= Far-downslope width of a constant-flux porous current
{title2=$Y_N\propto X^{\beta/(2\beta+1)}$}
In a slender steady <porous gravity current>, the dominant balance is $(h^\beta)_X=(h^\beta h_Y)_Y$. If its width and height scales are $W,H$, fixed downslope <volume flux> gives $H^\beta W=\text{constant}$, and transverse spreading gives $W^2\sim HX$. Eliminating $H$ yields the displayed width exponent. The porosity exponent affects transient storage but not this steady balance.
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