Harbour oscillations generated by shear flow

A new mechanism that could be responsible for excitation of long-period oscillations in partially enclosed harbours is discussed. This mechanism is based on the interaction between a shear flow and the harbour-basin natural mode and does not suppose any external exciting forces caused by wind waves, tsunami, etc. The growth rate of harbour oscillations is found in terms of a plane-wave reflection coefficient integrated on the wavenumber spectrum of the oscillating outflow field near the harbour entrance. Analytical considerations for simple shear flows (vortex sheet and jet) show that the growth rate changes its sign depending on the ratio of oscillation frequency to flow speed.

ESTIMATES OF LONG WAVES IN THE WESER ESTUARY

Long waves of small amplitudes can excite harbour oscillations as well as the motion of floating structures or vessels. Field data from the Weser Estuary, German Bight of the North Sea were analysed with respect to waves with periods greater than 8 s. After preprocessing of the mostly noisy data records, special analysis incorporated the reconstruction of incorrectly recorded frequency components below .03 Hz and bivariate distributions of heights and periods. Results suggest that long wave activity increases towards the inner estuary. Grouping properties are dependent on wind direction and on directionality of the sea state. Further investigations and model studies for the response of travelling vessels to this wave climate are recommended.

Resonator studies for Kincardine Harbour, Lake Huron

A 1:600 scale acoustic model of Kincardine Harbour originally built by the National Research Council of Canada (NRCC) was delivered to the Applied Dynamics Laboratory at McMaster University late in 1976. After preliminary testing, a second acoustic model was built to a scale of 1:200 in order to narrow the range of acoustic wave frequencies required to simulate the observed lake wave climate. Scale selection and the necessary acoustic frequency band are discussed. The response at eight locations inside the model harbour was measured in this frequency band and the harbour wave amplification determined. A comparison between the acoustic model results and the hydraulic model results (previously carried out by NRCC) is presented.A public opinion survey of recent users of Kincardine Harbour was carried out during the winter of 1976–1977. The purpose of this survey was to identify potential problems in the harbour. The survey was focused on (a) harbour entrance and resonator, (b) offshore breakwater, (c) rubble-mound breakwater, and (d) inner harbour. The results indicated that the users were generally of the opinion that the resonator had decreased inner harbour oscillations, but that it presented a navigational hazard, particularly at night.On the basis of the survey, a utility function was proposed; it indicates an average condition of the harbour in relation to outside wave conditions. Tests on the acoustic model were then carried out. Results of those tests showed that model beach reflectivity was comparable to that of the prototype, but reflectivity of the model breakwater was relatively low. When resonators were installed wave amplification in the harbour was reduced.

A harbour theory for wind-generated waves based on ray methods

In the paper we consider harbour oscillations excited by wind-generated gravity waves. The analysis is based on the fact that waves propagate along rays (wave orthogonals). In this way the elliptic boundary-value problem is turned into an initial-value problem along each ray. When a ray strikes the boundary (the harbour walls), reflected rays are produced in accordance with the law of reflexion. When a ray strikes an edge point of the boundary (e.g. the tip of a breakwater) diffracted rays are produced and emitted in all directions into the harbour. Algorithms for the tracing of incident, multiply reflected and singly diffracted rays as well as the computation of the field on each ray are presented. Attenuation mechanisms (e.g. partial reflexion), which limit the number of rays needed to compute the field, are included. Numerical examples for a rectangular and an actual harbour are given. A comparison between the results obtained by ray methods and finite difference methods is included.

A COMBINED FE-BIE METHOD FOR WATER WAVES

The finite element method and boundary integral equation method are general approximation processes applicable to a wide variety of engineering problems. After a brief description of the combined method, several examples are given for water waves problems : tides, harbour oscillations and waves diffraction and refraction.

Bottomless harbours

Does the harbour of an artificial island need a bottom? The excitation of waves inside a partially immersed open circular cylinder is considered. An incident plane wave is expanded in Bessel functions and for each mode the problem is formulated in terms of the radial displacement on the cylindrical interface below the cylinder. The solution is obtainable either from an infinite set of simultaneous equations or from an integral equation. It is shown that the phase of the solution is independent of depth and resonances are found at wave-numbers close to those of free oscillations in a cylinder extending to the bottom. If the resonances of the cylinder are made sharper (by increasing the depth of immersion) the peak response of the harbour increases, but the response to a continuous spectrum remains approximately constant. Numerical results are obtained by minimizing the least squares error of a finite numberNof simultaneous equations. Convergence is slow, but the error is roughly proportional to 1/Nand this is exploited. The solution obtained from a variational formulation using the incoming wave as a trial function is found to give a very good approximation for small wave-numbers, but is increasingly inaccurate for large wave-numbers. Away from resonance the amplitude of the harbour oscillation is less than 10% of the amplitude of the incoming wave provided the depth of the cylinder is greater than about ¼ wavelength, and it is argued that in practice at the resonant wave-number oscillations excited through the bottom of the harbour will leak out through the entrance before they can reach large amplitudes. In an appendix the excitation of harbour oscillations through the harbour entrance is discussed, and some results of Miles & Munk (1961) on an alleged harbour paradox are re-interpreted.