Analytical continuum mechanics \`a la Hamilton-Piola: least action principle for second gradient continua and capillary fluids

In this paper a stationary action principle is proven to hold for capillary fluids, i.e. fluids for which the deformation energy has the form suggested, starting from molecular arguments, for instance by Cahn and Hilliard. Remark that these fluids are sometimes also called Korteweg-de Vries or Cahn-Allen. In general continua whose deformation energy depend on the second gradient of placement are called second gradient (or Piola-Toupin or Mindlin or Green-Rivlin or Germain or second gradient) continua. In the present paper, a material description for second gradient continua is formulated. A Lagrangian action is introduced in both material and spatial description and the corresponding Euler-Lagrange bulk and boundary conditions are found. These conditions are formulated in terms of an objective deformation energy volume density in two cases: when this energy is assumed to depend on either C and grad C or on C^-1 and grad C^-1 ; where C is the Cauchy-Green deformation tensor. When particularized to energies which characterize fluid materials, the capillary fluid evolution conditions (see e.g. Casal or Seppecher for an alternative deduction based on thermodynamic arguments) are recovered. A version of Bernoulli law valid for capillary fluids is found and, in the Appendix B, useful kinematic formulas for the present variational formulation are proposed. Historical comments about Gabrio Piola's contribution to continuum analytical mechanics are also presented. In this context the reader is also referred to Capecchi and Ruta.Comment: 52 page

Modeling the Offshore Export of Subantarctic Shelf Waters From the Patagonian Shelf

It has been suggested that the Subtropical Shelf Front (STSF) could be a preferential site for the detrainment of Subantarctic Shelf Water (SASW) and related planktonic shelf species onto the open SW Atlantic Ocean. The offshore detrainment of SASW and planktonic shelf species might be an exportation mechanism, affecting the population abundances of fishing resources in Argentina, Uruguay, and Southern Brazil. In this study, we characterize for the first time the 3-D structure of the STSF and the main routes of offshore export of SASW from the Patagonian shelf during austral summer (summer and early fall) and winter (winter and early spring) by using numerical hydrodynamical model results and Lagrangian tracking simulations of neutrally buoyant floats. The transport of SASW toward the open ocean is ~1 Sv (1 Sv = 106 m3/s) during summer and ~0.8 Sv during winter. SASW are exported offshore mainly near the Brazil-Malvinas Confluence region during both seasons. The STSF appears to act as an important retention mechanism for the plankton over the inner and middle shelf mainly during late summer and early fall. Our findings could explain the life cycle of distinct fish species that are distributed in the region, as well as the population abundance variability of such species.Fil: Franco, Barbara Cristie. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Centro de Investigaciones del Mar y la Atmósfera. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Centro de Investigaciones del Mar y la Atmósfera; ArgentinaFil: Palma, Elbio Daniel. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca. Instituto Argentino de Oceanografía. Universidad Nacional del Sur. Instituto Argentino de Oceanografía; ArgentinaFil: Combes, Vincent. State University of Oregon; Estados UnidosFil: Acha, Eduardo Marcelo. Instituto Nacional de Investigaciones y Desarrollo Pesquero; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Saraceno, Martin. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Centro de Investigaciones del Mar y la Atmósfera. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Centro de Investigaciones del Mar y la Atmósfera; Argentina. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Centro de Investigaciones del Mar y la Atmósfera; Argentin

Distribution of sea-air CO 2 fluxes in the Patagonian Sea: Seasonal, biological and thermal effects

Sea-air CO2 fluxes (FCO2) in the Patagonian Sea (PS) were studied using observations collected in 2000-2006. Based on the PS frontal structures and the thermal and biological contributions to FCO2 we present a regional subdivision between distinct regimes that provide new insights on the processes that control these fluxes. The coastal regime (CR) is a net source of atmospheric CO2 (4.9 x 10-3mol.m-2.d-1) while the open shelf regime (SHR) is a net CO2 sink (-6.0 x 10-3mol.m-2.d-1). The interface between these two regions closely follows the location of along-shore fronts. In addition, based on the nature of the processes that drive the FCO2, the PS is subdivided between northern (NR) and southern (SR) regions. Both, NR and SR are CO2 sinks, but the CO2 uptake is significantly higher in NR (-6.4 x 10-3mol.m-2.d-1) than in SR (-0.5 x 10-3mol.m-2.d-1). The data reveal a strong seasonality in FCO2. The mean CO2 capture throughout the PS in austral spring is -5.8 x 10-3mol.m-2.d-1, reaching values lower than -50 x 10-3mol.m-2.d-1 in NR, while in winter FCO2 is close to equilibrium in SR. The analysis of the biological and thermal effects (BE and TE, respectively) on seasonal pCO2 variability indicates that regions of CO2 emission are dominated by the TE while regions of CO2 uptake are dominated by the BE. Our results indicate that the biological pump is the dominant process determining the sea-air CO2 flux in the PS.Fil: Kahl, Lucía Carolina. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Ciencias de la Atmósfera y los Océanos; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Ministerio de Defensa. Armada Argentina. Servicio de Hidrografía Naval. Departamento Oceanografía; ArgentinaFil: Bianchi, Alejandro A.. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Ciencias de la Atmósfera y los Océanos; Argentina. Ministerio de Defensa. Armada Argentina. Servicio de Hidrografía Naval. Departamento Oceanografía; ArgentinaFil: Osiroff, Ana Paula. Ministerio de Defensa. Armada Argentina. Servicio de Hidrografía Naval. Departamento Oceanografía; ArgentinaFil: Pino, Diana Ruiz. Universite Pierre et Marie Curie; FranciaFil: Piola, Alberto Ricardo. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Ciencias de la Atmósfera y los Océanos; Argentina. Ministerio de Defensa. Armada Argentina. Servicio de Hidrografía Naval. Departamento Oceanografía; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentin

Macroscopic description of microscopically strongly inhomogenous systems: A mathematical basis for the synthesis of higher gradients metamaterials

We consider the time evolution of a one dimensional $n$-gradient continuum. Our aim is to construct and analyze discrete approximations in terms of physically realizable mechanical systems, called microscopic because they are living on a smaller space scale. We validate our construction by proving a convergence theorem of the microscopic system to the given continuum, as the scale parameter goes to zero.Comment: 20 page