Theo Gerkema

Near-inertial waves in the ocean : beyond the 'traditional approximation'

The dynamics of linear internal waves in the ocean is analysed without adopting the ‘traditional approximation’, i.e. the horizontal component of the Earths rotation is taken into account. It is shown that non-traditional effects profoundly change the dynamics of near-inertial waves in a vertically confined ocean. The partial differential equation describing linear internal-wave propagation can no longer be solved by separation of spatial variables; it was however pointed out earlier in the literature that a reduction to a Sturm–Liouville problem is still possible, a line that is pursued here. In its formal structure the Sturm–Liouville problem is the same as under the traditional approximation, but its eigenfunctions are no longer normal vertical modes of the full problem. The question is addressed of whether the solution found through this reduction is the general one: a set of eigenfunctions to the full problem is constructed, which depend in a non-separable way on the two spatial variables; these functions are orthogonal and form, under mild assumptions, a complete basis. In the near-inertial range, non-traditional effects act as a singular perturbation; this is seen from the sub-inertial short-wave limit, which is present whenever the ‘non-traditional’ terms are there, but disappears under the traditional approximation. In the dispersion relation the sub-inertial modes represent a smooth continuation of the super-inertial ones. The combined effect of the horizontal component of rotation and a vertical inhomogeneity in the stratification is found to play a crucial role in the dynamics of sub-inertial waves. They are trapped in waveguides localized around minima of the buoyancy frequency. The presence of horizontal inhomogeneities in the effective Coriolis parameter (such as shear currents or beta effect) are shown to enable a transition from super-inertial to sub-inertial waves (and thus effectively an irreversible transformation of large-scale into small-scale motions). It is suggested that this transformation provides a mechanism for mixing in the deep ocean. The notion of critical reflection of internal waves at a sloping bottom is also modified by non-traditional effects, and they strongly increase the probability of critical reflection in the near-inertial to tidal range.

A linear stability analysis of tidally generated sand waves

A linear stability analysis is carried out to examine the initial stage of sand-wave growth under tidal flows and the occurrence of a preferred length scale. The fact that these bedforms typically have length scales small compared to the tidal excursion is exploited by adopting an asymptotic approach to solve the hydrodynamic part of the problem, i.e. to find the hydrodynamic response to an initially small bed perturbation. This method is shown to have important advantages over previously used methods, since it allows an exploration of the complete sand-wave regime (whereas other methods fail for short sand waves), and in general it is also more accurate. It is found that the selection of a preferred length scale depends mainly on only two parameters (the bed-slope coefficient, and the ratio of friction velocity to eddy viscosity), whereas there appears to be almost no dependence on the water depth.

Quantifying the residual volume transport through a multiple‐inlet system in response to wind forcing: The case of the western Dutch Wadden Sea

In multiple-inlet coastal systems like the western Dutch Wadden Sea, the tides (and their interaction with the bathymetry), the fresh water discharge, and the wind drive a residual flow through the system. In the current paper, we study the effect of the wind on the residual volume transport through the inlets and the system as a whole on both the short (one tidal period) and long (seasonal or yearly) time scales. The results are based on realistic three-dimensional baroclinic numerical simulations for the years 2009-2011. The length of the simulations (over 2000 tidal periods) allowed us to analyze a large variety of conditions and quantify the effect of wind on the residual volume transport. We found that each inlet has an anisotropic response to wind; i.e. the residual volume transport is much more sensitive to the wind from two inherent preferential directions than from any other directions. We quantify the effects of wind on the residual volume transport through the system and introduce the concept of the systems conductance for such wind driven residual transport. For the western Dutch Wadden Sea, the dominant wind direction in the region is close to the direction with the highest conductance and opposes the tidally driven residual volume transport. This translates a large variability of the residual volume transport and a dominance of the wind in its long-term characteristics in spite of the episodic nature of storms. This article is protected by copyright. All rights reserved.

The EUFAR transnational access project A.NEW (Airborne observations of Nonlinear Evolution of internal Waves generated by internal tidal beams)

Internal Solitary Waves (ISWs) are ubiquitous features in the coastal oceans. The propagation and breaking of ISWs contribute significantly to turbulent mixing in the near-surface layers, through the continual triggering of instabilities as they propagate into shallow water over the continental shelf. We report on the first results of an EU funded project denominated A.NEW (Airborne observations of Nonlinear Evolution of internal Waves generated by internal tidal beams). Here we show, for the first time, coincident multi-sensor airborne observations off the Portuguese coast, which reveal the 3D structure of air bubble entrainment in the internal wave field. Coincident thermal infrared imaging shows the surface thermal signatures of ISWs and reveals the turbulent character of some internal waves on the shelf.

Observations of suspended matter along the Dutch coast

Large amounts of suspended matter are transported through the Dutch coastal zone in the southern North Sea. Current estimates, based on budget studies, are in the order of 15 - 20 Mton per year transported in northward direction, which should take place in a small strip of 5 - 10 km wide. For this study we have performed a series of measurements on total suspended matter in an area in the most northerly extent of the Rhine region of fresh water influence. The measurements focused on observations both in the vertical and in the horizontal on the behavior of suspended matter in the nearshore zone up to 7 km from the shoreline. A peak in bottom concentrations is observed close to the coast along the coastal stretch. This hot spot location is found in the cross-shore direction at about 1.5 km from the coastline at a water depth of 15 m. Here, total suspended matter concentrations near the bottom exceed 200 mg/l. These peak concentrations have not been identified before and add to the suggestion that a large part of the northward suspended matter transport occurs very close to the coast.

Multidecadal variability in seasonal mean sea level along the NorthSea coast

Seasonal deviations from annual-mean sea level in the North Sea region show a large low-frequency component with substantial variability at decadal and multi-decadal timescales. In this study, we quantify low-frequency variability in seasonal deviations from annual-mean sea level and look for drivers of this variability. The amplitude, as well as the temporal evolution of this multi-decadal variability shows substantial variations over the North Sea region, and this spatial pattern is similar to the well-known pattern of the influence of winds and pressure changes on sea level at higher frequencies. The largest low-frequency signals are found in the German Bight and along the Norwegian coast. We find that the variability is much stronger in winter and autumn than in other seasons and that this winter and autumn variability is predominantly driven by wind and sea-level pressure anomalies which are related to large-scale atmospheric patterns. For the spring and summer seasons, this atmospheric forcing explains a smaller fraction of the observed variability. Large-scale atmospheric patterns have been derived from a principal component analysis of sea-level pressure. The first principal component of sea-level pressure over the North Atlantic Ocean, which is linked to the North Atlantic Oscillation (NAO), explains the largest fraction of winter-mean variability for most stations, while for some stations, the variability consists of a combination of multiple principal components. The low-frequency variability in season-mean sea level can manifest itself as trends in short records of seasonal sea level. For multiple stations around the North Sea, runningmean 40-year trends for autumn and winter sea level often exceed the long-term trends in annual mean sea level, while for spring and summer, the seasonal trends have a similar order of magnitude as the annual-mean trends. Removing the variability explained by atmospheric variability vastly reduces the seasonal trends, especially in winter and autumn.

North Sea coastal ecology: Preface

Worldwide, the marine environment and especially coastal zones show strong spatial and temporal variability in physical conditions and ecology, and are at the same time affected by a variety of anthropogenic influences. These waters include the European North Sea, a semi-enclosed shelf sea surrounded by the United Kingdom, Belgium, the Netherlands, Germany, Denmark and Norway. Long-term (millennia) inhabitation of these coastal areas has resulted in a strong anthropogenic footprint such as polluted waters, deteriorated marine habitats and depleted fish stocks. Ongoing and future impacts include the combined effects of climate change (e.g., warming, acidification, deoxygenation), and modern contaminants (e.g. microplastics). The consequences of human impacts on the North Sea proper is determined, amongst others, by the interactions between the central basin and the surrounding intertidal basins, estuaries and tributaries at one hand and the Atlantic Ocean at the other. Over the years, symposia have been held and numerous papers were published focusing on various aspects of the North Sea dynamics. This volume of the Journal of Sea Research does not intend to summarize the present state of knowledge concerning North Sea ecology, but should be considered as a broad (though not exhaustive) overview of ongoing research especially in the coastal zone and with an emphasis on spatial and temporal variabilities, with the aim to sketch some lines of future research based on in total 19 contributions.