Impulse of Vortex Knots from Diagram Projections

In this paper I extend the area interpretation of linear and angular momenta of ideal vortex filaments to complex tangles of filaments in space. A method based on the extraction of area information from diagram projections is presented to evaluate the impulse of vortex knots and links. The method relies on the estimate of the signed areas of sub-regions of the graph resulting from the pro- jection of the vortex axes on the plane of the graph. Some examples based on vortex rings interaction, vortex knots and links are considered for illustration. This method provides a complementary tool to estimate dynamical properties of complex fluid flows and it can be easily implemented in real-time diagnostics to investigate fluid dynamical properties of complex vortex flows.