We report our experimental study on spiral instabilities in an open spatial reactor using the Belousov-Zhabotinsky (BZ) reaction. A phase diagram showing different regimes of spiral dynamics is built. Two instabilities are identified in the phase diagram: the Doppler instability and the long wavelength instability. Both instabilities lead the system to a state of spatiotemporal chaos or chemical turbulence. Ln the regime of the Doppler instability, spiral waves break near the spiral core, when a Hopf bifurcation contributes to the spiral core, making the latter meander; in the regime of the long wavelength instability, a sustained long wavelength modulational spiral appears and is stable in a range of control parameters. At the same time, the trajectory of the spiral tip changes from circular to epicycloid, which is very similar to a meandering spiral. The essential difference to distinguish meandering spirals from those with long wavelength modulations is that the convective velocity of the former is zero, while the latter is nonzero. Beyond that range of the control parameter, spiral waves break and the system undergoes a transition to chemical turbulence.