A two--dimensional magnetohydrodynamic simulation of Kelvin--Helmholtz instability at the terrestrial magnetospheric boundary is performed by including gradients or plasma and magnetic field normal to the dayside low-latitude magnetospheric boundary. A magnetopause current layer is corrugated highly nonlinearly by the instability, and a plasma blob is formed by an interchange motion associated with the instability. The magnetosheath plasma flow momentum is diffused into the magnetosphere by the anomalous tangential (Reynolds plus Maxwell) stresses associated with the instability, and a wide velocity boundary layer is formed just inside the magnetopause current layer, while the thickness or the magnetopause current layer remains almost constant during the evolution or the instability. The convection voltage drop (integral of the convection electric field) across the velocity shear layer is amplified several times by the anomalous momentum transport associated with the instability. The anomalous momentum flux into the magnetosphere (tangential stress) reaches 0.6 to a few percent of the magnetosheath flow momentum flux, and this anomalous momentum flux into the magnetosphere is sufficient for accounting for the observed tailward momentum flux in the low-latitude boundary layer. The value of the anomalous viscosity vano depends importantly on the magnetosheath Alfv¿n Mach number MA, which is defined by a magnetosheath magnetic field component parallel to the magnetosheath flow velocity; for MA = 2.5, vano is equal to ~0.014 ¿ 2aV0, where 2a is the thickness of the initial velocity shear layer and V0 is the total jump of the flow velocity across the magnetospheric boundary, and it increases with MA, and for MA> 5.0 it is equal to ~0.2 ¿ 2aV0. For a reasonable set of parameters at the dayside magnetospheric boundary the anomalous viscosity obtained is just the right magnitude for driving a magnetospheric convection in the terrestrial magnetosphere. ¿American Geophysical Union 1987