Oceanic density/pressure gradients and slope currents

Eastern boundary currents are some of the most energetic features of the global ocean, contributing significantly to meridional mass, heat and salt transports. We take a new look at the form of an oceanic slope current in equilibrium with oceanic density gradients. We depth-integrate the linearised x and y momentum and continuity equations, assume an equilibrium force balance in the along-slope direction (no along-slope variation in the along-slope flow) and zero cross-slope flow at a coastal boundary. We relate the bottom stress to a bottom velocity via a simple boundary friction law (the precise details are easily modified), and then derive an expression for the slope current velocity by integrating upwards including thermal wind shear. This provides an expression for the slope current as a function of depth and of cross-slope coordinate, dependent on the oceanic density field and surface and bottom stresses. This new expression for the slope current allows for more general forms of oceanic density fields than have been treated previously. Wind stress is also now considered. The emphasis here is on understanding the simplified equilibrium force balance rather than the evolution towards that balance. There is a direct relationship between the slope current strength, friction and along-slope forcing (e.g. wind); also between the total along-slope forcing and bottom Ekman transport, illustrating that “slippery” bottom boundaries in literature are a direct consequence of unrealistically assuming zero along-slope pressure gradient. We demonstrate the utility of the new expression by comparison with a high resolution hydrodynamic numerical model

Leaky slope waves and sea level: unusual consequences of the beta-effect along western boundaries with bottom topography and dissipation

Coastal Trapped Waves (CTWs) carry the ocean’s response to changes in forcing along boundaries, and are important mechanisms in the context of coastal sea level and the meridional overturning circulation. Motivated by the western boundary response to high latitude and open ocean variability, we investigate how the latitude dependence of the Coriolis parameter (β-effect), bottom topography, and bottom friction, modify the evolution of western boundary CTWs and sea level using a linear, barotropic model. For annual and longer period waves, the boundary response is characterized by modified Shelf Waves and a new class of leaky Slope Waves that propagate alongshore, typically at an order slower than Shelf Waves, and radiate short Rossby waves into the interior. Energy is not only transmitted equatorward along the slope, but also eastward into the interior, leading to the dissipation of energy locally and offshore. The β-effect and friction result in Shelf and Slope Waves that decay alongshore in the direction of the equator, decreasing the extent to which high latitude variability affects lower latitudes, and increasing the penetration of open ocean variability onto the shelf - narrower continental shelves and larger friction coefficients increase this penetration. The theory is compared against observations of sea level along the North American east coast and qualitatively reproduces the southward displacement and amplitude attenuation of coastal sea level relative to the open ocean. The implications are that the β-effect, topography, and friction are important in determining where along the coast sea level variability hot spots occur

Idealised modelling of offshore-forced sea level hot spots and boundary waves along the North American East Coast

Hot spots of sea level variability along the North American East Coast have been shown to shift in latitude repeatedly over the past 95 years and connections with a number of forcing phenomena, including the North Atlantic Oscillation (NAO) and Atlantic Meridional Overturning Circulation (AMOC), have been suggested. Using a barotropic 1/12° NEMO model of the North American East Coast (to represent the upper ocean and a homogeneous shelf), we investigate the coastal sea level response to remote sea surface height (SSH) variability along the upper continental slope. Hilbert transform Complex EOF analysis is used to investigate the responses to interannual changes in the strength of the mean winds and an idealised NAO. Variability in the mean winds produces in-phase coastal sea level variability along the entire coastline and is driven by a SSH anomaly in the subpolar gyre. Variability due to the NAO forcing is in phase along the coast south of Cape Hatteras. Interannual coastal sea level variability at a given latitude is found to be driven by off-shore SSH anomalies originating many degrees of latitude (100s km) further north, and linear barotropic trapped wave theory is used to explain the mechanism. A comparison of the results from an analytical model with those from the numerical model is used to suggest that the boundary wave mechanism is also relevant for understanding the coastal response to interior sea level change over longer time periods. Nonlinear effects are found not to significantly modify the character of the linear solution

Preface: Developments in the science and history of tides

This special issue marks the 100th anniversary of the founding of the Liverpool Tidal Institute (LTI), one of a number of important scientific developments in 1919. The preface gives a brief history of how the LTI came about and the roles of its first two directors, Joseph Proudman and Arthur Doodson. It also gives a short overview of the research on tides at the LTI through the years. Summaries are given of the 26 papers in the special issue. It will be seen that the topics of many of them could be thought of as providing a continuation of the research first undertaken at the LTI. Altogether, they provide an interesting snapshot of work on tides now being made by groups around the world

Sea Level and the role of coastal trapped waves in mediating the influence of the open ocean on the coast

The fact that ocean currents must flow parallel to the coast leads to the dynamics of coastal sea level being quite different from the dynamics in the open ocean. The coastal influence of open-ocean dynamics (dynamics associated with forcing which occurs in deep water, beyond the continental slope) therefore involves a hand-over between the predominantly geostrophic dynamics of the interior ocean and the ageostrophic dynamics which must occur at the coast. An understanding of how this hand-over occurs can be obtained by considering the combined role of coastal trapped waves and bottom friction. We here review understanding of coastal trapped waves, which propagate cyclonically around ocean basins along the continental shelf and slope, at speeds which are fast compared to those of baroclinic planetary waves and currents in the open ocean (excluding the large-scale barotropic mode). We show that this results in coastal sea-level signals on western boundaries which, compared to the nearby open-ocean signals, are spatially smoothed, reduced in amplitude, and displaced along the coast in the direction of propagation of coastal trapped waves. The open-ocean influence on eastern boundaries is limited to signals propagating polewards from the equatorial waveguide (although a large-scale diffusive influence may also play a role). This body of work is based on linearised equations, but we also discuss the nonlinear case. We suggest that a proper consideration of nonlinear terms may be very important on western boundaries, as the competition between advection by western boundary currents and a counter-propagating influence of coastal trapped waves has the potential to lead to sharp gradients in coastal sea level where the two effects come into balance

Forcing factors affecting sea level changes at the coast

We review the characteristics of sea level variability at the coast focussing on how it differs from the variability in the nearby deep ocean. Sea level variability occurs on all timescales, with processes at higher frequencies tending to have a larger magnitude at the coast due to resonance and other dynamics. In the case of some processes, such as the tides, the presence of the coast and the shallow waters of the shelves results in the processes being considerably more complex than offshore. However, ‘coastal variability’ should not always be considered as ‘short spatial scale variability’ but can be the result of signals transmitted along the coast from 1000s km away. Fortunately, thanks to tide gauges being necessarily located at the coast, many aspects of coastal sea level variability can be claimed to be better understood than those in the deep ocean. Nevertheless, certain aspects of coastal variability remain under-researched, including how changes in some processes (e.g., wave setup, river runoff) may have contributed to the historical mean sea level records obtained from tide gauges which are now used routinely in large-scale climate research

The Northeast Atlantic margins

This subsection treats sectors of the North Atlantic ocean margin from Cape Ortegal in NW Spain around Biscay and the British Isles to the Norwegian shelf as far as 70N (Fig. 5.2.1). The Faroes, Iceland and East Greenland shelves are also included. The North Sea is excluded, being treated elsewhere as a marginal sea (Chapter 7.3). Another subsection treats the sub-polar Northwestern Atlantic which continues to Labrador and the American margin as far as Cape Hatteras (Chapter 5.3)

Numerical simulations of dense water cascading on a steep slope

The sinking of dense shelf waters down the continental slope (or "cascading") contributes to oceanic water mass formation and carbon cycling. Cascading over steep bottom topography is studied here in numerical experiments using POLCOMS, a 3-D ocean circulation model using a terrain-following s-coordinate system. The model setup is based on a laboratory experiment of a continuous dense water flow from a central source on a conical slope in a rotating tank. The governing parameters of the experiments are the density difference between plume and ambient water, the flow rate, the speed of rotation and (in the model) diffusivity and viscosity. The descent of the dense flow as characterized by the length of the plume as a function of time is studied for a range of parameters. Very good agreement between the model and the laboratory results is shown in dimensional and nondimensional variables. It is confirmed that a hydrostatic model is capable of reproducing the essential physics of cascading on a very steep slope if the model correctly resolves velocity veering in the bottom boundary layer. Experiments changing the height of the bottom Ekman layer (by changing viscosity) and modifying the plume from a 2-layer system to a stratified regime (by enhancing diapycnal diffusion) confirm previous theories, demonstrate their limitations and offer new insights into the dynamics of cascading outside of the controlled laboratory condition

On natural oscillations of connected ocean basins

Natural barotropic modes are found for systems of two or three circular basins (each of uniform depth and Coriolis parameter) linked by narrow straits. They are related to the individual basin modes for various basin and strait dimensions and Coriolis parameter values. For two basins joined by a short strait, the mode frequencies intersperse one for one the combined sequence of individual basin mode frequencies. There is no comparable result for three basins. Possible effects of the North Atlantic's open boundaries on its natural oscillations and diurnal tides are considered, and also the lowest modes of Green Bay and Lake Michigan

Oceanographic currents and the convexity of the uppermost continental slope

Immediately below the shelf edge where sea-level lay during the Last Glacial Maximum (LGM), the uppermost continental slope in many areas has a smooth, convex-upwards rounded shape in profile. This shape is an example of a clinoform "rollover", a sedimentary feature that arises in general terms from how declining "energy" with water depth allows sediments to steepen. Computer models using the diffusion transport equation with mobility K declining with depth can produce rollover shapes, but the models have yet to be properly justified and the controls on K have been unclear. In this contribution, aspects of morphologic data sets from the USA and Iberian Atlantic margins are shown to be indeed compatible with the diffusion model. From experiments and theory, the gravity effect on saltating particles leads to a downslope flux that is proportional to local bed gradient, as required by the diffusion model, if the bed is agitated by oscillating currents of small residual current, by contour-parallel currents, or by a combination of both. The predicted mobility K is then an increasing function of the current's average speed. Near-bottom current-meter data reveal how currents, enhanced around the shelf edge, decline with water depth in a way that is generally compatible with the rollover morphology. During the LGM, bed currents due to tides and surface waves were stronger than at present. Although difficult to predict, they are expected to produce a more sharply declining mobility with depth that would be compatible with the limited depth range below the shelf edge over which sand and gravel have deposited