= Melting-driven saline wall plume
{title2=$b=3\varepsilon Z/4,\quad w=[4g\beta_CU(C_\infty-C_s)/(5\varepsilon)]^{1/3}Z^{1/3}$}
A glacier supplies fresh meltwater at speed $U>0$ to a rising <wall line plume> whose buoyancy is dominated by <salinity>. With one entraining edge, <entrainment coefficient> $\varepsilon$, <volume flux> $Q=bw$ and negligible wall stress, $Q'=\varepsilon w+U$ and $(bw^2)'=g\beta_C(C_\infty-C)b$. Enthalpy and salt balances give $[Q(T_\infty-T)]'=U[L/c_p+T_\infty-T_s]$ and $[Q(C_\infty-C)]'=U(C_\infty-C_s)$. If latent heat dominates and entrainment dominates the volume supply, integration from a virtual origin $Z=0$ and power-law balance give the displayed width and speed. The temperature and salinity deficits are $ULZ/(c_pQ)$ and $U(C_\infty-C_s)Z/Q$, both proportional to $Z^{-1/3}$. The approximation is a far-field plume solution, not a solution at the virtual origin.
Back to article page
