TY - JOUR
T1 - Propagation of linear long water waves on a cycloidal breakwater
AU - Medina-Rodríguez, A.
AU - Bautista, E.
AU - Méndez, F.
AU - Bautista, O.
N1 - Publisher Copyright:
© 2016, Springer Science+Business Media Dordrecht.
PY - 2016/10/1
Y1 - 2016/10/1
N2 - In this work, we carried out a theoretical analysis of the reflection, transmission and surface deformation of long linear water waves, propagating on a submerged breakwater whose cross-section obeys a cycloidal geometric transition. We use the well-known one-dimensional governing equations for the propagation of linear shallow-water waves, which are presented in their dimensionless version. Considering harmonic wave propagation, the governing equations can be reduced to a dimensionless second-order differential equation with variable coefficients for predicting the elevation of water waves. This equation is solved using a matrix method based on Taylor polynomials. In particular, we evaluate the reflection and transmission coefficients for three breakwaters, namely, cycloidal, semi-cycloidal and quarter-cycloidal. The first case exhibits the smallest transmission coefficient. The present mathematical model is compared with a simple numerical solution and with another analytical solution expressed in terms of the Legendre functions. The present mathematical model can be used as a practical reference for design of the geometrical configurations of submerged cycloidal breakwaters under shallow-flow conditions.
AB - In this work, we carried out a theoretical analysis of the reflection, transmission and surface deformation of long linear water waves, propagating on a submerged breakwater whose cross-section obeys a cycloidal geometric transition. We use the well-known one-dimensional governing equations for the propagation of linear shallow-water waves, which are presented in their dimensionless version. Considering harmonic wave propagation, the governing equations can be reduced to a dimensionless second-order differential equation with variable coefficients for predicting the elevation of water waves. This equation is solved using a matrix method based on Taylor polynomials. In particular, we evaluate the reflection and transmission coefficients for three breakwaters, namely, cycloidal, semi-cycloidal and quarter-cycloidal. The first case exhibits the smallest transmission coefficient. The present mathematical model is compared with a simple numerical solution and with another analytical solution expressed in terms of the Legendre functions. The present mathematical model can be used as a practical reference for design of the geometrical configurations of submerged cycloidal breakwaters under shallow-flow conditions.
KW - Approximate analytical solution
KW - Linear long water waves
KW - Matrix method
KW - Reflection/transmission of water waves
KW - Submerged cycloidal breakwater
KW - Taylor polynomials
UR - http://www.scopus.com/inward/record.url?scp=84961195750&partnerID=8YFLogxK
U2 - 10.1007/s10665-015-9841-7
DO - 10.1007/s10665-015-9841-7
M3 - Artículo
SN - 0022-0833
VL - 100
SP - 187
EP - 210
JO - Journal of Engineering Mathematics
JF - Journal of Engineering Mathematics
IS - 1
ER -