The tsunami is transverse from where the earthquake starts under water until it reaches shore.
The tsunami is longitudinal when its at the shore and
longitudinal waves are when the waves are getting smaller and thinner and they are going to get in a smaller place.
Like all water waves a tsunami has elements of transverse wave motion and longitudinal wave motion.In a transverse wave motion the particles move perpendicular up and down to wave the direction. In water waves (including tsunami) the water particles move in a circular or elliptical pattern depending on the depth of the water.