We study the possible role played by sudden changes in the solar wind in triggering substorm onsets. We show that periodic substorms can occur when the IMF Bz is small and fluctuating between southward and northward. The period of the substorms during the fluctuating IMF is ~3 hours, nearly the same as that during strongly and continuously southward IMF. We also show that large sudden changes in the solar wind do not necessarily trigger substorm onsets. For example, a northward IMF turning with a change of 31 nT in the IMF Bz after 1.2 hours of strongly southward IMF (between -12 and -18 nT) did not cause a substorm onset. The observations show that the period of substorms is not controlled either directly by variations in the solar wind or indirectly by the energy transferred to the magnetosphere from the solar wind. We suggest that a sudden change in the solar wind can trigger a substorm onset if and only if the magnetosphere has reached a state conducive to the generation of substorms. Substorms will occur every ~3 hours, no matter whether the IMF is continuously southward or fluctuating between southward and northward.