Dice Question Streamline Icon: https://streamlinehq.com

Steady-state selection following grounding-line transitions

Determine, in scenarios where grounding-line movement converts a system from having a unique steady state to having multiple steady states, which of the available steady states is selected by the transient solution of the complementarity formulation for groundwater flow and seawater intrusion beneath a marine ice sheet, as a function of the dimensionless hydraulic conductivity K and the intervening time-dependent forcing.

Information Square Streamline Icon: https://streamlinehq.com

Background

The authors consider time-dependent forcing where grounding-line motion can change the number and type of steady states admitted by the model. They highlight that this can lead to disparate final outcomes—pocket or non-pocket states—depending on the evolution path and hydraulic properties.

They explicitly state that the selection among multiple steady states under such transitions is unclear, motivating the need to characterize the dependence of the final state on parameters like K and the trajectory of the forcing.

References

If grounding line movement brings about a change from a system with a unique steady state to one with multiple steady states, it is unclear towards which of the new available steady states the solution of Eq. eq:comp will relax.

eq:comp:

H−h−h+K[hpS+S+δs]=0,−h+K[hpS+S+δs]≥0,H−h≥0.\begin{aligned} {H-h}{- h + K \left[ h { p_S + S + \delta s} \right] } = 0 ,\\ - h + K \left[ h { p_S + S + \delta s} \right] \geq 0 ,\\ H-h \geq 0. \end{aligned}

— Groundwater dynamics beneath a marine ice sheet (2409.11848 - Cairns et al., 18 Sep 2024) in Section 4.3 (Pocket creation by grounding line advance)