A multi-scale asymptotic theory is derived for the evolution and interaction of currents and surface gravity waves in water of finite depth, under conditions typical of coastal shelf waters outside the surf zone. The theory provides a practical and useful model with which wave–current coupling may be explored without the necessity of resolving features of the flow on space and time scales of the primary gravity-wave oscillations. The essential nature of the dynamical interaction is currents modulating the slowly evolving phase of the wave field and waves providing both phase-averaged forcing of long infra-gravity waves and wave-averaged vortex and Bernoulli-head forces and hydrostatic static set-up for the low-frequency current and sea-level evolution equations. Analogous relations are derived for wave-averaged material tracers and density stratification that include advection by horizontal Stokes drift and by a vertical Stokes pseudo-velocity that is the incompressible companion to the horizontal Stokes velocity. Illustrative solutions are analysed for the special case of depth-independent currents and tracers associated with an incident surface wave field and a vortex with O(1) Rossby number above continental shelf topography.

The effects of wind-generated surface gravity waves on more slowly evolving long waves, currents and material distributions in stratified coastal waters are investigated using the wave-averaged, asymptotic equations developed in McWilliams et al. (2004), based on small wave slope and on scale separations in both time and horizontal space. Excluding non-conservative effects such as wave breaking, the lowest order radiation stress, introduced by Longuet-Higgins & Stewart (1960) and Hasselmann (1971), can be completely characterized in terms of wave set-up, forcing of long (infra-gravity) waves and an Eulerian current whose divergence cancels that of the primary waves' Stokes drift. The vortex force of Craik & Leibovich (1976) and its generalization for inhomogeneous waves and Earth's rotation are shown to be the dominant wave-averaged effects on currents, and these effects can occur at higher order than the apparent leading order for the radiation stress. The leading-order, wave-averaged dynamical effects are completed with material advection by Stokes drift, modified pressure-continuity and kinematic surface boundary conditions, and parameterized representations of wave generation by the wind and breaking near the shoreline.

[1] There is not yet widespread agreement as to the underlying cause of the 80-100 ppmv roughly 100-kyr-duration glacial-interglacial cycles in atmospheric pCO 2 . Most of the mechanisms which have been proposed to account for the observed pCO 2 variations appear to in some way violate interpretations of paleo proxy data. The inability of a single mechanism to explain the observed cycles in atmospheric CO 2 (which show amazing similarity over the past 430,000 years) is perplexing, and leads us to consider whether a combination of mechanisms might be consistent with available evidence. Consistent with previous work, we find that physical changes (ocean circulation, temperature, mixing) can only explain part of the observed atmospheric pCO 2 variability; changes in ocean chemistry are invoked to explain the remainder. In order to account for the initial pCO 2 drawdown (from ''interglacial'' to ''intermediate'' levels), we invoke physical changes in the ocean (mixing, temperature). The transition from intermediate atmospheric pCO 2 levels to full glacial conditions involves a small increase in mean ocean nutrient levels and mean ocean alkalinity, accomplished by falling sea level and subsequent erosion of organic-rich shelf sediments. The first part of the transition out of full glacial conditions is achieved through increased temperature and increased mixing in the Southern Ocean. The final part of the atmospheric pCO 2 rise up to full interglacial conditions is accomplished through rising sea level and the subsequent change in mean ocean alkalinity and phosphate, and a rise in the Northern Hemisphere temperature and ocean mixing. The proposed sequence of events is consistent with most existing proxy evidence for paleo-nutrient levels and changes in export production over the last glacial-interglacial cycle. Furthermore, it is consistent with evidence for a whole-ocean shift in d 13C toward significantly more negative values in the late glacial. The proposed scenario is also consistent with ice core-based timing constraints, as summarized by Broecker and Henderson (1998). We show that we are able to explain the full magnitude of the glacial-interglacial cycle in atmospheric pCO 2 without the need to invoke iron-fertilization in the Southern Ocean.

We describe an example of a structurally stable heteroclinic network for which nearby orbits exhibit irregular but sustained switching between the various sub-cycles in the network. The mechanism for switching is the presence of spiralling due to complex eigenvalues in the flow linearised about one of the equilibria common to all cycles in the network. We construct and use return maps to investigate the asymptotic stability of the network, and show that switching is ubiquitous near the network. Some of the unstable manifolds involved in the network are two-dimensional; we develop a technique to account for all trajectories on those manifolds. A simple numerical example illustrates the rich dynamics that can result from the interplay between the various cycles in the network.

Greater Cook Strait (GCS) lies between the North and the South Islands of New Zealand. Its location at the convergence of the Pacific and IndoAustralian tectonic plates leads to interesting bathymetry with an adjacent shallow shelf and deep ocean trench as well as numerous crossing faults and complex shoreline geometry. Our purpose in this study is to examine tides and currents in GCS and, in particular, identify the major forcing mechanisms for the residual currents. Toward this end, we use an unstructured-grid numerical model to reproduce the tides and currents, verify these results with observations and then use the model to separate the various forcing mechanisms.

Tsunami risk reduction activities rely on a sound knowledge of the hazard characteristics. Our understanding of these characteristics is derived from empirical measurements, numerical models or established rules. Conventional methods used to delineate areas vulnerable to tsunami inundation are often calculated from estimated maximum wave height at the coast and ''rules-of-thumb''. Applying such rules may give unreliable results for decision-makers. Using basic hydraulic principles and assumptions, this paper improves on the existing rules by developing and testing new equations for predicting tsunami maximum depth profiles and inundation distances. The proposed equations require knowledge of shoreline wave-crest level, the onshore ground profile and an index for onshore roughness (a ratio of distance between protrusions to a local friction factor). As a tsunami wave moves inland, the equations demonstrate that there will usually be an exponential decline in peak water depth. The equations also confirm that a smaller spacing between onshore roughness elements, such as trees or houses, will give a steeper decline in peak depth due to increased friction as a wave moves inland. Furthermore, where ground level is rising faster than friction head is being lost, it is predicted that the water level of a tsunami will rise above the shoreline wave-crest level. The ground slope at which run-up starts to exceed shoreline wave-crest level can be predicted from the shoreline wave-crest level and roughness spacing. Results predicted by the new equations are verified by comparison with tsunami run-up measurements made in Samoa and Java.

We use the vortex force formalism to analyze the effect of rip currents on their own wave forcing. The vortex force formalism allows us to decompose the wave forcing into the nonconservative flux of momentum due to wave breaking and the conservative vortex force. Following Yu and Slinn (2003), we consider rip currents initially generated by alongshore variation of wave breaking due to a perturbation of a barred bottom topography. This variation is reduced in magnitude by two current effects on waves: wave ray bending and the flux of wave energy by currents. We compute the change in wave energy caused by these two effects on their own and use this to show that their relative magnitude scales with the square of the ratio of the length to width of the rip current. Both effects increase the wave height over the channels of the longshore bar, which leads to more wave breaking and counterbalances its longshore variation due to bottom refraction. In comparison to wave breaking, the change in the vortex force is negligible. Next, we show how the reduction in wave breaking is similar to an enhanced bottom friction. We then analyze the dependence of this relationship on the breaking parameterization, angle of incidence of the waves, and bottom drag law.

Abstract. An examination of the coastal geomorphology of bays along the Otago coastline, SE New Zealand, has identified a geomorphology consistent with tsunami inundation. A tsunami geomorphology consisting of a number of elements including dune pedestals, hummocky topography, parabolic dune systems, and post-tsunami features resulting from changes to the nearshore sediment budget is discussed. The most prominent features at Blueskin Bay are eroded pedestals although it is speculated that hummocky topography may be present in the bay. Tsunami geomorphology at Long Beach is more comprehensive with a marked association between pedestals and a hummocky topography. A full suite of potential geomorphological features however, is not present at either site. The type of features formed by a tsunami, and the ability to detect and interpret a tsunami geomorphology, hinges on the interaction between five key variables; sand availability, embayment type, nature of the coast, accumulation space, and landward environmental conditions. An appreciation of the geomorphic setting and history of a coast is therefore of fundamental importance when identifying what to look for and where to look for tsunami evidence. It is also important to realise that these features can also be formed by other processes.