TY - JOUR
T1 - Propagation of shallow water waves in an open parabolic channel using the WKB perturbation technique
AU - Bautista, E. G.
AU - Méndez, F.
AU - Bautista, O.
AU - Mora, A.
N1 - Funding Information:
This research is financially supported by the research grant number 084600 from the Consejo Nacional de Ciencia y Tecnologa and project SIP 20101607.
PY - 2011/7
Y1 - 2011/7
N2 - A singular perturbation analysis based on the WKB technique to study the hydrodynamic performance of periodic ocean waves that are incident on an open parabolic channel of constant depth is proposed. We derive a linear model to predict the propagation of the long ocean waves into the channel. In this manner, the spatial distribution for the surface elevation of the ocean waves inside the channel as a function of two dimensionless parameters, namely, a kinematical parameter, Κ and a geometrical parameter ε, is governed by a second-order ordinary differential equation. The kinematical parameter Κ denotes the ratio of the potential head, due to gravity, to the kinetic head of the ocean waves along the longitudinal axis of the parabolic channel. Meanwhile, ε is a dimensionless geometrical parameter that represents a characteristic ratio of the parabolic channel. Using matching conditions, simple expressions for the reflection and transmission coefficients are obtained.
AB - A singular perturbation analysis based on the WKB technique to study the hydrodynamic performance of periodic ocean waves that are incident on an open parabolic channel of constant depth is proposed. We derive a linear model to predict the propagation of the long ocean waves into the channel. In this manner, the spatial distribution for the surface elevation of the ocean waves inside the channel as a function of two dimensionless parameters, namely, a kinematical parameter, Κ and a geometrical parameter ε, is governed by a second-order ordinary differential equation. The kinematical parameter Κ denotes the ratio of the potential head, due to gravity, to the kinetic head of the ocean waves along the longitudinal axis of the parabolic channel. Meanwhile, ε is a dimensionless geometrical parameter that represents a characteristic ratio of the parabolic channel. Using matching conditions, simple expressions for the reflection and transmission coefficients are obtained.
KW - Long wave propagation
KW - Open channel
KW - Shallow water
KW - WKB perturbation technique
UR - http://www.scopus.com/inward/record.url?scp=79957907234&partnerID=8YFLogxK
U2 - 10.1016/j.apor.2011.03.002
DO - 10.1016/j.apor.2011.03.002
M3 - Artículo
SN - 0141-1187
VL - 33
SP - 186
EP - 192
JO - Applied Ocean Research
JF - Applied Ocean Research
IS - 3
ER -