Shallow water equations

Imagine you're in a kiddie pool or at the beach where the water is only up to your ankles. This is shallow water. When waves move through shallow water, they behave differently than in deep water.

The shallow water equations are a set of mathematical rules used to describe how waves move through shallow water. These equations help us understand things like tsunamis, storm surges, and tides.

Think of it like playing with a toy boat in a bathtub. You can make waves with your hand, but the waves behave differently depending on how much water is in the bathtub. If the water is shallow, the waves will be shorter and move more slowly. If the water is deeper, the waves will be taller and move more quickly.

The shallow water equations help us understand how waves in shallow water move and how they affect the things around them. They are important because they help us make predictions about how waves might behave in real life. For example, if we know there is a storm coming, we can use these equations to predict how high the waves will be and how far they might spread inland.