  Tokamaks with up-down asymmetric poloidal cross-sections spontaneously rotate
due to turbulent transport of momentum. In this work, we investigate the effect
of the Shafranov shift on this intrinsic rotation, primarily by analyzing
tokamaks with tilted elliptical flux surfaces. By expanding the Grad-Shafranov
equation in the large aspect ratio limit we calculate the magnitude and
direction of the Shafranov shift in tilted elliptical tokamaks. The results
show that, while the Shafranov shift becomes up-down asymmetric and depends
strongly on the tilt angle of the flux surfaces, it is insensitive to the shape
of the current and pressure profiles (when the geometry, total plasma current,
and average pressure gradient are kept fixed). Next, local nonlinear
gyrokinetic simulations of these MHD equilibria are performed with GS2, which
reveal that the Shafranov shift can significantly enhance the momentum
transport. However, to be consistent, the effect of $\beta'$ (i.e. the radial
gradient of $\beta$) on the magnetic equilibrium was also included, which was
found to significantly reduce momentum transport. Including these two competing
effects broadens the rotation profile, but leaves the on-axis value of the
rotation roughly unchanged. Consequently, the shape of the $\beta$ profile has
a significant effect on the rotation profile of an up-down asymmetric tokamak.
