Numerical evidence of persisting surface roughness when deposition stops

Do evolving surfaces become flat or not with time evolving when material deposition stops? As one qualitative exploration of this interesting issue, modified stochastic models for persisting roughness have been proposed by Schwartz and Edwards (2004 Phys. Rev. E 70 061602). In this work, we perform numerical simulations on the modified versions of Edwards–Wilkinson (EW) and Kardar–Parisi–Zhang (KPZ) systems when the angle of repose is introduced. Our results show that the evolving surface always presents persisting roughness during the flattening process, and sand dune-like morphology could gradually appear, even when the angle of repose is very small. Nontrivial scaling properties and differences of evolving surfaces between the modified EW and KPZ systems are also discussed.

Cahn–Hilliard equations on an evolving surface

We describe a functional framework suitable to the analysis of the Cahn–Hilliard equation on an evolving surface whose evolution is assumed to be given a priori. The model is derived from balance laws for an order parameter with an associated Cahn–Hilliard energy functional and we establish well-posedness for general regular potentials, satisfying some prescribed growth conditions, and for two singular non-linearities – the thermodynamically relevant logarithmic potential and a double-obstacle potential. We identify, for the singular potentials, necessary conditions on the initial data and the evolution of the surfaces for global-in-time existence of solutions, which arise from the fact that integrals of solutions are preserved over time, and prove well-posedness for initial data on a suitable set of admissible initial conditions. We then briefly describe an alternative derivation leading to a model that instead preserves a weighted integral of the solution and explain how our arguments can be adapted in order to obtain global-in-time existence without restrictions on the initial conditions. Some illustrative examples and further research directions are given in the final sections.

A bird's-eye view on turbulence: seabird foraging associations with evolving surface flow features

Understanding physical mechanisms underlying seabird foraging is fundamental to predict responses to coastal change. For instance, turbulence in the water arising from natural or anthropogenic structures can affect foraging opportunities in tidal seas. Yet, identifying ecologically important localized turbulence features (e.g. upwellings approximately 10–100 m) is limited by observational scale, and this knowledge gap is magnified in volatile predators. Here, using a drone-based approach, we present the tracking of surface-foraging terns (143 trajectories belonging to three tern species) and dynamic turbulent surface flow features in synchrony. We thereby provide the earliest evidence that localized turbulence features can present physical foraging cues. Incorporating evolving vorticity and upwelling features within a hidden Markov model, we show that terns were more likely to actively forage as the strength of the underlying vorticity feature increased, while conspicuous upwellings ahead of the flight path presented a strong physical cue to stay in transit behaviour. This clearly encapsulates the importance of prevalent turbulence features as localized foraging cues. Our quantitative approach therefore offers the opportunity to unlock knowledge gaps in seabird sensory and foraging ecology on hitherto unobtainable scales. Finally, it lays the foundation to predict responses to coastal change to inform sustainable ocean development.

Supplemental Material: Time-evolving surface and subsurface signatures of Quaternary volcanism in the Cascades Arc

Additional description of the datasets, analyses, and results presented in this study.<br>

Supplemental Material: Time-evolving surface and subsurface signatures of Quaternary volcanism in the Cascades Arc

Additional description of the datasets, analyses, and results presented in this study.<br>