= Outlet layer in a deep unconfined aquifer
Even when most of an <unconfined aquifer with depth-dependent permeability> is deep, its height vanishes at an absorbing outlet. Near that outlet, finite outward <volume flux per unit width> $Q$ gives $u_bhh_x\simeq Q$ and hence $h\simeq(2Qx/u_b)^{1/2}$. The high-depth outer approximation instead has $h\simeq[6Qx/(u_b\beta)]^{1/3}$. Their crossover lies at height of order $1/\beta$ and distance of order $u_b/(\beta^2Q)$; the thin inner <boundary layer> transmits the same leading discharge.
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