The interactions of two like-signed vortices in viscous fluid are investigated using two-dimensional numerical simulations performed across a range of vortex strength ratios,
$\unicode[STIX]{x1D6EC}=\unicode[STIX]{x1D6E4}_{1}/\unicode[STIX]{x1D6E4}_{2}\leqslant 1$
, corresponding to vortices of circulation,
$\unicode[STIX]{x1D6E4}_{i}$
, with differing initial size and/or peak vorticity. In all cases, the vortices evolve by viscous diffusion before undergoing a primary convective interaction, which ultimately results in a single vortex. The post-interaction vortex is quantitatively evaluated in terms of an enhancement factor,
$\unicode[STIX]{x1D700}=\unicode[STIX]{x1D6E4}_{end}/\unicode[STIX]{x1D6E4}_{2,start}$
, which compares its circulation,
$\unicode[STIX]{x1D6E4}_{end}$
, to that of the stronger starting vortex,
$\unicode[STIX]{x1D6E4}_{2,start}$
. Results are effectively characterized by a mutuality parameter,
$MP\equiv (S/\unicode[STIX]{x1D714})_{1}/(S/\unicode[STIX]{x1D714})_{2}$
, where the ratio of induced strain rate,
$S$
, to peak vorticity,
$\unicode[STIX]{x1D714}$
, for each vortex,
$(S/\unicode[STIX]{x1D714})_{i}$
, is found to have a critical value,
$(S/\unicode[STIX]{x1D714})_{cr}\approx 0.135$
, above which core detrainment occurs. If
$MP$
is sufficiently close to unity, both vortices detrain and a two-way mutual entrainment process leads to
$\unicode[STIX]{x1D700}>1$
, i.e. merger. In asymmetric interactions and mergers, generally one vortex dominates; the weak/no/strong vortex winner regimes correspond to
$MP<,=,>1$
, respectively. As
$MP$
deviates from unity,
$\unicode[STIX]{x1D700}$
decreases until a critical value,
$MP_{cr}$
is reached, beyond which there is only a one-way interaction; one vortex detrains and is destroyed by the other, which dominates and survives. There is no entrainment and
$\unicode[STIX]{x1D700}\sim 1$
, i.e. only a straining out occurs. Although
$(S/\unicode[STIX]{x1D714})_{cr}$
appears to be independent of Reynolds number,
$MP_{cr}$
shows a dependence. Comparisons are made with available experimental data from Meunier (2001, PhD thesis, Université de Provence-Aix-Marseille I).