Turbulence associated with sheared radial electric fields such as those arising in tokamak edge plasmas is investigated analytically. Two driving mechanisms are considered: in the region of maximum vorticity (maximum electric field shear), the electric field is the dominant driving mechanism. Away from the maximum, turbulence is driven by the density gradient. In the latter case, previous work is extended to include the effects of the electric field on the spatial scales of density correlation in the frequency‐Doppler‐shifted, density‐gradient‐driven turbulence. For radial‐electric‐field‐driven turbulence, the effects of magnetic shear on linear instability and on fully developed turbulence are examined. In the case of weak magnetic shear, saturation occurs through an enstrophy cascade process which couples regions of driving and dissipation in wavenumber space. For stronger magnetic shear, such that the width of the dissipation region resulting from parallel resistivity is comparable to the radial electric field scale length, saturation occurs through nonlinear broadening of the mode structure, which pushes enstrophy into the region of dissipation. Estimates of mode widths, fluctuation levels, and scalings are obtained for both mechanisms. Comparison is made with the results of fluctuation measurements in the TEXT tokamak [Phys. Fluids27, 2956 (1984)].