Multi-mode surface wave diffraction by a right-angled wedge

Abstract

This paper extends the phenomenological theory of multi-mode surface wave diffraction to a right-angled wedge configuration. The solution to a two-mode problem is obtained under the edge condition \[ ∑ j = 0 2 | ∂ j u ∂ x j | = 0 ( r − [ 1 + h ] ) , 0 ≤ h > 2 / 3 \sum \limits _{j = 0}^2 {\left | {\frac {{{\partial ^j}u}}{{\partial {x^j}}}} \right | = 0\left ( {{r^{ - \left [ {1 + h} \right ]}}} \right ),0 \le h > 2/3} \] as r → 0 r \to 0 . It is conjectured that the same procedure may be used to construct the solution to the corresponding N N -mode problem under the edge condition \[ ∑ j = 0 N | ∂ j u ∂ x j | = 0 ( r − [ ( 2 N − 1 ) / 3 + h ] ) , 0 ≤ h ≤ 2 / 3 \sum \limits _{j = 0}^N {\left | {\frac {{{\partial ^j}u}}{{\partial {x^j}}}} \right |} = 0\left ( {{r^{ - \left [ {\left ( {2N - 1} \right )/3 + h} \right ]}}} \right ),0 \le h \le 2/3 \] as r → 0 r \to 0 .