Fluid Maxwell’s equations in the language of geometric algebra

A comparison of the vorticity field tensor with the electromagnetic tensor is done. An attempt is made to express the vorticity and its dual in the language of geometric algebra using bivectors. In the language of geometric algebra, all four fluid Maxwell’s equations are reduced to a single equation in two ways, i.e., using a bivector \(\textbf{F}\) $\mathbf{F}$ and also its Hodge dual \(\mathbf {F^*}\) ${\mathbf{F}}^{\ast }$ , and these are analogous to the corresponding results in electromagnetism. The complex structure \(\textbf{F}=\textbf{L}-I\textbf{W}\) $\mathbf{F}=\mathbf{L}-I\mathbf{W}$ in fluid dynamics is a novel approach in this work. A multivector representation of Maxwell’s equations and an expression for the Poynting vector are also obtained.