  The vorticity dynamics of the two-dimensional (2D) Taylor-Green vortex (TGV)
problem is investigated in its multi-cellular configuration by solving the
incompressible Navier-Stokes equation for long time intervals using a
pseudo-spectral method. This helps follow the vorticity dynamics of periodic
free shear layer flows by solving an extremely accurate algorithm to explain
vortex interactions that lead to vortex stripping (forward cascade), merger,
and reconnection (inverse cascade) during various stages of evolution of
periodic arrangements of a large number of TGV vortical cells. This latter
aspect has been adopted so as not to be affected by the periodicity constraints
of a single periodic cell and the various imposed symmetries that attenuate
disturbance growth. The analytic solution of the TGV provides the initial
condition and the spatially accurate Fourier spectral method enables one to
track the first instability of the initial doubly periodic vortices. Despite a
plethora of studies following the primary instability to relate it with
transition to turbulence and the subsequent decay of turbulence in the
literature, the topic of bifurcation sequence for periodic TGV is rare, and
that is one of the main aims of the present research. Instead of restricting
one's attention on a single periodic TGV cell, here it is purposely reported
for multiple cells of the TGV in both directions, without invoking any
asymmetries extraneously. For such an ensemble, one can study various vortical
interactions giving rise to atypical energy spectra, a topic that has also been
seldom addressed to distinguish between successive instabilities that can upon
a conjecture, lead to transition and subsequent relaminarization, versus the
bifurcation sequences leading from one equilibrium state to subsequent ones.
The present study shows the dominance of the latter for 2D TGV at post-critical
Reynolds number.
