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We have modelled planetary nebulae (PNe) using a 2-wind interacting-stellar-winds (ISW) model. If the two interacting winds have constant properties, the velocity of the PN shell tends towards a constant with time and the shape becomes self-similar. Additionally, if the velocity of the fast wind is much higher than the expansion velocity of the shell, the interior of the hot shocked bubble becomes isobaric. We have computed the shapes of PNe in the self-similar stage with both semi-analytic methods and numerical hydrodynamic simulations. An asymmetric density profile was assumed for the slow wind. We include the effects of the ambient wind velocity. Though the ambient velocity is often comparable to the expansion velocity of the PN, it has not received much attention since the work of Kahn \& West (1985). The morphological appearance depends on the density contrast, steepness of the density profile with polar angle and velocity of the ambient medium; classification of PNe purely on the basis of the first two factors may be misleading. In particular the ambient wind velocity determines whether the PN will show a bulge or a cusp at the equator. Moderate values of the density contrast result in a cusp at the equator. Higher density contrast coupled with a low velocity for the external medium gives rise to extremely bipolar nebulae. For large density contrasts and a significant value of the slow wind velocity, the surface density maximum of the shell shifts away from the equator, giving rise to peanut-shaped structures with pronounced equatorial bulges. Our work shows that bipolar nebulae result when the expansion velocity of the PN is much larger than that of the external wind. An asymmetry in the external wind velocity can also lead to a bipolar shape if the equatorial velocity is sufficiently low. Our simulations indicate that all PNe may not reach the isobaric, self-similar shape. A ratio of interior sound speed to shell velocity $\ga 10$ is found to yield nebulae whose shapes match those given by the isobaric approximation. Furthermore, asymmetric PNe shells are corrugated by the presence of Kelvin-Helmholtz instabilities.
