Sketch the streamlines for the following stationary 2-dimensional flows, determine whether the flow is compressible, and evaluate its vorticity. The coordinates are Cartesian in parts (a) and (b), and are circular polar with orthonormal bases {e_ω̅ , e_∅} in (c) and (d).

(a) v_x = 2xy, v_y = x²,
(b) v_x = x², v_y =−2xy,
(c) v_ω̅ = 0, v_∅ = ω̅,
(d) v_ω̅ = 0, v_∅ = ω̅⁻¹.