We explore three versions of the Laplacian coflow of G₂-structures on circle fibrations over Calabi--Yau 3-folds, interpreting their dimensional reductions to the K\"ahler geometry of the base. Precisely, we reduce Ans\"atze for the Laplacian coflow, modified or not by de Turck's trick, both on trivial products CY³× S¹ and on contact Calabi--Yau 7-manifolds, obtaining in each case a natural modification of the K\"ahler--Ricci flow.
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Earp et al. (2024) studied this question.
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