= Non-Boussinesq triangular-profile line-plume balances
For a <triangular-profile line plume> with centreline density $\rho$, speed $W$, half-width $b$, ambient density $\rho_0$, and inward relative edge speed $e$, <volume>, <mass> and <momentum> conservation give
$$
(2b)_t+(bW)_z=2e,\quad [b(\rho+\rho_0)]_t+[bW(\rho_0+2\rho)/3]_z=2\rho_0e,
$$
$$
[bW(\rho_0+2\rho)/3]_t+[bW^2(\rho_0+3\rho)/6]_z=gb(\rho_0-\rho).
$$
Subtracting <mass conservation> from $\rho_0$ times <volume> conservation also gives buoyancy conservation. <Batchelor entrainment> supplies a closure for $e$.
Back to article page
