The generation of electrostatic drift wave turbulence is modelled by the Charney–Hasegawa–Mima equation. The equilibrium density gradient n0=n0(x) is chosen so that dn0 /dx is nonzero and spatially variable (i.e., v*e is sheared). It is shown that this sheared diamagnetic flow leads to localized turbulence which is concentrated at max(grad n0), with a large dv*e/dx inhibiting the spread of the turbulence in the x direction. Coherent structures form which propagate with the local v*e in the y direction. Movement in the x direction is accompanied by a change in their amplitudes. When the numerical code is initialized with a single wave, the plasma behaviour is dominated by the initial mode and its harmonics.