Related Experiment Video
Updated: May 17, 2026

06:27
Simulating Impacts of Ice Storms on Forest Ecosystems
Published on: June 30, 2020
Chaotic variability in a model of coupled ice streams
Kolja Kypke1,2, Peter Ashwin3, Peter Ditlevsen2
1University of Guelph, Department of Mathematics and Statistics, Guelph, Canada.
Physical Review. E
|May 16, 2026
Summary
Ice streams, fast-flowing regions in ice sheets, can oscillate between build-up and surge phases due to basal thermomechanical coupling. A new model demonstrates this variability can become chaotic in branching ice stream systems.
Area of Science:
- Glaciology
- Ice sheet dynamics
- Climate science
Background:
- Ice streams are critical components of ice sheets, influencing global sea levels.
- Theories suggest basal conditions can drive oscillatory behavior in ice streams.
- Understanding ice stream dynamics is key to predicting ice sheet response to climate change.
Purpose of the Study:
- To investigate the potential for build-up/surge oscillations in coupled ice stream models.
- To explore the occurrence of chaotic variability in these systems.
- To replicate the configuration of branching ice streams found in Greenland.
Main Methods:
- Development of a simple three-coupled ice stream model.
- Simulation of thermomechanical coupling at the ice-bed interface.
- Analysis of model output for steady-flow and oscillatory behaviors, including chaotic dynamics.
Main Results:
- The model successfully replicates steady-flow conditions.
- The model exhibits build-up/surge oscillatory variability.
- Chaotic variability was observed due to nonlinear coupling of incommensurate frequencies.
Conclusions:
- Branching ice stream configurations can exhibit internal chaotic variability.
- Thermomechanical coupling at the base of ice streams can drive complex dynamic behaviors.
- This study provides a mechanism for chaotic internal variability within ice sheets.
Related Concept Videos
Rapidly Varying Flow
Rapidly varying flow (RVF) in open channels is characterized by abrupt changes in flow depth over a short distance, with the rate of depth change relative to distance often approaching unity. These flows are inherently complex due to their transient and multi-dimensional nature, making exact analysis difficult. However, approximate solutions using simplified models provide valuable insights into their behavior.Key Features of Rapidly Varying FlowRVF is commonly observed in scenarios involving...
Gradually Varying Flow
Gradually varying flow (GVF) in open channels describes situations where water depth changes slowly along the channel due to factors like non-uniform bed slope, channel shape variations, or obstructions. This flow type occurs when the depth adjusts gradually to balance gravitational forces, shear forces, and energy requirements, resulting in a low rate of depth change.Characteristics of Gradually Varying FlowGVF is commonly observed in natural streams, rivers, and canals, where flow depth...
Bernoulli's Equation for Flow Along a Streamline
Bernoulli's equation relates the energy conservation in a fluid moving along a streamline. The equation applies to incompressible and inviscid fluids under steady flow. For such a flow, Newton's second law is applied to a small fluid element, which experiences forces due to pressure differences, gravity, and velocity variations. The force balance leads to the following form of Bernoulli's equation:
Irrotational Flow
Irrotational flow is characterized by fluid motion where particles do not rotate around their axes, resulting in zero vorticity. For a flow to be irrotational, the curl of the velocity field must be zero. This imposes specific conditions on velocity gradients. For instance, to maintain zero rotation about the z-axis, the gradient condition:
Uniform Depth Channel Flow
Uniform depth channel flow keeps fluid depth consistent along channels such as irrigation canals. In natural channels, such as rivers, approximate uniform flow is often assumed. This condition occurs when the channel’s bottom slope matches the energy slope, balancing potential energy lost from gravity with head loss due to shear stress. This balance prevents depth changes along the channel length, resulting in a steady, uniform flow.Uniform flow in open channels with a constant cross-section...
Uniform Depth Channel Flow: Problem Solving
To calculate the flow rate for a trapezoidal channel, first, identify the bottom width, side slope, and flow depth of the channel. The cross-sectional area (A) corresponding to the depth of flow (y), channel bottom width (B), and side slope (θ) is determined by:Next, calculate the wetted perimeter, which includes the bottom width and the sloped side lengths in contact with the water. Using the values of the cross-sectional area and the wetted perimeter, determine the hydraulic radius by...

