A new look at 2D shallow water equations of fluid dynamics via multidimensional Kirchhoff paradigm

We discuss a new method of how the (nonlinear) 2D shallow water fluid dynamic problems inspired by ocean hydraulics, meteorology etc. can be modeled by internally passive multidimensional Kirchhoff circuits which subsequently pave the way for robust numerical simulation of the system by wave digital techniques. While the specific fluid dynamic equations dealt with in this paper are important in their own right and can be used to model a number of physical phenomena, the treatment is only one of many examples of the basic tenet that it should be possible to model all properly described physical systems by multidimensional internally passive Kirchhoff circuits. We refer to this as the Kirchhoff paradigm. In the context of the present specific problem, the paper thus helps to bridge connections between physics and circuits and systems theory at a deeper level than has been exploited before.