Side view of a fire plume carrying glowing embers upward until they hover and drift, with plume-speed and landing graphs.
The science
A fire is a point source of buoyancy. Its convective heat Q_c (70 % of the output) gives the buoyancy flux F = g Q_c / (rho_0 c_p T_0). In the classic Morton-Taylor-Turner plume the air entrained at rate alpha makes the plume widen as b = 6 alpha z / 5, while its centreline speed and temperature fall as w = (5 / 6 alpha) (9 alpha F / 10)^(1/3) z^(-1/3) and dT ~ z^(-5/3).
A glowing ember is a small sphere with quadratic drag a = -(3 rho_a Cd / 4 rho_e d) |v_rel| v_rel - g. It is carried upward while the plume speed exceeds its terminal speed v_t = sqrt(4 g d rho_e / 3 Cd rho_a) and hovers where w(z) = v_t; fine, light embers hover high and drift far in a wind. With a crosswind the plume axis bends along the parcel path x = 3 U z^(4/3) / (4 C).
Simplifications: steady, axisymmetric point-source plume in still, uniform air (no stratification), Gaussian cross-profile, a constant drag coefficient of 1, embers burn down linearly to 35 % of their diameter in 45 s (so they eventually descend and land), no other combustion physics, and random turbulent kicks standing in for eddies. This is educational physics, not a fire-spread prediction tool.