The horizontally ($\mathrm{\Omega }\perp {\mathbf{v}}_{\mathrm{ns}}$) and axially ($\mathrm{\Omega }\parallel {\mathbf{v}}_{\mathrm{ns}}$) rotating counterflow of superfluid ${}^4\mathrm{He}$ (He II) generated thermally in a square channel is studied using the second sound attenuation technique, detecting the statistically steady state and temporal decay of the density of quantized vortex lines $L(t,\mathrm{\Omega })$. The array of rectilinear quantized vortices created by rotation at an angular velocity $\mathrm{\Omega }$ strongly affects the transient regimes of quantum turbulence characterized by the counterflow velocity ${\mathbf{v}}_{\mathrm{ns}}$, differently in both geometries. Two effects are observed, acting against each other and affecting the late temporal decay $L(t,\mathrm{\Omega })$. The first is the gradual decrease of the decay exponent $\mu$ of the power law $L(t,\mathrm{\Omega })\propto t^{-\mu }$, associated with the fact that under rotation the thermal counterflow acquires two-dimensional features, clearly observed and recently reported by us [Phys. Fluids 36, 105121 (2024)] in the $\mathrm{\Omega }\parallel {\mathbf{v}}_{\mathrm{ns}}$ geometry. It exists in the $\mathrm{\Omega }\perp {\mathbf{v}}_{\mathrm{ns}}$ geometry as well, however, it is screened here by the influence of the effective Ekman layer built within the effective Ekman time of order seconds. For faster rotation rates $L(t,\mathrm{\Omega })$ gradually ceases to display a clear power law. Instead, rounded and ever steeper decays occur, gradually shifting toward shorter and shorter times, significantly reducing the time range for a possible self-similar decay of the vortex line density. This effect is not observed in $\mathrm{\Omega }\parallel {\mathbf{v}}_{\mathrm{ns}}$ geometry, as here the much longer effective Ekman time of order minutes cannot affect the observed $L(t,\mathrm{\Omega })$ decay appreciably.

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• Rotating turbulence
• Turbulence
• Helium-4 superfluids