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  "body": "\n## Summary\n\nThe shallow water equations describe a layer of fluid whose depth is small compared with the horizontal length scale of its motion.\nTheir unknowns are the depth of the layer and the horizontal velocity, both depending on horizontal position and time.\nThey form a system of [[hyperbolic conservation laws|XN081NCPF5]] for mass and momentum.\nThey model tides, tsunamis, floods and large-scale flows in the atmosphere and the ocean.\n\n## Explanations\n\n### L1 human\n\nWhen water is shallow compared with the size of its waves, the water in a vertical column moves together.\nSo one only needs to know how deep the water is and how fast it moves horizontally at each place.\nWater flows from where the surface is high to where it is low, and the amount of water is conserved.\nSmall waves travel at speed $\\sqrt{g h}$, where $h$ is the depth and $g$ the gravitational acceleration, so a tsunami in a deep ocean is very fast.\nLike other conservation laws, the equations can develop jumps, which model hydraulic jumps and bores.\n",
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