Ice-dammed lakes form next to, on the surface of, and beneath glaciers
and ice sheets. Some lakes are known to drain catastrophically,
creating hazards, wasting water resources and modulating the flow of
the adjacent ice. My work aims to increase our understanding of such
drainage. Here I will focus on lakes that form next to glaciers and
drain subglacially (between ice and bedrock) through a channel. I will
describe how such a system can be modelled and present results from
model simulations of a lake that fills due to an input of meltwater
and drains through a channel that receives a supply of meltwater along
its length. Simulations yield repeating cycles of lake filling and
drainage and reveal how increasing meltwater input to the system
affects these cycles: enlarging or attenuating them depending on how
the meltwater is apportioned between the lake and the channel. When
inputs are varied with time, simulating seasonal meteorological
cycles, the model simulates either regularly repeating cycles or
irregular cycles that never repeat. Irregular cycles demonstrate
sensitivity to initial conditions, a high density of periodic orbits
and topological mixing. I will discuss how these results enhance our
understanding of the mechanisms behind observed variability in these
systems.