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Numerical and closed-form solutions for the Maxwell equations of incompressible flow

The equations of fluid dynamics governing an incompressible flow may be recast into the form of a set of Maxwell equations for the Lamb vector and vorticity, which play a role analogous to the electric and magnetic fields, respectively. The challenge in utilizing this approach is that analogous source terms, analogous to the charge density and current density, must be known in order to solve the Maxwell equations directly. In this paper, we explore the construction of source terms for laminar incompressible flow. To demonstrate the utility of this approach, we use the newly formed source terms and demonstrate that common mathematical techniques may be borrowed from classical electrodynamics and used to solve the fluid Maxwell system. We illustrate the approaches using the classic nonlinear problem of the incompressible Blasius boundary layer flow. Four different methods commonly used in electrostatics are applied to arrive at numerical and closed-form solutions of the Blasius boundary layer flow. The results compare very well to the accepted solution and to each other.