TY - JOUR
T1 - Three dimensional application of the complementary mild-slope equation
AU - Toledo, Yaron
AU - Agnon, Yehuda
N1 - Funding Information:
This research was supported by the US–Israel Binational Science Foundation (grant 2004-205 ) and by the Germany–Israel (BMBF-MOST) Joint Research program (grant 1946 ).
PY - 2011/1
Y1 - 2011/1
N2 - The complementary mild-slope equation (CMSE) is a depth-integrated equation, which models refraction and diffraction of linear time-harmonic water waves. For 2D problems, it was shown to give better agreements with exact linear theory compared to other mild-slope (MS) type equations. However, no reference was given to 3D problems. In contrast to other MS-type models, the CMSE is derived in terms of a stream function vector rather than in terms of a velocity potential. For the 3D case, this complicates the governing equation and creates difficulties in formulating an adequate number of boundary conditions. In this paper, the CMSE is re-derived using Hamilton's principle from the Irrotational Green-Naghdi equations with a correction for the 3D case. A parabolic version of it is presented as well. The additional boundary conditions needed for 3D problems are constructed using the irrotationality condition. The CMSE is compared with an analytical solution and wave tank experiments for 3D problems. The results show very good agreement.
AB - The complementary mild-slope equation (CMSE) is a depth-integrated equation, which models refraction and diffraction of linear time-harmonic water waves. For 2D problems, it was shown to give better agreements with exact linear theory compared to other mild-slope (MS) type equations. However, no reference was given to 3D problems. In contrast to other MS-type models, the CMSE is derived in terms of a stream function vector rather than in terms of a velocity potential. For the 3D case, this complicates the governing equation and creates difficulties in formulating an adequate number of boundary conditions. In this paper, the CMSE is re-derived using Hamilton's principle from the Irrotational Green-Naghdi equations with a correction for the 3D case. A parabolic version of it is presented as well. The additional boundary conditions needed for 3D problems are constructed using the irrotationality condition. The CMSE is compared with an analytical solution and wave tank experiments for 3D problems. The results show very good agreement.
KW - Coastal and offshore engineering
KW - Linear waves
KW - Mild-slope equation
KW - Stream function formulation
UR - http://www.scopus.com/inward/record.url?scp=78349308382&partnerID=8YFLogxK
U2 - 10.1016/j.coastaleng.2010.06.001
DO - 10.1016/j.coastaleng.2010.06.001
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AN - SCOPUS:78349308382
SN - 0378-3839
VL - 58
SP - 1
EP - 8
JO - Coastal Engineering
JF - Coastal Engineering
IS - 1
ER -