Head-on collision of two Lamb dipoles

Details on the computation and presentation

Dipoles:     velocity: U = 2; maximum initial vorticity 22.1
             radius: a = 1  
             angle of dipole axis with X-axis: 0 and 180 degrees
             positions: (-1.8,0) and (+1.8,0)
Computation: domain: X = (-3, ..., 3), Y = (-6, ..., 6) computed
                     X = (-4, ..., 4), Y = (-4, ..., 6) shown
             no. of grid points from wall to wall: (129, 257)
             boundary conditions: stress-free along all walls 
                (for this case similar to periodic conditions
                 due to the symmetry of the problem)
             standard Arakawa scheme used
             no rotation effects included
             no bottom topography
             viscosity: nu = 10^-3 (i.e. Re=1000 at T=0)
             time step: dt = 0.01
             final time: T = 2 (shown; computed until 3)
Tracers:     along vorticity contours (i.e. along streamlines) 
             of both Lamb dipoles at vorticity levels: 0.1, 6.0, 
             12.0, 18.0; and a single tracers at each extremum
Some results

Courant number CFL vs. time
The Courant number CFL is a measure for the maximum velocity in the domain, which is lowest at the time of the collision. Due to the viscosity, the overall velocity decreases in time, though that cannot be seen clearly in this graph; see for instance the details on Lamb dipole in a domain with stress-free walls.


The tracer lines are not always smooth. The reason for this is that the representation of the lines by points is not always accurate enough. But since these tracers only passively follow the flow, this has no effect on the computations. It needs repair, though.

<=== Head-on collision of two Lamb dipoles

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last modified: 26 May 2001