Open Access

The paper is devoted to the simulation of maritime two-phase flows of air and water. Emphasis is put on an extension of the classical Volume-of-Fluid (VoF) method by a diffusive contribution derived from a Cahn-Hilliard (CH) model and its benefits for simulating immiscible, incompressible two-phase flows. Such flows are predominantly simulated with implicit VoF schemes, which mostly employ heuristic downwind-biased approximations for the concentration transport to mimic a sharp interface. This strategy introduces a severe time step restriction and requires pseudo time-stepping of steady flows. Our overall goal is a sound description of the free-surface region that alleviates artificial time-step restrictions, supports an efficient and robust upwind-based approximation framework, and inherently includes surface tension effects when needed. The Cahn-Hilliard Navier-Stokes (CH-NS) system is verified for an analytical Couette-flow example and the bubble formation under the influence of surface tension forces. 2D validation examples are concerned with laminar standing waves reaching from gravity to capillary scale as well as a submerged hydrofoil flow. The final application refers to the 3D flow around an experimentally investigated container vessel at fixed floatation for Re = 1.4 × 10 7 and Fn = 0.26. Results are compared with data obtained from VoF approaches, supplemented by analytical solutions and measurements. The study indicates the superior efficiency, resharpening capability, and wider predictive realm of the CH-based extension for free-surface flows with a confined spatial range of interface Courant numbers.

In recent decades, severe declines in biodiversity have been observed globally, with agricultural intensification being one of the key drivers. However, the abandonment of traditional land-use practices may also negatively affect diversity. Setting aside steep-slope vineyards, driven by heavy workloads and diminishing profitability, may pose a major challenge to biodiversity conservation and related ecosystem services in Germany. Here, we compare ground-dwelling beetle taxonomic and functional diversity across four management categories: (1) conventionally managed vineyards, (2) set-aside vineyards that are now managed as grazed grasslands, (3) set-aside vineyards that are now managed as mown grasslands, and (4) vineyard fallows. Using pitfall traps, we examined 10 sites per management category along the Upper Middle Rhine Valley in southwestern Germany. We show that conventionally managed vineyards and grazed grasslands exhibited the highest species richness, taxonomic and functional diversity, while fallows showed strongly reduced values. The same applies to the ‘conservation value’ of beetle assemblages, being highest on conventionally managed vineyards and grazed grasslands but lowest on fallows. Especially open landscape and xerothermic beetle species were negatively affected by abandonment. Beetle diversity was additionally affected by landscape composition, with (semi)-natural habitats having positive effects. Thus, our findings suggest that conventionally managed vineyards can provide valuable habitats for taxonomically and functionally diverse ground beetle communities, and that grazing represents an appropriate alternative for set-aside sites. Implications for insect conservation Our results show that some sort of management is important to halt secondary succession in xerothermic landscapes to preserve landscape heterogeneity and promote ground-dwelling beetle diversity. To this end, grazing seems to be especially suitable.

Hildegard von Bingen articulated a wide range of reflections on the nature and activity of the Holy Spirit. Her statements concerning His nature address both the Holy Spirit in Himself and His identity as the third divine Person of the Trinity. Regarding His activity, Hildegard emphasizes the Holy Spirit’s continuous creative work as well as His action in relation to humanity, including His involvement in the life and mission of the Church. This article brings together and systematizes the central aspects of these thematic areas. On this basis, it draws valuable conclusions for both the content of faith and the act of faith. Regarding the content of faith, the article demonstrates how Hildegard’s writings enrich pneumatological understanding in diverse and vivid ways. With respect to the act of faith, the analysis yields both general insights pertinent to lived faith and concrete implications for the fundamental practices of the Church.