The Kelvin--Helmholtz (K-H) instability at the Venus ionopause is investigated using a two-dimensional global hybrid (particle ions, massless fluid electrons) model for the case where the interplanetary field is oriented transverse to the flow. In order to self-consistently study the kinetic processes at the Venus ionopause, we calculate the entire Venus ionopause--solar wind interaction region kinetically, including the ionosphere, ionopause transition layer, magnetosheath, and solar wind regions, by applying boundary-fitted coordinates to the particle-in-cell code. Calculations are done for the unmagnetized ionospheric condition. It is found that the distribution of ionopause surface waves generated by the K-H instability exhibits a clear asymmetry between hemispheres of upward and downward solar wind motional electric fields. In the hemisphere where the motional electric field points away from the ionosphere, our two-dimensional model observes the development of the instability from the subsolar location, where the Venus ionopause has been thought to be stable due to small velocity shear and stabilizing effects such as gravity stabilization. Ionospheric filaments (streamers) are highly elongated in this hemisphere, and perturbations on the scale of the planetary radius are observed at the flank of the ionotail. In the opposite hemisphere, the instability develops only in a limited region between solar zenith angles (SZA) of ~40¿ and 90¿, and the surface of the ionotail appears rather smooth except for some special cases. The wavelength of the dominant mode is very long (2000--3000 km) in this hemisphere due to the finite Larmor radius (FLR) stabilizing effect. We show that the process operating at the ionopause is not a localized one but is important for the dynamics of the ionosphere and other regions. The asymmetrical momentum transport across the ionopause yields an asymmetrical convection pattern of the ionosphere. Our model also shows the dynamic nature of the interaction. The dynamic ion removal process associated with the K-H instability is found to play a significant role in the ion escape from the planet (O+ removal rate of approximately several times 1025 particles per second).