An incoming tide can form a moving surge that propagates upstream against a river's current. A discontinuous idealization is a shock wave of the shallow water equations, while weaker or dispersive bores can have an undular wave train. A boundary overtaking upstream-propagating characteristic curves warns that a smoothly attached quasi-steady description may fail; the appropriate discontinuity must satisfy the conservative jump conditions of the chosen model.
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A tidal bore is a phenomenon that occurs in certain rivers and estuaries where the incoming tide creates a sudden and strong surge of water that moves upstream against the river's current. This can happen when the tide rises rapidly in a narrow or funnel-shaped body of water, causing a tidal wave to travel up the river. Tidal bores generally occur in areas with large tidal ranges, meaning there is a significant difference between high and low tide.