= Rigid-lid approximation
{title2=$\nabla_h\cdot\mathbf u=0\quad(H=\mathrm{constant})$}
= Rigid lid
{synonym}
The rigid-lid approximation suppresses <free surface> displacement in a fluid layer while retaining a variable pressure that enforces the mass constraint. At constant depth it gives horizontally nondivergent motion. In a one-layer <quasi-geostrophic approximation>, removing free-surface stretching eliminates the $-\psi/R_D^2$ term from <shallow-water quasi-geostrophic potential vorticity>. This is also the small-horizontal-scale limit compared with the <Rossby deformation radius>, when that term is negligible rather than exactly absent.
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