We study a reduced electrostatic fluid model for the tokamak scrape-off layer, which incorporates temperature gradient and vorticity gradient as two free energy fields. Two scenarios of field coupling are addressed: (1) sheath condition; (2) vortex wave coupling. For the sheath condition induced field coupling, the poloidal flow shear is coupled with the temperature gradient. Combining an eigenmode analysis and the nonlinear phase dynamics approach, our findings indicate that in the absence of a vorticity gradient, the overall effect of the sheath condition induced flow shear can either stabilize or destabilize the interchange mode, depending on the competition between the flow shear suppression and the temperature gradient driving. This is different from the case where the gradient drive and shear damping are decoupled. When the field coupling is mediated by wave interactions, by setting an idealized step-like temperature and vorticity profiles, a joint mode forms through resonant interaction between the interfacial waves driven by the temperature and vorticity gradients, respectively. Near the phase locking condition, the joint mode can be more unstable than pure temperature gradient driven mode.