function [zp] = lvdemo_vel4quiv(t,z,lvs,circs)
  % The velocity field to be used for the quiver plot for line
  % vorticies demo.
  % IMPORTANT: !!it is not appropriate to use this function for the
  % odefile!!  this is because the lvs parameter will be fixed
  % during any ode45 call.  trust me just don't do it.
    
  % this code is nasty
  % don't read it - actually just don't read the perturbation by
  % not(MASK)
  % also it will occasionally cause a div by zero in lvdemo when
  % the velocity field is divided by its magnitude.
  
  % VORTEX_RAD_SQ specifies the square of the radius of an area
  % around each line vortex where the effects of that particular LV
  % are not felt.
  global VORTEX_RAD_SQ;
  
  
  MASK = (lvdemo_dist(z,lvs(1)) > VORTEX_RAD_SQ);
  zp = -i*circs(1)/2*pi * MASK .* 1./(z - lvs(1) + not(MASK));
  for j = 2:length(lvs)
    MASK = (lvdemo_dist(z,lvs(j)) > VORTEX_RAD_SQ);
    zp = zp - i*circs(j)/2*pi * MASK .* 1./(z - lvs(j) + not(MASK));
  end
  zp = conj(zp);