Force at the surface of a swirl in a fluid obeying the 3D-wave equation: closed form equations from our novel nonharmonic solutions to the wave equation in spherical coordinates.

This writer discovered in the 1990s new nonharmonic closed solutions for the three-dimensional homogeneous classical wave equation (3D-HCWE) in spherical coordinates [1-3]. Here we report for the first time the force at the surface of a swirl formed in a classical fluid described by the 3D-HCWE. Force is obtained in closed form, and calculation does not require time consuming numerical methods. [1] Munera H A, Buritica D, Guzman O and Vallejo J I (1995) ``Non-conventional solutions for the travelling wave equation'' (in Spanish) \textit{Revista Colombiana de Fisica }(\textit{Colombian Journal of Physics}) \textbf{27} (1) 215-218. [2] Munera H A and Guzman O (1997) ``New explicit nonperiodic solutions of the homogeneous wave equation'' \textit{Found. Phys. Lett.} \textbf{10} (1) 31-41. [3] Munera H A (2000) ``New closed solutions in spherical coordinates for the three dimensional homogeneous wave equations'' (in Spanish) \textit{Momento} \textbf{20} 1-30.