PORAT A COMPUTER SIMULATION OF THE PROPAGATION OF SEA WAVES

Transcription

1 PORAT A COMPUTER SIMULATION OF THE PROPAGATION OF SEA WAVES Marjan Sikora, M.Sc.E.E. Sv. Klare 14, HR Split, Croatia, marjan.sikora@st.hinet.hr WITH COURTESY OF THE OWNER - OBALA D.D. SPLIT INTRODUCTION - PORAT is a computer simulation of the propagation of sea waves - it calculates the refraction of sea waves - it is an engineering application made for civil engineers - it is used for design of breakwaters and other harbor elements - the traditional method of calculation was a combination of numerical and graphical methods - this method is tedious and time consuming - it requires about one day s work for few characteristic winds - for every change in input parameters and direction everything has to be recalculated

2 - there is a relatively big error margin because of the inaccuracy of graphical tools and because of the precision of an operator s readings Fig. 1. Calculation of the propagation of sea waves made by traditional method - the computerized method is much faster and much more accurate - after the input of DTM of the sea bottom is competed, the calculations are over in the matter of minutes - calculation for different winds are not time consuming they are based on the same DTM Fig. 2. Computerized calculation of the propagation of sea waves

3 WAVE PROPAGATION AND REFRACTION - to determine the propagation of sea waves one has to make several approximations: the waves are monochromatic propagates in only two-dimensions the fluid is homogenous and incompressible the Corioliss effect is not taken into account the bottom is hard and flat the amplitude of the wave is small - based on these assumptions in Airy gave the theory of small amplitude waves (based on Euler equations) Fig. 3. Propagation of the sea wave Fig. 4. Diffraction of the sea waves

4 H y = sin( kx σt) (1) 2 c = gt 2ΠD th 2Π L (2) H 2 L E = ρg (3) 8 H 0 = H k r k p (4) B = (5) B k r 0 2 k 2ch ( kd) = s 2kD + (6) sh(2kd) - computation is done by the implementation of finite element method (FEM) - propagation and diffraction is calculated by numerical integration of differential equations if the sea waves - the sea bottom is divided into triangles depth is defined in the triangle endpoints Fig. 5. Refraction for ideal cliff

5 PORAT APPLICATION - input parameters: DTM of the sea bottom, T 0, H 0, L 0, T - DTM of the sea bottom is digitized from the map, by scanning and digitizing contours (this process can be either manual or automatic) Fig. 6. Map with the contours of the sea bottom Fig. 7. DTM of the sea bottom with shaded depth - the parameters of the wave in the deep water are gathered by measuring and by statistical methods for period of 10 or 100 years

6 - the time increment T defines the density of calculated frontlines - the starting frontline is defined in the deep water - the direction of the frontline is orthogonal to the wind, and the number of its segments determines the number (density) of the ortholines calculated by the simulation Fig. 9. Simulation of the propagation of sea waves Fig.10. Refraction height of the wave is shaded in blue - simulation calculates the height, the speed and the energy of the waves and displays it in the graphical and tabular form

7 CONCLUSION - the accuracy of the simulation was checked against manual method and the error was under 5% (the computer simulation was probably more accurate) - for design of breakwater the phenomena of diffraction is of uttermost importance, and is being implemented into simulation Fig. 11. The diffraction of the sea waves - other relevant phenomena such as reflection would also in future versions be taken into account - beside the importance for the engineering part of the design process, there is also possibility for the visualization Fig. 12. Visualization of the underwater part of new breakwater in Makarska

8 Fig. 13. Visualization of depth ranges of Resnik Fig. 13. Visualization of Makarska Riviera