This study investigates the onset of convection in a uniformly rotating fluid layer by varying the Taylor number ( \(\textrm{Ta}\) ), solute Rayleigh number ( \(\mathrm {Ra_S}\) ), Prandtl number ( \(\textrm{Pr}\) ), Schmidt number ( \(\textrm{Sc}\) ), and boundary conditions. The control parameters are varied over the ranges \(\textrm{Ta} \in [0, 10^5]\) , \(\textrm{Pr} \in (0, 10]\) , \(\textrm{Sc} \in (0, 10^3]\) , and \(\mathrm {Ra_S} \in [-3 \times 10^3, 3 \times 10^3]\) . Using a staggered grid Chebyshev spectral collocation method, the analysis reveals that rotation brings stability to the system and reduces the cell size at the onset of convection. Rotation also suppresses zero critical wave number convection and concavity of stationary neutral stability curve towards the origin under the non-identical temperature and concentration boundary conditions, as discussed by D. A. Nield [“The thermohaline Rayleigh-Jeffreys problem,” J. Fluid Mech. 29(3):545-558, 1967] in the absence of rotation. It is observed that a positive solute Rayleigh number promotes stationary convection, whereas a negative solute Rayleigh number tends to favor an oscillatory onset, depending on the fluid properties. Under no-slip velocity boundaries, three transition regimes are identified: oscillatory-stationary (O-S), stationary (S), and stationary-oscillatory (S-O). In contrast, only stationary convection occurs at onset when water-ethanol is confined between two stress-free plates at fixed rotation rate and concentration gradients. Moreover, reversing the solute boundary conditions does not affect the onset threshold when both plates are perfectly thermally conducting.
