Convective momentum transport associated withV⋅@/B∇Vin the momentum equation is calculated for arbitrary values of the poloidalE×BMach numberMp. Here,Vis the plasma flow velocity. The physics origin of the convective momentum transport is associated with the coupling of the poloidal variation of the viscosity‐driven flux to that of the flow velocity in the magnetic surface. When the radial gradient scale length of the plasma velocity is of the order of the ion poloidal gyroradius, &rgr;pi, the convective momentum transport becomes comparable to the ion viscosity. AtMp&bartil;1, the ion viscosity associated with shock—the shock viscosity—approximately balances the convective momentum transport to maintain the lowest‐order ambipolarity. The implications of the effects of shock and convective momentum transport for the previous L–H transition bifurcation theory [K. C. Shaing and E. C. Crume, Jr., Phys. Rev. Lett.63, 2369 (1989)] are discussed, and an extended bifurcation theory including these effects is presented. It is shown that the experimentally relevant plasma viscosity,effectiveplasmaviscosity, is very similar to that obtained without including compressibility effects, even if shock exists.