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Home Science News Mathematics

Scientists Investigate Whether Motion Is Subsonic or Supersonic

August 5, 2026
in Mathematics
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Scientists Investigate Whether Motion Is Subsonic or Supersonic

Scientists Investigate Whether Motion Is Subsonic or Supersonic

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A crack racing through a snowpack may appear to break the laws of fracture mechanics. In some avalanche scenarios, researchers have reported evidence suggesting that the fracture front can travel faster than the limiting wave speed predicted for the material. Such a “supersonic” crack would release energy with extraordinary speed, potentially increasing the destructive power of an avalanche. Yet a new theoretical study argues that the apparent paradox may arise because snow is not a single, uniform material. Instead, it is a complex stack of layers, each with its own stiffness, density and strength.

The study, led by Nicola Pugno, Full Professor of Solids and Structural Mechanics at the University of Trento, examines why avalanche cracks may sometimes appear to propagate faster than expected. The work addresses a long-running debate in avalanche science and fracture mechanics. Some numerical simulations and experiments have indicated that cracks responsible for slab avalanches can reach supershear or supersonic speeds. Other studies have interpreted the same phenomenon differently, suggesting that the crack remains locally subsonic even if its overall motion appears to exceed the classical limit.

That classical limit is usually calculated by treating the material as homogeneous and describing how mechanical disturbances travel through it. In a uniform solid, a rapidly advancing crack is constrained by the speeds of elastic waves moving through the material. The Rayleigh wave speed, associated with surface motion, is commonly used as an important reference for crack propagation, while shear-wave speed provides another upper benchmark in fracture dynamics. A crack moving below the relevant limit is described as sub-Rayleigh; one that exceeds the shear-wave speed may be classified as supershear. Snow, however, does not behave like the idealized solid assumed by these definitions.

A snowpack is built from successive layers formed under changing weather conditions. Fresh, low-density snow may sit above a dense slab, while a fragile layer of faceted crystals or depth hoar can separate the slab from the underlying snow. The mechanical properties of each layer can differ dramatically. Stiffness, density, porosity and bonding determine how stress is transmitted and how energy is released. A fracture may therefore move through the slab, along a weak layer, or across the interface between them, encountering a changing mechanical environment rather than one universal wave-speed limit.

Pugno’s analytical approach focuses on this layered structure and identifies a transition between two fracture regimes. In one regime, the crack is governed mainly by the snow slab that detaches during the avalanche. In the other, it is controlled by the weak layer or by the interface along which the fracture travels. This distinction is crucial because the local material governing the crack may be stiffer than the snowpack considered as a whole. A crack can consequently appear to move at a globally supersonic speed when measured against the average properties of the snowpack, while remaining locally subsonic relative to the layer or interface immediately controlling its motion.

The mechanism can be understood through the way energy is concentrated around a moving crack tip. Fracture propagation depends not only on the total energy available in the structure, but also on the length scale over which that energy is transferred and dissipated. The study uses a characteristic energy length previously introduced to describe the transition between the two propagation regimes. In a multilayered snowpack, this length helps determine whether the slab dominates the fracture process or whether the weak layer and its interface take control. The result offers a possible explanation for why different studies have reached apparently contradictory conclusions about avalanche crack speeds.

The findings do not prove that every avalanche crack is genuinely supersonic, nor do they eliminate the possibility of supershear fracture under particular conditions. Instead, they suggest that the answer depends on the snowpack’s layering, mass and mechanical contrasts. A crack that looks supershear from a large-scale perspective may not be violating the local physics of fracture. The distinction between global and local propagation speeds could reconcile observations of unusually rapid cracks with classical mechanics, while still leaving open the possibility that certain configurations support truly faster-than-shear propagation.

The research appears as a Matter of Opinion article in Matter, a Cell Press journal, under the title “Sub-Rayleigh or supershear crack propagation in snow avalanches?” Pugno describes the work as a concise analytical contribution that builds on pioneering numerical studies by other mechanicians. He emphasizes that snow is not linearly elastic and that its constitutive laws remain uncertain. Those complications, combined with the snowpack’s layered architecture, make it difficult to apply simple models developed for engineered materials or uniform geological solids. More detailed theoretical, computational and experimental investigations will be needed to determine how closely real avalanches follow the proposed regimes.

Understanding the speed of avalanche fracture is more than an academic exercise. A faster release of stored energy could influence how quickly a slab detaches, how far the fracture front travels and how violently the snow mass begins to move. Those factors matter when engineers design avalanche barriers, protective structures and buildings exposed to mountain hazards. Improved models could eventually help forecast not only whether a slope is likely to fail, but also how the failure will spread through the snowpack. By treating snow as a dynamic layered material rather than a uniform block, the new theory may bring researchers closer to explaining one of avalanche science’s most striking questions: how a seemingly fragile crack can trigger a massive and rapidly accelerating collapse.

Subject of Research: Not applicable

Article Title: Sub-Rayleigh or supershear crack propagation in snow avalanches?

News Publication Date: 5-Aug-2026

Web References: https://doi.org/10.1016/j.matt.2026.102957

References: Matter, DOI: 10.1016/j.matt.2026.102957

Image Credits: ph. Luca Nervo

Keywords: snow avalanches, crack propagation, fracture mechanics, supershear cracks, sub-Rayleigh cracks, snowpack layering, weak layers, avalanche science, Nicola Pugno, structural mechanics

Tags: avalanche destructive potentialavalanche energy releaseavalanche fracture mechanicsavalanche research debatecomplex material behavior in snowfracture front speed in snowinfluence of snow heterogeneitylayered snow structure impactsnowpack layer propertiessubsonic versus supersonic crack speedsupershear crack propagationtheoretical models of crack propagation
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