 Horizontal forced-plume trajectory

For zero source volume flux, constant Batchelor entrainment, and a horizontal source, the near-source trajectory is cubic: $z\sim \alpha \sqrt{\pi }{f}_0{x}^3/(3m_0^{3/2})$. Far from the source the centreline approaches a vertical asymptote, with its horizontal distance from that asymptote proportional to $z^{-1/3}$.