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Water wave propagation equation from expanded form of Leibniz rule
Abstract The Leibniz integral rule for the first derivative with variable limits of integration is expanded for the second and the third order derivatives by using the chain rule here. Water wave propagation equation in the x-z plane containing second derivatives is depth-integrated by using the Leibniz rule. The integrated wave equation is then applied to wave transmission and reflection over an inclined step, and the computed reflection coefficients agree well with those from existing theories such as full linear equation, mild slope equation, and modified mild slope equation.
Water wave propagation equation from expanded form of Leibniz rule
Abstract The Leibniz integral rule for the first derivative with variable limits of integration is expanded for the second and the third order derivatives by using the chain rule here. Water wave propagation equation in the x-z plane containing second derivatives is depth-integrated by using the Leibniz rule. The integrated wave equation is then applied to wave transmission and reflection over an inclined step, and the computed reflection coefficients agree well with those from existing theories such as full linear equation, mild slope equation, and modified mild slope equation.
Water wave propagation equation from expanded form of Leibniz rule
Kim, Hyoseob (author) / Jang, Changhwan (author)
KSCE Journal of Civil Engineering ; 17 ; 257-261
2013-03-01
5 pages
Article (Journal)
Electronic Resource
English
Water wave propagation equation from expanded form of Leibniz rule
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