Symmetries of flow structures are often prescribed by their mechanical instability and geometry. In this study, as an example, we present the homotopy of a rotating threefold spiral state that is robust in a spherical Couette flow toward a hybrid system with thermal stratification effects. The rotating wave state has not yet been confirmed to smoothly connect to the thermal stratification system. Through continuation, the most dangerous mode at a purely spherical Couette flow of m = 4 modes of spherical harmonics is replaced by l = 4 and m = 3 in a purely thermal convective system. For the state obtained at the limit under only the thermal effect, the residual quantities of both the torque to the outer sphere and meridional circulation are discussed in detail.
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