A tidal bore forms when a large incoming tide is funneled up a narrowing, shoaling estuary faster than the river's own discharge and channel width can absorb it, so the tidal flood front steepens into a breaking wave that runs upstream against the current — the same mechanism that produces bores on the Qiantang, Severn and Amazon rivers.
bore height h = max(0, tide·1.08 − flow/520 − width/380)
wave speed v = 4 + √(9.81·max(0.2,h))·3.6 [km/h]
The height term grows with tidal range and shrinks with both river discharge and channel width — a bigger, faster river or a wider mouth spreads the same tidal volume thinner, so the front barely steepens. The speed term is the classic shallow-water gravity-wave relation c = √(g·h): taller bores are intrinsically faster, exactly as on the real river.
- Tidal range — the incoming ocean tide's amplitude; the main driver of bore height.
- River discharge — the river's own outflow, which resists and flattens the incoming front.
- Channel width — a narrower estuary mouth concentrates the same tidal volume into a taller front.
- Trigger spring tide — launches the bore from the river mouth so you can watch it run upstream in real time; orbit-drag the scene to follow it from any angle.