With a little help to get started, the water erodes a channel, transporting sediment to the ocean.
For what it’s worth (and it seems a reasonable explanation to me):
The beach sits at the base of a valley which has a small stream running through it. Due to wave action, sand gets pushed up into a large hill in front of the stream each winter. This creates a natural dam that the stream water collects behind for months which is about 20 feet above the level of the ocean on the other side of the sand berm. Every year some one digs a trench through the sand releasing millions of gallons of fresh water into the ocean.
– YouTube User:Hackfleischhasser comments on the video Waimea River