The water from the trough also spreads to the sides creating a crest to both sides of the original pile. The original wave has spread to the side. The gravitational pul of the earth and the inertia of the motion of the water both played a role in the creation of the moving wave crest. This type of water wave is called a gravity wave. There is another type of water wave in which the crests are pulled down by the surface tension of the water.
Surface tension drives waves shorter in wavelength than a few centimeters.
So the big waves we see on the ocean are gravity waves. Waves in the ocean are powered by wind. The wind first builds surface tension waves. It then pushes on the surface tension waves giving them energy, increasing their amplitude and waqvelength until they become gravity waves. Winds can deform waves from a simple sinusoid.