There are four cases:

the monopole is weaker than each dipole half,

and the encounter is:

• head-on -- main run
• with an offsett

the monopole is nearly as strong as each dipole half,

and the encounter is:

• head-on
• with an offsett

Initialisation 
Monopole:    Bessel monopole of radius 0.5 centred at (0,0)
             and strength (=circulation) :+4 or +8
              ==> extremum of initial vorticity: 
                                       +11.8 or +23.6
Dipole:      Lamb dipole of radius 0.75 and velocity +2
             centred at (-2,0) or (-2,+0.5)
              ==> extrema of initial vorticity: +/- 29.5
                  circulation per dipole half : +/- 10.2
Tracers:     tracer contours:
              - monopole: at radii 0.2 0.35 and 0.5
              - dipole: at vorticity levels 0.01, 10 and 20
             single tracer points:
              - monopole: at the centre
              - dipole: at the extrema of vorticity
Computation: domain: X = (-3, ..., 3), Y = (-3, ..., 3)
             no. of grid points from wall to wall: (257, 257)
             boundary conditions: stress-free along all walls 
             standard Arakawa scheme used
             rotation effects: none
             bottom topography: none
             solver for streamfunction: FACR
             viscosity: nu = 10^-3 (i.e. Re=1000 at T=0)
             time step: dt = 0.0025
             final time: T = 2 [800 time steps]

Contour plots:

Contours of vorticity are at 1, 2, ..., 11, 12, 15, 20 and 25, both positive and negative; there is no 0 contour.

Tracer plots:

Tracer contours are along streamlines, shown by the drawn lines; areas between the contours are filled with colours: red for the positive and bleu for the negative half of the dipole, and green for the monopole.

Some other graphs

For the main run of a weaker monopole and a head-on encounter:

The maximum and -minimum of vorticity as
function of time (averaged over 20 time steps).

 

The extrema of vorticity are initially of course in the two halfs of the dipole. The decrease until T=1 is due to the viscouse decay. After that the effects of the merger of the weaker monopole into the dipole set in and both vorticity extrema are affected.

 

The Courant number CFL, a measure for the
maximum velocity in the domain, function
of time (averaged over 20 time steps).

The maximum and -minimum of vorticity as
function of time (averaged over 20 time steps).

 

The Courant number CFL, a measure for the
maximum velocity in the domain, function
of time (averaged over 20 time steps).

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created: 12 September 1999
last modified: 26 May 2001