ABSTRACT

A tanker moored in irregular head waves in combination with or without current performs large amplitude low frequency surge motions. Due to low frequency motions in combination with or, without the current field the second order wave, drift forces will be a function of the tanker velocities.

By means of 3-D potential theory the quadratic transfer function of the wave drift force for zero speed and low forward speed were computed. By means of the gradient-method the transfer function of the constant speed dependent wave drift force and the wave drift damping coefficient, were derived. The transfer function of the wave drift damping coefficient is compared with the results of model tests.

By means of the obtained results time-domain computations on the low frequency surge motions in irregular waves with and without current were carried out. The results of the computed low frequency motions were' compared with the results of model tests. The time-domain computations are based on the wave train registrations as were adjusted for the model tests.

Prior to solving the equation of motion the mean wave drift damping coefficient and the registration of the wave drift force with and without current were computed. The results of the computed wave drift force registration with and without current in terms of spectral densities were compared with the results of model tests.

INTRODUCTION

The motions of a moored tanker in irregular head waves consist of small amplitude high (= wave) frequency surge, heave and pitch motions and large amplitude low frequency surge motions. The frequencies of the, low frequency surge motions are concentrated around the natural frequency of the system, see Fig. 1.

To study the motions use has been made of two different systems of axes as indicated in Fig. 2; the system of axes Ox(1)x(3) is fixed in space, with the OX(1)- and the Ox(3)-axis coinciding with the ship-fixed system of axes Gx1x3, at rest.

We shall assume that the surge, heave and pitch motions can be decoupled into the following form:

• (Mathematical equation available in full paper)

with ? and ? being small parameters, viz.:
• ? relates to the wave steepness;

• ? considers the ratio between the two time scales of the motions: the p frequency range of the natural frequency of the system and the W frequency range of the wave spectrum frequencies.

and further:
• x1(1), X3{1) and x5(1) relate to the wave frequency surge, heave and pitch motions;

• x11f(2), x31f(2) and X51f(l) stands for the large amplitude low frequency second order surge, heave and pitch motions;

• x1hf(2), x3hf(2) and X5hf(2) represent the second order motions of which the frequency range is twice the wave frequency range.

Of the second order motions only the low frequency part will be considered and will be denoted as x(2).

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