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We show how the temperature-dependent chiral vortical effect can generatehypermagnetic fields and matter-antimatter asymmetries, in the symmetric phaseof the early Universe, in the temperature range $100\mbox{GeV} \le T\le10\mbox{TeV}$, even in the presence of the weak sphaleron processes. We takeinto account all perturbative chirality-flip processes, as well as thenonperturbative Abelian and non-Abelian anomalous effects for all threegenerations. Using the constraints and conservation laws in the plasma, wereduce the number of required evolution equations. We also simplify theanomalous transport coefficients, accordingly. We consider both monochromaticand continuous spectra for the hypermagnetic and velocity fields to solve theanomalous magnetohydrodynamics equations. We then show that overlapping smalltransient fluctuations in the temperature of some matter degrees of freedom andvorticity of the plasma can generate a chiral vortical current, resulting inthe generation of strong hypermagnetic fields and matter-antimatterasymmetries, all starting from zero initial values. We obtain the baryonasymmetry $\eta_{B}\simeq 5\times10^{-10}$ and a positive helicityhypermagnetic field with amplitude $B_{Y}(x)\simeq10^{19}G$, at the onset ofthe electroweak phase transition. Although the sphaleron processes tend towashout the generated $(\rm B +L)$ asymmetry, the anomalous processes prevailand the baryogenesis and leptogenesis occur without $(\rm B-L)$ violation.

The generation of baryon asymmetry and hypermagnetic field by the chiral vortical effect in the presence of sphalerons