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At the Earth’s low-latitude magnetopause, the Kelvin-Helmholtz (KH) waves, which are driven by the super-Alfvénic velocity shear across the magnetopause, have been frequently observed during periods of northward interplanetary-magnetic-field (IMF) and believed to contribute to efficiently transporting the solar wind plasmas into the magnetosphere. On the other hand, during southward IMF periods, the signatures of the KH waves are much less frequently observed and how the KH waves contribute to the solar wind transport has not been well explored. Recently, the Magnetospheric Multiscale (MMS) mission successfully detected signatures of the KH waves near the dusk-flank of the magnetopause during southward IMF. In this study, we analyzed a series of two- and three-dimensional fully kinetic simulations modeling this MMS event. The results show that a turbulent evolution of the lower-hybrid drift instability (LHDI) near the low-density (magnetospheric) side of the edge layer of the KH waves rapidly disturbs the structure of the layer and causes an effective transport of plasmas across the layer. The obtained transport rate is comparable to or even larger than that predicted for the northward IMF. These results indicate that the diffusive solar wind transport induced by the KH waves may be active at the flank-to-tail magnetopause during southward IMF.