A novel coupling of the transverse betatron motion to the longitudinal microwave instability is studied. Besides the radial coherent dipole mode space charge field, simulation and theoretical studies in this paper show that the longitudinal coherent dipole mode space charge field due to deformation of beam shape also plays an important role in the isochronous regime, it induces betatron oscillation frequencies in temporal evolutions of growth rates spectra of longitudinal charge densities, radial offsets and energy deviations of local centroids, it makes the instantaneous instability growth rates dependent on both the amplitudes and phases of modulations of the above parameters. This paper also introduces a 2D dispersion relation incorporating the Landau damping effects due to finite energy spread and emittance, simulation results show it is more suitable for accurate prediction of the microwave instability growth rates than the conventional 1D growth rates formula. Nonlinear beam dynamics is also studied by co-rotational motion of two-macro-particle model in EXB field, energy spread measurements and simulations. Show Partial Abstract