MODELING OF THE WATER SURFACE UNDER THE CONDITIONS OF MARINE WAVES ON THE BASE OF WAVELET-LIKE FUNCTIONS
DOI:
https://doi.org/10.17721/2519-481X/2024/84-03Keywords:
surface modeling, sea waves, wavelet functions, ship rocking, pitchingAbstract
The assessment of a ship's seakeeping performance is a crucial stage in its design. This concept is determined by a set of vessel properties, including the behavior of its rolling motion, the evaluation of slamming occurrence, deck wetness, and propeller racing. All these phenomena are sufficiently hazardous, and one of the primary factors influencing them is the characteristic of the water surface on which the vessel operates. When information about this surface is available, it becomes possible to conduct direct dynamic modeling of hull behavior on waves, allowing for an assessment of the listed seakeeping factors. Thus, the development of methods for defining the wave surface to model hull behavior on it is highly relevant.
A traditional approach approximates the wave surface by superimposing harmonic dependencies, such as the flat wave equation. However, this does not account for the actual characteristics of sea waves, which are limited in width (in cross-section) and do not form a periodic pattern. To bring the wave surface model closer to its real form, it is advisable to shift to using wavelets instead of harmonic functions. Wavelets possess a central main region that is practically equivalent to a sea wave, as well as small oscillatory regions at the edges. To reduce the influence of these side regions, this work proposes raising the traditional wavelet function to a power (greater than one), allowing almost complete elimination of these regions when the exponent is set to a value up to 3 or 4. One-dimensional functional dependencies are suggested to be combined into two-dimensional structures, which, by assigning different wave numbers (i.e., wavelengths) along different coordinate axes, enables the creation of realistic sea wave patterns.
The work includes the implementation of software that allows dynamic animations of wave propagation based on the proposed functional dependencies. The results obtained may be useful for modeling hull movement modes on waves using anti-roll devices and for evaluating their effectiveness.
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