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A force density is force per unit volume, measured in $\mathrm{N}{\mathrm{m}}^{-3}$. Pressure gradients, the divergence of a viscous stress and gravitational body force have this dimension in a local momentum balance.

Subtract the background hydrostatic pressure. A relief amplitude $h$ produces a restoring pressure perturbation $p^{\prime }\sim \rho gh$ and horizontal gradient $\rho gh/\lambda$. Incompressibility makes the disturbance penetrate a depth of order its horizontal scale. For sinusoidal viscous rebound, with relaxation speed $v\sim h/\tau$, the viscous force density is $\eta v/{\lambda }^2$. Balancing givesThis is a small-amplitude viscous half-space estimate; numerical factors from the sinusoidal geometry are absent from a scaling argument.

Unsteady inertial force density scales as $\rho v/\tau$, whereas viscous force density scales as $\eta v/{\lambda }^2$. Using the preceding timescale givesConvective inertia has ratio $\rho v\lambda /\eta$. Since $v\sim h/\tau$, this is smaller by $h/\lambda$ for small relief. Thus the displayed estimate controls the larger inertial contribution in this model.