= Lake-coupled Röthlisberger drainage instability
{title2=$S_t=S^{4/3}-SN^3,\quad N_t=S^{4/3}-\mu$}
A lake supplies a melt-opened subglacial channel while its changing hydrostatic head changes <effective pressure in subglacial drainage>[effective pressure] and <material creep> closure. In the displayed scaled model the positive <equilibrium> is $S=\mu^{3/4}$, $N=\mu^{1/12}$. Its <Jacobian matrix>[Jacobian] has <matrix trace>[trace] $\mu^{1/4}/3>0$ and <determinant> $4\mu^{7/6}$. The instability becomes oscillatory when $\mu>1/1728$. Growing linear <oscillations> signal departure from steady drainage; they do not prove unbounded physical lake discharge after nonlinear effects and lake depletion become important.
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