  We study the evolution of the matter-antimatter asymmetry ({\eta}), the
vorticity, and the hypermagnetic field in the symmetric phase of the early
Universe, and in the temperature range 100 GeV < T < 10 TeV. We assume a
configuration for the hypermagnetic field which includes both helical and
non-helical (Bz) components. Consequently, the hypermagnetic field and the
fluid vorticity can directly affect each other, the manifestations of which we
explore in three scenarios. In the first scenario, we show that in the presence
of a small vorticity and a large {\eta}eR, helicity can be generated and
amplified for an initially strong Bz. The generation of the helical seed is due
to the chiral vortical effect (CVE) and/or the advection term, while its growth
is mainly due to the chiral magnetic effect (CME) which leads to the production
of the baryon asymmetry, as well. The vorticity saturates to a nonzero value
which depends on Bz, even in the presence of the viscosity, due to the
back-reaction of Bz on the plasma. Increasing the initial vorticity, makes the
values of the helicity, {\eta}s, and vorticity reach their saturation curves
sooner, but does not change their final values at the onset of the electroweak
phase transition. The second scenario is similar to the first except we assume
that all initial {\eta}s are zero. We find that much higher initial vorticity
is required for the generation process. In the third scenario, we show that in
the presence of only a strong hypermagnetic field, {\eta}s and vorticity can be
generated and amplified. Increasing the initial helicity, increases the final
{\eta}s and vorticity. We find that although the presence of a nonzero initial
Bz is necessary in all three scenarios, its increase only increases the final
values of vorticity.
