A Generalized Birkhoff-rott Equation for 2d Active Scalar Problems∗

@inproceedings{Sun2011AGB,
  title={A Generalized Birkhoff-rott Equation for 2d Active Scalar Problems∗},
  author={Hui Sun and David Uminsky and Andrea L. Bertozzi},
  year={2011}
}
In this paper we derive evolution equations for the 2D active scalar problem when the solution is supported on 1D curve(s). These equations are a generalization of the Birkhoff-Rott equation when vorticity is the active scalar. The formulation is Lagrangian and they are valid for nonlocal kernels K that may include both a gradient and an incompressible term. We develop a numerical method for implementing the model which achieves second order convergence in space and fourth order in time. We… CONTINUE READING