Julius

5/10 THEORIES AND METHODS Shallow Water Wave Equation: 𝝏𝜼 𝝏𝒕 + 𝝏𝑴 𝝏𝒙 + 𝝏𝑵 𝝏𝒚 =𝟎   Equations of motion: 𝝏𝑴 𝝏𝒕 + 𝝏 𝝏𝒚 𝑴 𝟐 𝑫 + 𝝏 𝝏𝒚 𝑴𝑵 𝑫 =−𝒈𝑫 𝝏𝜼 𝝏𝒙 − 𝒈 𝒏 𝟐 𝑫 𝟕/𝟑 𝑴 𝑴 𝟐 + 𝑵 𝟐   𝝏𝑵 𝝏𝒕 + 𝝏 𝝏𝒙 𝑴𝑵 𝑫 + 𝝏 𝝏𝒚 𝑵 𝟐 𝑫 =−𝒈𝑫 𝝏𝜼 𝝏𝒚 − 𝒈 𝒏 𝟐 𝑫 𝟕/𝟑 𝑵 𝑴 𝟐 + 𝑵 𝟐 𝜂 : wave amplitude 𝑡 : time 𝑀, 𝑁 : discharge fluxes in the x and y directions D : total water depth n : roughness coefficient References: Imamura et al.; 2006, Koshimora, 2009