= Solution
The <filling box model> requires the first outflow to spread across the enclosure and remain above unmodified fluid, while a narrow nearly vertical plume rises below it. Several mechanisms can defeat those assumptions. A tall narrow box makes the plume a substantial fraction of the width, so its compensating return <velocity> is no longer small and modifies both <fluid entrainment> and <momentum flux>. A fast ceiling current can descend the sidewalls and overturn the initially stable upper region. In both cases a horizontally uniform slowly descending <filling-box first front> is inappropriate. Strong plume displacement from the centre, imposed crossflow, large source volume, vents or substantial wall cooling likewise alter the volume and heat budgets.
A useful diagnostic is whether the ceiling outflow's inertial acceleration, of order $U_c^2/\ell_c$, overwhelms the restoring <buoyancy> of the nascent layer. If $U_c^2/(G_H d_c)$ is not small for its depth $d_c$, the outflow can penetrate or overturn the stratification rather than remain trapped above it. This is a diagnostic <Froude number>, not a universal threshold without specifying the wall-current geometry and mixing. Low <Reynolds number> invalidates a constant turbulent <entrainment coefficient>, and thermal diffusion or wall heat loss can erase the sharp first-front jump. Thus \b[large aspect ratio, strong return circulation, overturning, ventilation or diffusion require a model beyond the standard filling-box approximation].
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