John Hale, of Dunedin, asks :-
The harbour surface often shows wrinkled lines of water moving at right angles to each other. How can these ripples criss-cross without losing shape?
Daniel Schumayer, a physicist at the University of Otago, responded.
What you observed on the harbour surface is called interference,which means the interaction of waves with each other. Two waves can be present at the same location at a given instant and affect the resultant motion together. Overlapping waves can enhance or cancel each other out, depending on how their crests and troughs line up. If two crests meet each other, they add together (constructive interference) and the result is an even bigger crest. However, a crest and a trough reduce each other's effect and the resultant ripple will be smaller (destructive interference).
However, the phenomenon of interference only partially answers your question. To answer it fully, we have to discuss what a "wave" is. Let me use an analogue example, the so-called Mexican wave, when the crowd in a stadium stands up and sits down in an organised, undulating manner. For a distant observer it seems that a wave is propagating along the terraces, although none of the fans actually left his seat! A wave, therefore, is only a disturbance which propagates in a medium. The same phenomenon occurs with water waves. The wave is a disturbance, while the water is only a medium in which this disturbance travels. Therefore two "disturbances" can be at the same place at the same time.
Back to our example; if we instructed the fans to start two waves, one propagating from the left to the right and another one travelling from the top to the bottom of the terraces, these Mexican-waves would propagate independently of each other. There would be some confusion (interference) at the overlap, but the waves would carry on undisturbed outside the overlap area.