You also want an ePaper? Increase the reach of your titles
YUMPU automatically turns print PDFs into web optimized ePapers that Google loves.
74 ANAIS DO INSTITUTO HIDROGRÁFICO N.º 15<br />
Finally, the last and may by the most important is the<br />
fact that it is enough only one run of the model for a<br />
complete characterization of the area of interest, while<br />
all the additional computations are being made in real<br />
time outside the model.<br />
6. Index of Symbols<br />
Diss – energy dissipation per unit time,<br />
DLENC – global variable, length of the grid in directional<br />
space,<br />
Dspr – directional width of the spectrum (directional spreading),<br />
DXC1,2 – length of the meshes in x direction,<br />
DYC1,2 – length of the meshes in y direction,<br />
s, u – energy density spectrum,<br />
FLENC – global variable, length of the grid in frequency space,<br />
Fspr – frequency width of the spectrum (frequency spreading),<br />
g – acceleration of gravity,<br />
k sh – advanced shore coefficient,<br />
Llj – j-line length,<br />
MDC – global variable, number of meshes in directional space,<br />
MFC – global variable, number of meshes in frequency spaces,<br />
MXC1,2 – number of meshes in x direction,<br />
MYC1,2 – number of meshes in y direction ,<br />
N (s, u) – action density spectrum,<br />
Npj – number of points on the j-line,<br />
Ste – wave steepness,<br />
TM01 – wave period,<br />
wd – imposed water depth for the isolines,<br />
Wl – wavelength (respectively deep water wavelength,<br />
(x 1j , y 1j ), (x 2j , y 2j ) – j-line end points,<br />
XoX, YoY, ZoZ – grid matrices corresponding to x, y and<br />
respectively depth directions,<br />
XCO2 – x coordinate of the origin of the reshaped grid,<br />
XLENC1,2 – length in x direction<br />
YCO2 – y coordinate of the origin of the reshaped grid,<br />
YLENC1,2 – length in y direction,<br />
dst r – minimum grid step,<br />
dst j – step for the j-line,<br />
V – MATLAB ceil function,<br />
C , C * – isoline operators,<br />
r – density water,<br />
s (s – ) – relative frequency (respectively mean frequency),<br />
u – mean wave direction,<br />
j 3 – deep water form of the Iribarren number,<br />
* – indices 1 and 2 refer of the initial and respectively the<br />
reshaped grids.<br />
7. Acknowledgments<br />
This work is a contribution for two projects developed<br />
in <strong>Instituto</strong> Hidrografico of the Portuguese Navy:<br />
PAMMELA2 (Nearshore Wave Forecasting: Spectral<br />
Models and Data Assimilation) supported by grant<br />
PDCTM/P/MAR/15242/1999 from Fundação para Ciência<br />
e a Tecnologia and MOCASSIM (Oceanographic Model-<br />
ing Implementation with Data Assimilation) also<br />
supported by a grant from Fundação para Ciência e a<br />
Tecnologia.<br />
Eugen Rusu acknowledges a fellowship for scientific<br />
investigation from «Fundação para a Ciência e<br />
Tecnologia».<br />
8. References<br />
Banner, M.L.; Young, I.R. (1994) – Modeling spectral dissipation in<br />
the evolution of wind waves. Part I: Assessment of existing<br />
model performance, J. Phys. Oceanogr., 24, No. 7, 1550-1571.<br />
Battjes, J.A.; Janssen, J.P. (1978) – Energy Loss and Set-up Due to<br />
Breaking of Ran<strong>do</strong>m Waves. 16 th International Conference on<br />
Coastal Engineering, ASCE, (USA), pp. 569-587.<br />
Bertotti, L.; Cavaleri, L. (1994) – Accuracy of wind and wave evaluation<br />
in coastal regions, Proc. 24 Th Int. Conf. Coastal Engineering,<br />
ASCE, 57-67.<br />
Dingemans, M.W. (1997) – Water wave propagation over uneven<br />
bottoms. Part 1 – linear wave propagation, Advanced Series on<br />
Ocean Engineering, 13, World Scientific, 471.<br />
Eldeberky, Y.; Battjes, J.A. (1996) – Spectral Modeling of Wave<br />
Breaking: Application to Boussinesq Equations. Journal of<br />
Geophysical Research, 101, C1, pp. 1253-1264.<br />
Elgar, S.; Guza, R.T.; Raubenheimer, B.; Herbers T.H.C.; Gallagher,<br />
E.L. (1997) – Spectral evolution of shoaling and breaking waves<br />
on a barred beach, J. Geophys. Res., 102, C7, 15797-15805.<br />
Kaminski, G.; Krauss, N.C. (1993) – Evaluation of depth-limited<br />
wave breaking criteria. Waves 193, Amer. Soc. Civil Engrs.,<br />
180-193.<br />
Komar, P.D. (1998) – Beach Processes and Sedimentation. New<br />
Jersey (USA), Library of Congress Cataloging-in-Publication<br />
Data, Prentice-Hall Inc.<br />
Luo, W.; Monbaliu, J. (1994) – Effects of the bottom friction formulation<br />
on the energy balance for gravity waves in shallow<br />
water, J. Geophys. Res., 99, C9, 18,501-18,511.<br />
Mastenbroek, C.; Burgers, G.; Janssen, P.A. (1993) – The dynamical<br />
coupling of a wave model in a storm surge model through the<br />
atmospheric boundary layer, J. Phys. Oceanogr., 23, 1856-1866.<br />
Pires Silva, A.A.; Makarynskyy, O.; Monbaliu, J.; Soares C. V.;<br />
Coelho, E. F. (2000) – Modeling Wave Transformation in a<br />
Open Beach on the West Coast of Portugal. International workshop<br />
on coastal waves, Barcelona (Spain), University of<br />
Barcelona.<br />
Ris, R.C.; Booij, N.; Holthuijsen, L.H.; Padilla-Hernandez, R;<br />
Haagsma, IJ.G. (1998) – SWAN User Manual. Delft, (The<br />
Netherlands), Delft University of Technology.<br />
Rusu, E.; Soares, C.V. Coelho, E.F.; (2001) – Aplicação em Ambiente<br />
MATLAB para Estimar as Características de Agitação<br />
Marítima em Águas Pouco Profundas. Seminar ‘Hydroinformática<br />
em Portugal’ Lisbon, November 2001.<br />
Soares, C.V.; Rusu, E.; Coelho, E.F.; Pires Silva, A.A.; Makarynsky,<br />
O. (2000) – A Nowcast Tool to Assess Wave Parameters in<br />
Coastal Areas. The 6 th International Workshop on Wave Hindcasting<br />
and Forecasting, Monterey (USA), 6-10 November 2000.<br />
Thornton, E.B.; Guza, R.T. (1983) – Transformation of Wave<br />
Height Distribution. Journal of Geophysical Research., 88, C10,<br />
5925-5938.<br />
Whitham, G.B. (1974) – Linear and Nonlinear Waves, Wiley, New<br />
York.<br />
Young, I.R.; Banner, M.L. (1992) – Numerical Experiments on the<br />
evolution of fetch limited waves, Int.Union of Theor. and Appl.<br />
Mech. (IUTAM), Sydney, Australia, 267-275.<br />
The MathWorks, Inc. (2000) – MATLAB User’s Guide, Version 6.<br />
Natick (USA).