Presets
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Apparatus
Model checks
The science
What is modelled
Hot, light fluid from the vents rises as a turbulent plume and mixes in the surrounding water at a rate proportional to its speed. Because deep ocean water is stratified (denser with depth) the plume loses its buoyancy as it entrains heavier water, overshoots, and finally spreads at its own density level.
Equations
- Volume flux Q, momentum flux M, buoyancy flux F:
dQ/dz = 2α√(πM),dM/dz = QF/M,dF/dz = −N2Q. - Buoyancy flux of a heat flux H:
F = g αT H / (ρ cp). - Rise height scaling
zmax = C F1/4 N−3/4, with C found from the integration. - Pure plume (N = 0):
w = (5/6α)(9αF/10π)1/3 z−1/3,b = 6αz/5.
Checks run in the page
- The integrated plume against the pure-plume similarity solution.
- The scaling of the rise with F and N.
- The neutral height against the top of the rise.
- The heat to buoyancy conversion and the entrained volume budget.
Honest simplifications
The model is the classic top-hat plume with a constant entrainment coefficient, uniform stratification, no background current, a single point source and a fixed thermal expansion coefficient. Real vent plumes are bent over by currents and carry particles, and the equation of state of seawater is nonlinear.
What to try
- Press Strong stratification and see the plume stop much lower.
- Press Nearly uniform water and watch it climb much higher.
- Use the last graph to see that a hundred-fold heat flux only triples the rise.