A new study published in Ocean Dynamics by Feidong Zheng of PowerChina Kunming Engineering Corporation Limited and colleagues, including researchers at Nanjing Hydraulic Research Institute and Nanjing University of Information Science and Technology, now offers a predictive framework that spans the full spectrum of wave energy. The work extends the team’s earlier high-energy investigations with a fresh set of controlled laboratory experiments focused specifically on low-energy responses, allowing the researchers to stitch the two regimes into one coherent model. The result is a suite of equations that predicts not only how tall the waves will be, but how they attenuate with distance, how their periods and wavelengths evolve through dispersion, and how the energy of the collapsing granular mass is transferred into the water.

The physics of the problem is deceptively intricate. A subaerial granular landslide is not a rigid block; it is a porous, deformable collection of grains that disintegrates as it slides, impacts the free surface, and continues to move underwater. The wave that emerges depends on the slide’s volume, velocity, thickness, and impact angle, as well as the water depth and the geometry of the reservoir. Classical approaches, such as the widely used model of Heller and Hager developed at ETH Zurich, condense these variables into an impulse product parameter that captures the strength of the landslide impact. That framework has proven robust for the largest, most energetic waves, but its performance for gentler, Stokes-like waves, in which the free surface oscillates in a nonlinear but still wave-like fashion, had not been systematically tested.

Zheng and his co-authors began by doing exactly that: validating the Heller and Hager model against their new low-energy data across the entire energy spectrum. The model held up remarkably well. For maximum wave height, the mean deviation between prediction and measurement was about 15 percent, a figure the authors describe as confirming the reliability of the classical formulation from the weakest oscillatory responses up to the most violent surges. In practical terms, this means engineers can continue to use the established height model with confidence, knowing it does not silently fail when a landslide is smaller or slower than the laboratory benchmarks on which it was originally calibrated.

But wave height alone does not tell the whole hazard story. The maximum amplitude, the single highest excursion of the water surface above still-water level, is often the quantity that determines whether a wave overtops a dam or floods a shoreline bench. Here the team went beyond validation and derived a novel maximum amplitude model of their own, and the improvement is striking: prediction errors fell to 7.80 percent, roughly half the deviation of the height model. The tighter fit is not merely a statistical achievement. The new equation is consistent with a specific physical interpretation of how Stokes-like waves are born, namely that the vertical, kinematic displacement of the free surface, driven by the slide pushing water upward and outward at the impact zone, dictates amplitude generation, rather than the deep transfer of mass momentum through the water column.

That distinction matters because it changes how one thinks about the hazard. If amplitude were controlled by bulk momentum injected deep into the water, then the mass and submerged motion of the landslide would dominate, and mitigation strategies would focus on the underwater runout. If instead the kinematic free-surface displacement is the governing mechanism, as the new model suggests for Stokes-like regimes, then the geometry and speed of the slide at the moment it crosses the shoreline become the critical controls. The authors’ laboratory observations support the latter picture, giving hazard assessors a clearer target for the parameters that most influence the worst-case water-surface excursion near the impact site.

The framework does not stop at the wave crest. Zheng and colleagues developed type-specific governing equations for wave attenuation, describing how the impulse waves lose height as they propagate away from the impact zone, and for the dispersive evolution of wave period and wavelength, capturing how an initially impulsive disturbance stretches into a longer, more regular wave train as frequency components separate with distance. These propagation characteristics are essential for translating a near-field measurement or prediction into an estimate of what a wave will look like when it reaches a dam face or a lakeside community kilometers downstream. A wave that is modest at the source may still carry dangerous energy if its period lengthens in a way that resonates with the geometry of a narrow reservoir arm.

Perhaps the most conceptually interesting component is the team’s energy model, which captures what the authors call mass-dependent momentum coupling. In their experiments, the porous granular mass does not behave as an impermeable piston. Instead, water can percolate into and through the disintegrating slide, and the granular skeleton buffers the interaction between the solid and fluid phases. The model demonstrates physically how this buffering regulates the efficiency of energy transfer from the landslide to the water: a highly porous, rapidly disintegrating mass dissipates more of its kinetic energy internally and in grain-fluid friction, delivering less to the wave, while a denser, more coherent mass couples its momentum more effectively into the free surface. This provides a mechanistic explanation for why granular landslides of equal volume and speed can produce markedly different waves depending on their internal structure and grain-size distribution.

The experimental campaign behind these results sits within a broader body of work by the same group, which has previously examined impulse waves across a broad spectrum of grain diameters, waves generated by subaerial cylinders, and the influence of rigid vegetation on wave characterization, as well as numerical simulations using coupled smoothed particle hydrodynamics and discrete element methods. By anchoring the new low-energy experiments to that earlier high-energy dataset, the authors avoid the common pitfall of building a model that fits one regime beautifully and another not at all. The unified framework is explicitly empirically derived, meaning its coefficients come from measurement rather than assumption, yet each equation carries an explicit physical interpretation, a combination that should make it easier for practitioners to judge when the model can be extrapolated and when it cannot.

For reservoir operators and geohazard agencies, the practical payoff is a set of tools that can be applied across the full range of plausible landslide scenarios, from small rockfalls that generate gentle oscillations to large collapses that launch near-field surges. The research was supported by Yunnan Fundamental Research Projects, a POWERCHINA Science and Technology Project, and Yunnan’s Technology Innovation Center for Digital Water Engineering, reflecting the acute relevance of landslide-generated waves to the hydropower reservoirs of southwestern China, where steep terrain, seismicity, and monsoonal loading keep slopes in a state of perpetual tension with the water below. With validated height predictions, a high-accuracy amplitude model, propagation and dispersion equations, and an energy-transfer framework grounded in the physics of granular porosity, the study moves the field closer to the long-sought goal of a single, trustworthy forecast: given a landslide on the slope, how big will the wave be, how fast will it decay, and how much of the slide’s energy will the reservoir ultimately absorb.

Subject of Research: Predictive modeling of impulse waves generated by subaerial granular landslides in reservoirs

Article Title: Unified predictive framework for subaerial granular landslide-generated stokes-like waves across energy regimes

Article References: Zheng, F., Liu, Q., Xue, Z., Li, C., Yang, Y., Yao, C., Huang, T., Liu, G., Xu, J., & Lin, X. (2026). Unified predictive framework for subaerial granular landslide-generated stokes-like waves across energy regimes. Ocean Dynamics, 76(10), Article 104. https://doi.org/10.1007/s10236-026-01862-z

Image Credits: AI Generated

DOI: 10.1007/s10236-026-01862-z

Keywords: landslide-generated impulse waves, Stokes-like waves, subaerial landslides, reservoir geohazards, wave amplitude prediction, wave attenuation, energy conversion, granular flows, laboratory experiments, Heller and Hager model, Ocean Dynamics, hazard assessment