Physics
Point vortices
A Hamiltonian vortex system with dye tracers.
What happens
Explore a softened point-vortex model in a plane: a translating dipole, a co-rotating pair, a cluster and a vortex street. Dye tracers reveal the induced flow without pushing it back. The Hamiltonian is conserved by the continuous model; its numerical drift depends on the time step. Soft cores regularize close encounters, and this model has no viscosity or solid boundaries.
Equations used in the module
Equations r_jk² = (x_k−x_j)²+(y_k−y_j)² x_k′ = −Σ_(j≠k) Γ_j(y_k−y_j)/(2π(r_jk²+ε²)) y_k′ = Σ_(j≠k) Γ_j(x_k−x_j)/(2π(r_jk²+ε²)) H = −Σ_(j<k) Γ_jΓ_k ln(r_jk²+ε²)/(4π)
