The effect of bottom friction in 2D non-homogeneous wave resonance phenomena

Abstract

In this research, we study the effect of bottom friction on the resonance in 2Dxy rectangular basin using a mathematical model. The governing equations used are the shallow water equations with bottom friction. To obtain the natural wave period that cause a resonance, the mathematical model is solved analytically and numerically. Moreover, we investigate the resonance occurred for various wave modes. To validate the numerical model, comparisons against the analytical solutions are provided. Results from both methods turn out to be in very good agreement. The effects of the modes and dimensions on resonance are analyzed. This research can be beneficial for consideration to protect lakes.

Keywords

• Wave resonance
• Natural resonant period
• 2D shallow water equations
• Finite volume method