fluid dynamics - Why do tsunami waves begin with the water flowing away from shore?

A sign of a tsunami is that the water rushes away from the shore, then comes back to higher levels. It seems that waves should be both + and - polarized and that some tsunamis should go in the opposite direction. That is the first indication of them would be that the water begins rising. However, other than situations very close to the source, it seems that the wave always begins with the water drawing away from the coast.

For example, the wikipedia article on tsunamis states that:

In the 2004 Indian Ocean tsunami drawback was not reported on the African coast or any other eastern coasts it reached. This was because the wave moved downwards on the eastern side of the fault line and upwards on the western side. The western pulse hit coastal Africa and other western areas.

The above is widely repeated. However, when you search the scientific literature, you find that this is not the case:

Proc. IASPEI General Assembly 2009, Cape Town, South Africa., Hermann M. Fritza, Jose C. Borrerob, "Somalia Field Survey after the December 2004 Indian Ocean Tsunami":

The Italian-speaking vice council, Mahad X. Said, standing at the waterfront outside the mosque upon the arrival of the tsunami (Figure 10a), gave a very detailed description of the initial wave sequence. At first, a 100-m drawback was noticed, followed by a first wave flooding the beach. Next, the water withdrew again by 900 m before the second wave partially flooded the town. Finally, the water withdrew again by 1,300 m offshore before the third and most powerful wave washed through the town. These drawbacks correspond to 0.5-m, 4-m, and 6-m depths. The detailed eyewitness account of the numerous drawbacks is founded on the locations of the offshore pillars.

So is there a physical reason why tsunamis, perhaps over longer distances, tend to be oriented so that the first effect is a withdrawal of the water?

Answer

Water waves are rather complicated, and the differential equations which describe them are call Boussenesq equations. A tsunami is not a transverse wave. It is a pressure wave with a longitudinal mode. It also travels very fast at about 700km/hr. What happens is that this travels as a pressure wave in the open ocean, but when it reaches a continental shelf the wave is reflected partially upwards. This has the effect of converting it into a transverse wave as water moving along is now pushed upwards. This is a very nonlinear process and nontrivial to model. This pushing up of the water does initially cause water at the shore to recede outwards. The wave which seconds later reaches shore is much more slow moving, and a lot of that wave energy is converted into the towering wave front that sweeps in.