We consider the classical problem of a single-layer homogeneous fluid at rest and a low, slowly varying, long and positive bottom obstacle, which is abruptly started from rest to move with a constant speed V. As a result a system of transient waves will develop, and we assume that locally in the region over the obstacle dispersion can be ignored while nonlinearity cannot. The relevant governing equations for the nearfield solution are therefore the nonlinear shallow water (NSW) equations. These are bidirectional and can be formulated in terms of a two-family system of characteristics. We analytically integrate and eliminate the backward-going family and achieve a versatile unidirectional single-family formulation, which covers subcritical, transcritical and supercritical conditions with relatively high accuracy. The formulation accounts for the temporal and spatial evolution of the bound waves in the vicinity of the obstacle as well as the development of the transient free waves generated at the onset of the motion. At some distance from the obstacle, dispersion starts to play a role and undular bores develop, but up to this point the new formulation agrees very well with numerical simulations based on a high-order Boussinesq formulation. Finally, we derive analytical asymptotic solutions to the new equations, providing estimates of the asymptotic surface levels in the vicinity of the obstacle as well as the crest levels of the leading non-dispersive free waves. These estimates can be used to predict the height and speed of the leading waves in the undular bores. The numerical and analytical solutions to the new single-family formulation of the NSW equations are compared to results based on the forced Korteweg-de Vries/Hopf equation and to numerical Boussinesq simulations.

<p>Extreme water levels in the micro-tidal transition zone between the North Sea and the semi-enclosed Baltic sea are predominantly determined by wind forcing associated with synoptic-scale weather systems. This connection between the two seas is partly blocked by low-lying islands, and the bathymetry comprises a complex mixture of narrow, deep channels and shallow sills. Coastlines in the Southern Kattegat and the Western Baltic Sea are therefore exposed to wind forcing from a large range of directions, and the extent of water build-up varies strongly between locations.</p><p>In the present study, we aim to determine the most critical wind direction for most of the Danish coastlines by employing numerical modelling experiments. The simulations are conducted with two different regional 3D ocean models to enable model inter-comparison. The DMI-HBM model implements a structured grid with fully dynamic 2-way nesting, while the MIKE 3 FM invokes an unstructured mesh. Both models have grid resolutions of ~0.5–1 km within the Danish Straits and 4–6 km in the offshore Baltic Sea. The models are forced by synthetic wind fields, where both wind speed and wind direction are maintained at fixed levels over the entire model domains. Pairs of model simulations are then obtained by varying the angle from which the wind is blowing.</p><p>From the model outputs, we describe the temporal evolution of the water level by the site-specific peak water level, and the time required for the response to reach its peak value. Our results show a steady rise of the water level up until the peak value. The peak water level significantly overshoots the final equilibrium water level, which develops further into the simulations. Our study facilitates a better understanding of the sea level's response to extreme and persistent winds in a region with highly complex geometry.</p>

As part of the investigations for a major expansion of the Port of Hanstholm a series of hydraulic studies were carried out involving: field measurements of waves and currents, establishment of design conditions for waves and currents, analysis of the wave disturbance, laboratory tests of breakwater stability, analysis of the future conditions for sediment bypass and sedimentation and possible impact on the surrounding coastlines. In this paper the extensive sediment studies made by application of numerical modelling is described.

<p>The potential impacts of extreme sea level events are becoming more apparent to the public and policy makers alike. As the magnitude of these events are expected to increase due to climate change, and increased coastal urbanization results in ever increasing stakes in the coastal zones, the need for risk assessments is growing too.</p><p>The physical conditions that generate extreme sea levels are highly dependent on site specific conditions, such as bathymetry, tidal regime, wind fetch and the shape of the coastline. For a low-lying country like Denmark, which consists of a peninsula and islands that partition off the semi-enclosed Baltic Sea from the North Sea, a better understanding of how the local sea level responds to wind forcing is urgently called for.</p><p>We here present a map for Denmark that shows the most efficient wind directions for generating extreme sea levels, for a total of 70 locations distributed all over the country’s coastlines. The maps are produced by conducting simulations with a high resolution, 3D-ocean model, which is used for operational storm surge modelling at the Danish Meteorological Institute. We force the model with idealized wind fields that maintain a fixed wind speed and wind direction over the entire model domain. Simulations are conducted for one wind speed and one wind direction at a time, generating ensembles of a set of wind directions for a fixed wind speed, as well as a set of wind speeds for a fixed wind direction, respectively.</p><p>For each wind direction, we find that the maximum water level at a given location increases linearly with the wind speed, and the slope values show clear spatial patterns, for example distinguishing the Danish southern North Sea coast from the central or northern North Sea Coast. The slope values are highest along the southwestern North Sea coast, where the passage of North Atlantic low pressure systems over the shallow North Sea, as well as the large tidal range, result in a much larger range of variability than in the more sheltered Inner Danish Waters. However, in our simulations the large fetch of the Baltic Sea, in combination with the funneling effect of the Danish Straits, result in almost as high water levels as along the North Sea coast.</p><p>Although the wind forcing is completely synthetic with no spatial and temporal structure of a real storm, this idealized approach allows us to systematically investigate the sea level response at the boundaries of what is physically plausible. We evaluate the results from these simulations by comparison to peak water levels from a 58 year long, high resolution ocean hindcast, with promising agreement.</p>