Uniqueness for SQG patch solutions

This paper is about the evolution of a temperature front governed by the surface quasi-geostrophic equation. The existence part of that program within the scale of Sobolev spaces was obtained by the third author (2008). Here we revisit that proof introducing some new tools and points of view which allow us to conclude the also needed uniqueness result.Ministerio de Economía y CompetitividadJunta de AndalucíaEuropean Research Counci

The Rayleigh-Taylor condition for the evolution of irrotational fluid interfaces

For the free boundary dynamics of the two-phase Hele-Shaw and Muskat problems, and also for the irrotational incompressible Euler equation, we prove existence locally in time when the Rayleigh-Taylor condition is initially satisfied for a 2D interface. The result for water waves was first obtained by Wu in a slightly different scenario (vanishing at infinity), but our approach is different because it emphasizes the active scalar character of the system and does not require the presence of gravity.Ministerio de Educación y CienciaEuropean Research Counci

Interface evolution: water waves in 2-D

We study the free boundary evolution between two irrotational, incompressible and inviscid fluids in 2-D without surface tension. We prove local-existence in Sobolev spaces when, initially, the difference of the gradients of the pressure in the normal direction has the proper sign, an assumption which is also known as the Rayleigh-Taylor condition. The well-posedness of the full water wave problem was first obtained by S. Wu. Well-posedness in Sobolev spaces of the full water wave problem in 2-D. Invent. math. 130, 39-72, 1997. The methods introduced in this paper allows us to consider multiple cases: with or without gravity, but also a closed boundary or a periodic boundary with the fluids placed above and below it. It is assumed that the initial interface does not touch itself, being a part of the evolution problem to check that such property prevails for a short time, as well as it does the Rayleigh-Taylor condition, depending conveniently upon the initial data. The addition of the pressure equality to the contour dynamic equations is obtained as a mathematical consequence, and not as a physical assumption, from the mere fact that we are dealing with weak solutions of Euler’s equation in the whole space.Ministerio de Educación y CienciaMinisterio de Ciencia e InnovaciónEuropean Research Counci

Porous media: the Muskat problem in 3D

The Muskat problem involves filtration of two incompressible fluids throughout a porous medium. In this paper we shall discuss in 3-D the relevance of the RayleighTaylor condition, and the topology of the initial interface, in order to prove its local existence in Sobolev spaces.Ministerio de Ciencia e InnovaciónEuropean Research CouncilNational Science Foundatio

A maximum principle for the Muskat problem for fluids with different densities

We consider the fluid interface problem given by two incompressible fluids with different densities evolving by Darcy’s law. This scenario is known as the Muskat problem for fluids with the same viscosities, being in two dimensions mathematically analogous to the two-phase Hele-Shaw cell. We prove in the stable case (the denser fluid is below) a maximum principle for the L∞ norm of the free boundary.Ministerio de Educación y CienciaJunta de Castilla-La Manch

Contour dynamics of incompressible 3-D fluids in a porous medium with different densities

We consider the problem of the evolution of the interface given by two incompressible fluids through a porous medium, which is known as the Muskat problem and in two dimensions it is mathematically analogous to the two-phase Hele-Shaw cell. We focus on a fluid interface given by a jump of densities, being the equation of the evolution obtained using Darcy’s law. We prove local well-posedness when the smaller density is above (stable case) and in the unstable case we show ill-posedness

Biocorrosion of Carbon Steel under Controlled Laboratory Conditions

In the Iberian Pyritic Belt (SW Europe), Acid Mine Drainage (AMD) is the consequence of the interaction of physical-chemical and biological factors, where aerobic Fe and/or S oxidizing chemolithotrophic and anaerobic sulfate reducing bacteria play an essential role. As a result, the polluted waters are highly acidic (pH 2–3) and contain numerous dissolved or suspended metals, which gives them a powerful corrosive action on constructions related to mining activities with high economic losses. To verify the role of bacteria in the corrosion of carbon steel, a common material in buildings exposed to corrosion in acidic waters, several experiments have been carried out under controlled conditions using carbon steel bars and acidic water containing bacteria consortia from an AMD river of the Iberian Pyritic Belt. In all the experiments carried out, a remarkable oxidation of supplemented iron was observed in the presence of bacteria. Using carbon steel as the sole iron source, we observed a slight corrosion of the bars, but when culture media was supplemented with elemental sulfur, steel bars was severely damaged. Since the bacteria inoculum come from the surface water, well oxygenated, nutrient-poor river, the obtained results are discussed based on facultative metabolism of acidophilic chemolithotrophic bacteria.This research was funded by Ministry of Science and Innovation (Spain), grant number PID2021-123130OBI0

Lack of uniqueness for weak solutions of the incompressible porous media equation

In this work we consider weak solutions of the incompressible 2-D porous media equation. By using the approach of De Lellis-Sz´ekelyhidi we prove non-uniqueness for solutions in L∞ in space and time.Ministerio de Ciencia e InnovaciónEuropean Research CouncilNational Science Foundatio

Fishways as downstream routes in small hydropower plants: Experiences with a potamodromous cyprinid

Producción CientíficaFish need to move upstream and downstream through rivers to complete their life cycles. Despite the fact that fishways are the most commonly applied solution to recover longitudinal connectivity, they are not considered viable for downstream migration. Therefore, alternative facilities are recommended to facilitate downstream migration. However, a few recent studies have disagreed with this general assumption, showing the potential for bidirectional movements. This study advances our understanding of the potential of fishways for downstream migration by studying their efficiency in a run-of-the-river hydropower plant in the Duero River (Spain). To achieve this, downstream movements of the Iberian barbel (n = 299) were monitored in a stepped fishway for two years with passive integrated transponder (PIT)-tag technology, considering the effect of fish origin and release zone. The results showed that 24.9% of barbels descended through the fishway, with the origin and release zone affecting the fishway location. In addition, downstream movements were observed throughout the whole year, except in winter. The study concludes that, under specific scenarios, fishways could act as safe alternative routes for downstream migration.Unión Europea H2020 - (grant 727830)Ayudas Torres Quevedo - (grants PTQ2018-010162 and PTQ2016-08494)Universidad de Valladolid - (grant PIF-UVa 2017