kelvin waves (forced by the westerly-convective phase of the MJO) reach the Indonesian region at the eastern boundary of the Indian Ocean, a coastally trapped Kelvin wave appears to propagate southeast along the Indonesian coastline. At the same time, the suppressed convection/easterly phase of the MJO arrives in the eastern Indian Ocean, with increased heat flux into the ocean due to reduced latent heat flux and increased insolation. The coastally trapped Kelvin waves do not appear to get onto the Western Australian coast. Rather, the increased heat flux and Ekman-induced downwelling onto the northwest (NW) coast in the suppressed/easterly phase of the MJO drive an increase in sea surface temperature on the NW Australian shelf. The piling up of warm water and associated sea level rise on the NW shelf is then communicated down the Western Australian coast as a coastally trapped wave, resulting in an increase in the Leeuwin current. Thus we conclude that the MJO signal in sea level along the west coast of Australia does not result from transmission of equatorial waves onto the Western Australian coast, but rather a southward-propagating coastal trapped wave that is directly forced on the NW shelf through Ekman-induced vertical advection and surface heat fluxes in the easterly phase of the MJO. Additionally, subtropical coastal sea level variability is reinforced locally via a teleconnection of the MJO to the local meridional wind off the southwest Australian coast. Considering the capability to predict the MJO to about 4 weeks lead time plus the 2 weeks taken for the MJO signal on the NW shelf to influence sea level at Fremantle, the use of MJO forecasts in management of the Western Australian marine environment should be considered for future application.     

Coastal trapped waves,with application to the northeast pacific ocean

The dispersion relation is derived for long coastal trapped waves of sub‐inertial frequency that propagate along a single‐step continental shelf in a two‐layer fluid. When the internal (Rossby) deformation radius is smaller than the shelf width, we show that the dispersion relation can be factored exactly, giving two possible modes: i. an internal Kelvin wave modified by topography;

ii. a continental shelf wave modified by the stratification.

A detailed discussion of the eigen‐functions associated with each of these modes is presented. Then the shelf wave dispersion relation is plotted for parameters applicable to the Oregon‐Washington coast. Theoretical values for the periods and wavelengths predicted from these plots are shown to agree favorably with observed values for this region.     

有关沿岸山地俘获波的研究

在采用线性化的浅水方程组并假设地形坡度沿山脉走向不变的情况下,本文对具有底面地形坡度的沿岸山地俘获波作了研究,结果表明,当底面地形缓变时,可用摄动法得到沿岸山地俘获波的结构,此时零级近似为经典Kelvin波解,一级近似体现了Rossby变形半径内的底面地形对经典Kelvin波解的修正;直至一级近似,沿岸山地俘获波仍是非频散的。在沿岸处当底面地形坡度平缓时,沿岸山地俘获波表现为Kelvin波结构,此时扰动位势高度最大值出现在沿岸;而当底面地形坡度陡峭时,其表现为修正Kelvin波结构,此时扰动位势高度最大值偏离沿岸,在沿岸则扰动位势高度相对为低值,而在沿岸外侧则有位势高度的高值。在沿岸底面地形高度越高,地形坡度越大,扰动位势高度廓线的变化就越剧烈。     

A study of current structures in a two-layer shelf model

A fully two-layered simple model of a continental shelf is studied in order to develop a simple coastal hydraulics theory for currents flowing onto the continental shelf. Previous studies of simpler systems have identified criticalities to Kelvin-type (class I) and shear/shelf-type (class II) waves. The present study confirms these results for small flows along the shelf, with hydraulic points associated with each of the criticalities being identified. For larger flows, a point of exchange of criticality is found to replace these control points and the corresponding flow is always supercritical to one type of wave.     

A note on the use of two-layer models of coastally trapped waves

Several aspects of coastally trapped wave behavior in two-layer models and in continuously stratified models are considered. A two-layer model and a uniformly stratified model are compared over a step shelf showing that, although they predict qualitatively different free-wave dispersion properties, some features of their long wave behavior are qualitatively similar. A sharp pycnocline model (a continuously stratified approximation to the two-layer model) is used to show that the presence of a vertical coastal wall (required in most two-layer models) produces substantial changes in the free-wave behavior. With a vertical coastal wall, baroclinic motions may be trapped close to the coast when the bottom there appears locally flat. Without a vertical coastal wall, such near-cost trapping apparently does not occur and the lowest mode of the sharp pycnocline model behaves more like the lowest mode of a uniformly stratified model.     

Shelf wave dispersion in a geophysical ocean

We consider subinertial, free waves trapped along three coastlines (i.e., shelf waves) in an ocean governed by a geophysical model in which stratification is explicitly obtained by taking the Vaisala frequency N much greater than the inertial frequency f. The behavior is generalized in terms of the parameter S = (N/f)a where a is the bottom slope of the trapping region. Only when $\text{S}\text{\$}\text{?}\text{0.2}$, are the predicted shelf waves like those predicted by Laplace's tidal equations (LTE) on an f-plane. When 0.2 ? S < 1, LTE are inappropriate because the shelf waves are only qualitatively like those predicted by LTE, and when S 1, the shelf waves are like baroclinic Kelvin waves in that they can occur at any subinertial frequency up to f (in qualitative disagreement with the predictions of LTE). Since N/f is usually a large number in the real ocean (of order 50–250), S is likely to be large unless the bottom slope is very gentle throughout the trapping region. Some applications to coastal current observations are discussed.     

Evolution of a Southeast Australian Coastally Trapped Disturbance

Summary  The southeast Australian coastally trapped disturbance (CTD) of 9–11 November 1982 that was previously studied by Holland and Leslie is re-visited. Additional observational data not considered by these authors and a numerical simulation using the Colorado State University Regional Atmospheric Modeling system (RAMS) are used for this purpose. Following initiation of the event on the south coast, mesoscale ridging propagated along the east coast to just north of Brisbane. Associated with the arrival of the event were a marked increase in surface pressure, drop in temperature and a shift and strengthening of the wind. While the simulation does not appear to capture the details of the boundary layer as well as one would like, it does represent the main features of the event, including the speed of propagation along the coast, reasonably well. Similar to the observed, the model event shows gravity current-like characteristics. The significance of topographic variability (e.g., large gap in the coastal mountains at the Hunter Valley) is considered. It is suggested that the topography and ambient stratification in southeastern Australia are less favourable for CTD occurrence than those in southern Africa and western North America where these systems have been extensively studied. Consequently, when CTD do occur in southeastern Australia, the less pronounced topography and weaker stratification may enable local effects to mask the CTD signal to some extent, thereby posing challenges in observation and forecasting. Received March 2, 1999     

Multiple criticalities in coastal flows

Using a simple model, it is shown that a coastal current (composed of water of given dynamical structure) can occur in one of several different forms. The classification of these possible forms for the current is closely associated with the categorization of the behaviour of the various waves able to propagate along the coast. Among the forms of the current found are those differing in the criticality (direction of propagation) of long shelf waves as noted by Collings and Grimshaw, and the criticality of long Kelvin-waves as noted by Gill and Schumann. Earlier studies have considered these criticalities in isolation. The present study attempts to set them in a more coherent framework.     

Analysis of internal solitary waves observed in Davis Strait

Abstract

Current meters and a thermistor chain deployed in the proximity of a drill‐ship over the continental shelf off Baffin Island revealed the presence of large amplitude internal waves. This paper reviews the properties of the internal waves, observed to propagate away from the coast and to coincide with the local low water phase of the tide at the drill‐ship. The observations are considered in terms of internal solitary wave models. A detailed comparison is presented of wave properties with a long‐wave model incorporating continuous stratification and shear.     

Coastally trapped stratus events in British Columbia

Abstract

Coastally trapped stratus events involve the alongshore propagation of a low‐level mesoscale ridge of high pressure, and generally occur only during summer in British Columbia. During these events, a body of cool dense air overlain by stratus cloud propagates northwards in the marine layer. This situation results because Coriolis effects trap the dense air against the coastal mountains and an inversion layer prevents vertical leakage of energy. Detailed analysis of a late summer event and comparison of the observations with available theory are presented. It is shown that the theoretical speeds for the event agree reasonably with observations except near major topographic variability. The theoretical trapping scale (internal Rossby radius) computed from the sounding data matches the observed width of the coastal stratus seen on satellite imagery. It is found that the properties of the event may be accounted for by the propagation in the marine layer of a coastally trapped intrusion with steep leading edge or shock. Attention is drawn to the role that the complex topography of Vancouver Island plays in influencing the propagation of the event, and some suggestions for forecasting these phenomena are made.     

Internal tides in the coastal zone of the Sea of Japan in autumn

The results are presented of hydrological studies in the coastal zone of the Sea of Japan in autumn in different years. It is revealed that the typical density stratification of water is formed there in autumn. The amplitudes are estimated of regular (with the periodicity of tidal harmonic M₂) vertical displacements of isotherms in the intermediate layer and maximum values of flow velocity in the surface and bottom layers. It is demonstrated that temperature perturbations are induced at the shelf edge and propagate to the coastal zone with the velocity that is close to the velocity of the first mode of internal gravity waves with the frequency of the tidal harmonic M₂.     

Dynamics of the Leeuwin Current: Part 2. Impacts of mixing,friction, and advection on a buoyancy-driven eastern boundary current over a shelf

The boundary currents over the Western Australian continental shelf and slope consist of the poleward flowing Leeuwin Current (LC) and the equatorward flowing Leeuwin Undercurrent (LUC). Key properties of the LC are its poleward strengthening, deepening to the south, and shelfbreak intensification. The alongshore flow reverses direction below about 300 m, forming the LUC at greater depths. To investigate the processes that cause these features, we obtain solutions to an idealized, regional ocean model of the South Indian Ocean. Solutions are forced by relaxing surface density to a prescribed, meridionally varying density profile ρ^*(y) with a timescale of δt. In addition, vertical diffusion is intensified near the ocean surface. This diffusion establishes the minimum thickness over which density is well-mixed. We define this thickness as the “upper layer”. Solutions are obtained with and without a continental shelf and slope off Western Australia and for a range of values of δt and mixing parameters. Within this upper layer, there is a meridional density gradient that balances a near-surface, eastward geostrophic flow. The eastward current downwells near the eastern boundary, leading to westward flow at depth. The upper layer's meridional structure and zonal currents crucially depend on coastal processes, including the presence of topography near the eastern boundary. Kelvin waves inhibit the upper layer from deepening at the coast. Rossby waves propagate the coastal density structure offshore, hence modifying the interior currents. A comparison of the solutions with or without a continental shelf and slope demonstrate that topographic trapping of Rossby waves is a necessary process for maintaining realistic eastern boundary current speeds. Significant poleward speeds occur only onshore of where the upper layer intersects the slope, that is, at a grounding line. Its poleward transport increases when surface-enhanced vertical mixing is applied over a greater depth. When the timescale δt is sufficiently short, the poleward current is nearly barotropic. The current's spatial structure over the shelf is controlled by horizontal mixing, having the structure of a Munk layer. Increasing vertical diffusion deepens the upper layer thickness and strengthens the alongshore current speed. Bottom drag leads to an offshore flow along the bottom, reducing the net onshore transport and weakening the current's poleward acceleration. When δt is long, poleward advection of buoyancy forms a density front near the shelf break, intensifying poleward speeds near the surface. With bottom drag, a bottom Ekman flow advects density offshore, shifting the jet core offshore of the shelf break. The resulting cross-shelf density gradient reverses the meridional current's direction at depth, leading to an equatorward undercurrent.     

Impacts of atmosphere–sea ice–ocean interaction on Southern Ocean deep convection in a climate system model

Deep convection in polar oceans plays a critical role in the variability of global climate. In this study, we investigate potential impacts of atmosphere–sea ice–ocean interaction on deep convection in the Southern Ocean (SO) of a climate system model (CSM) by changing sea ice–ocean stress. Sea ice–ocean stress plays a vital role in the horizontal momentum exchange between sea ice and the ocean, and can be parameterized as a function of the turning angle between sea ice and ocean velocity. Observations have shown that the turning angle is closely linked to the sea-ice intrinsic properties, including speed and roughness, and it varies spatially. However, a fixed turning angle, i.e., zero turning angle, is prescribed in most of the state-of-the-art CSMs. Thus, sensitivities of SO deep convection to zero and non-zero turning angles are discussed in this study. We show that the use of a non-zero turning angle weakens open–ocean deep convection and intensifies continental shelf slope convection. Our analyses reveal that a non-zero turning angle first induces offshore movement of sea ice transporting to the open SO, which leads to sea ice decrease in the SO coastal region and increase in the open SO. In the SO coastal region, the enhanced sea-ice divergence intensifies the formation of denser surface water descending along continental shelf by enhanced salt flux and reduced freshwater flux, combined with enhanced Ekman pumping and weakened stratification, contributing to the occurrence and intensification of continental shelf slope convection. On the other hand, the increased sea ice in the open SO weakens the westerlies, enhances sea-level pressure, and increases freshwater flux, whilst oceanic cyclonic circulation slows down, sea surface temperature and sea surface salinity decrease in the open SO response to the atmospheric changes. Thus, weakened cyclonic circulation, along with enhanced freshwater flux, reduced deep–ocean heat content, and increased stability of sea water, dampens the open–ocean deep convection in the SO, which in turn cools the sea surface temperature, increases sea-level pressure, and finally increases sea-ice concentration, providing a positive feedback. In the CSM, the use of a non-zero turning angle has the capability to reduce the SO warm bias. These results highlight the importance of an accurate representation of sea ice–ocean coupling processes in a CSM.     

有地形坡度的非线性Kelvin行波

提出了一个考虑地形坡度的非线性Kelvin行波解的模型，在假定了地形坡度沿山脉走向不变而仅在垂直于山脉走向的方向有改变的情况下，求得了该模型的解析解，这有助于加深对沿海山地捕获波的认识。文中还将该解与经典情形(即侧边界取为垂直刚壁而底面为水平)的解作了比较，发现前者的波速与扰动振幅均较后者要小，这与我国东南沿海武夷山区的沿海山地捕获波的情况相一致。     

A tidal model of the northeast pacific

Abstract

The development of a tidal model for the west coast of Canada is described. The model is intermediate in resolution between coarse‐gridded global models and fine‐gridded local models; it provides a good representation of the main shelf regions and also includes a substantial area of the neighbouring ocean. The physical processes relevant to tides in both deep and shallow water are included. Calculations have been carried out for the M₂ and K₁ constituents and the model results were compared with extensive tide‐gauge observations and empirically based charts. For M₂, the agreement between model results and observations is generally excellent, but for K₁, which contains more small‐scale variability, the model results are not quite so good. The variability in K₁ is associated with tidally generated continental shelf waves. Examination of the computed currents and energy fluxes suggests that shelf‐wave components are present in the model solution but, for the Vancouver Island shelf, their propagation is not reproduced accurately. This may be due to deficiencies in the model and/or to the influences of stratification and mean currents, which are neglected here. The model predicts that shelf‐wave components should also occur in diurnal tides on the Alaskan shelf.

The significance of the tide‐generating potential and advection are also examined and further work proposed.     

On inertial currents over a sloping continental shelf

Using simple mathematical models, it is shown that an equatorward flowing coastally confined eastern boundary current (or poleward flowing western boundary current) may have two conjugate forms which transport the same flux of each water type. In a slowly varying environment, these two conjugate forms coalesce at some critical latitude which depends on the flow. For lower latitudes there is no defined form. As the coalescence latitude is approached from higher latitudes, one of the two conjugate forms narrows, while the other widens. Furthermore, in the neighborhood of the critical latitude the wider form is subcritical and the narrower form is supercritical to possible long small amplitude shelf waves. It is also shown that a poleward flowing coastally confined eastern boundary current (or an equatorward flowing western boundary current) may be traced poleward to some critical latitude beyond which the possibility of a current in juxtaposition with the coast terminates. For latitudes higher than this terminating latitude the current separates from the coast.     

Internal tide generation at a continental shelf/slope junction: A comparison between theory and a laboratory experiment

Observations of internal tide generation over continental slopes in a laboratory experiment have been carried out, with the objectives of making comparisons with linear generation theory and investigating its limitations. Both continuous and layered stratification have been considered. A measure of the amplitude of the barotropic tidal forcing (and hence of non-linearity) is given by the Froude Number F = u_sb/c_w, where u_sb is the maximum barotropic tidal velocity at the shelf break, and c_w is the long-wave speed of the lowest internal mode.For continuous stratification, good agreement was obtained for “steep” slopes (α/c > 1), where α is the slope at the continental slope and c is the slope of the internal wave rays of tidal frequency), even for quite large amplitude motions (F < 1.6), and the upper limit of its quantitative usefulness was not reached. For “flat” slopes (α/c < 1) reasonable agreement was also obtained, even up to quite amplitudes (F < 3.1), although some departure from linear theory was apparent.For two-layer flows the applicability of linear theory was much more restricted. For F 0.5 there was only qualitative agreement and for larger F (>1) significant differences were observed. The latter were due to the substantial advection and associated hydraulic jumps which occured seaward of the shelf-break during the ebb-phase of the barotropic tide. Shelf-break values of F > 1 are common in the ocean.     

理想海域中台风引起的潮、流及波的分析 Ⅱ.海岸及陆架的影响

采用理想的大陆架地形和台风模型计算了不同方向登陆的台风所激发的海洋响应。结果表明,岸边的潮位变化主要是由于台风引起的强迫振动造成的。而对于登陆型台风来说,在远离台风路径的地方,潮位的变化则是由于边缘波效应。对地平直海岸和二维大陆架,自由边缘波的振幅远小于强迫波的振幅。平行海岸移行台风在岸边产生随台风一起移动的强制波,其中当台风沿着与Kelvin波相同的方向移行时,岸边有陆架波产生,反之则没有陆架波。此外,还讨论了与风暴潮相关的近岸环流。