| The motion of a marine vehicle moving in a sea and subjected to wind-induced waves can be analyzed adequately only when the random nature of the wind-induced sea wave is properly taken into consideration. Ideally, the randomness should be characterized in terms of the encounter spectra of the sea surface elevation and slopes; the encounter spectra describe the spectral contents of the elevation and slopes the vehicle experiences as it proceeds in the sea.; So far, however, most studies of analytical and particularly numerical nature, dealing with the encounter spectra and its effect on vehicle motion, have been confined to those cases where conditions of fully developed long-crested seas prevail. A recent exception is the effort by Shinozuka and Wai who developed a method by which the wave profile in a short-crested sea can be idealized and digitally generated as a three-dimensional homogeneous Gaussian random process with mean zero and a specified two-dimensional spectral density in the wave number domain. The spectral density represents a state of fully developed wind-induced short-crested sea condition and can be derived from a more often used directional spectral density through a transformation of frequency and directional angle into two components of the wave number. The same method can be used to predict and generate an encounter wave profile along an arbitrary vehicular path specified in the mean sea water plane. However, to do so is usually an extremely costly, if not totally prohibitive, proposition in terms of computer expense since then the encounter wave profile can only be obtained numerically by generating frozen patterns of the two-dimensional wave profile at appropriately spaced time instants over a sufficiently long duration of time.; The present investigation has developed a method to derive analytical expressions of encounter spectral density functions for ocean surface elevations and slopes in the transverse and longitudinal directions along a straight-line path of vehicular movement in a fully-developed short-crested sea. The encounter wave spectral density functions are then numerically evaluated and the time histories consistent with these spectra are generated with the aid of a method of random process simulations that takes advantage of the FFT algorithm. This method of generation has been developed specifically to accomodate such spectra as the encounter wave spectra that extend over physically genuine (as opposed to mathematically devised) negative frequencies. These time histories are of essential importance in performing the time domain analysis of vehicular heave, roll and pitch motions, particularly when the nonlinearity of these motions cannot be disregarded. |
