Antonio García-Olivares

Variational subgrid scale formulations for the advection–diffusion-reaction equation

Abstract The exact variational multiscale (VMS) and the subgrid scale (SGS) methods have been developed for the advection-reaction and the advection–diffusion-reaction equations. From the element Greens function, approximate intrinsic time scale parameters have been derived for these cases and are shown to be similar to other expressions obtained in the literature out of the maximum principle and convergence/error analysis. The methods have been compared with typical stabilized finite element methods. As expected, the VMS is nodally exact for the one-dimensional case.

The instability growth leading to a liquid sheet breakup

The instability growth leading to a liquid sheet breakup has been studied with the objective of improving the understanding of the fundamental mechanisms of atomization. A three-dimensional Lagrangian code based on vortex dynamics methods has been implemented to track the air/liquid interfaces treated as inviscid vortex sheets. The results of these numerical simulations indicate a possible explanation for the presence of transverse and longitudinal filaments observed in liquid sheet air-assisted atomization experiments.

Non-Gaussian Velocity Probability Density Functions: An Altimetric Perspective of the Mediterranean Sea

Abstract Velocity probability density functions (PDFs) are a key tool to study complex flows and are of great importance to model particle dispersion. The PDFs of geostrophic velocities derived from sea level anomalies maps for the Mediterranean Sea have been computed and analyzed, guided by recent results found in studies of two-dimensional and geostrophic turbulence. At the basin scale results show that the geostrophic velocity PDF derived from SLA maps is non-Gaussian. To understand the origin of this non-Gaussianity, a topological partition of the flow based on the Okubo–Weiss parameter is applied to separate the contribution of coherent vortices from the background field. After such separation the non-Gaussian part of the PDF appears mostly associated with the presence of such structures. Only about 20% of the vortices identified in the dataset are mainly responsible for this deviation. These vortices, called intense vortices in previous works, are those vortices with values of the amplitude larger t...

Analytic solution of partial differential equations with Adomian's decomposition

Adomians method is completed to obtain the analytic solution of any partial differential equation with boundary conditions defined on the four sides of a rectangle. Adomians decomposition method is first used to obtain the N‐order approximant to the one direction partial solution that satisfies the boundary conditions on that direction. Then the functions obtained are variationally modified on the four sides to make them compatible with a given experimental error. The product of these transformations is an analytic approximation to the solution which is compatible with both the weak norm imposed on the boundaries and the accuracy imposed in the whole domain.

Impact of anthropogenic CO 2 on the next glacial cycle

The model of Paillard and Parrenin (Earth Planet Sci Lett 227(3–4):263–271, 2004) has been recently optimized for the last eight glacial cycles, leading to two different relaxation models with model-data correlations between 0.8 and 0.9 (García-Olivares and Herrero (Clim Dyn 1–25, 2012b)). These two models are here used to predict the effect of an anthropogenic CO2 pulse on the evolution of atmospheric CO2, global ice volume and Antarctic ice cover during the next 300 kyr. The initial atmospheric CO2 condition is obtained after a critical data analysis that sets 1300 Gt as the most realistic carbon Ultimate Recoverable Resources (URR), with the help of a global compartmental model to determine the carbon transfer function to the atmosphere. The next 20 kyr will have an abnormally high greenhouse effect which, according to the CO2 values, will lengthen the present interglacial by some 25 to 33 kyr. This is because the perturbation of the current interglacial will lead to a delay in the future advance of the ice sheet on the Antarctic shelf, causing that the relative maximum of boreal insolation found 65 kyr after present (AP) will not affect the developing glaciation. Instead, it will be the following insolation peak, about 110 kyr AP, which will find an appropriate climatic state to trigger the next deglaciation.

Analytical solution of nonlinear partial differential equations of physics

A general method is proposed to approximate the analytical solution of any time‐dependent partial differential equation with boundary conditions defined on the four sides of a rectangle. To ensure that the approximant satisfies the boundary conditions problem the differential operator is modified with one additional term which takes into account the effect of boundary conditions. Then the new problem can be directly integrated in the same way as an ordinary differential equation. In this work Adomians decomposition method with analytic extension is used to obtain the first‐order approximant to the solution of a test case. The result is an analytic approximation to the solution which is compatible with both the exact boundary conditions and the accuracy imposed in the whole domain. The solution obtained is compared with the analytic approximation obtained with a Tau‐Legendre spectral method.

Analytical approximants of time-dependent partial differential equations with tau methods

Tau spectral methods and Adomians decomposition can be fruitfully combined to quickly approximate the analytical solution of any time-dependent partial differential equation with boundary conditions defined on the four sides of a rectangle. In this work, combinations of Legendre polynomials have been used to generate orthogonal two-dimensional polynomials on a rectangular domain. The time evolution of the solution is condensed in a set of nonlinear differential equations for the polynomial coefficients. This system can be integrated by using Adomians decomposition method with analytic extension or, alternatively, successive approximations, which generate a time series that can be truncated at the required precision order. The result is an analytic approximation to the final solution which can be easily obtained by using any commercial symbolic processor.

Global constraints on net primary production and inorganic carbon supply during glacial and interglacial cycles

[1] Relaxation-type models have good skill at reproducing glacial-interglacial transitions in climatic variables. Here we propose a simple two-box and two-state relaxation-type model for the upper ocean (surface and permanent thermocline layers) where dissolved inorganic carbon/nutrients are supplied by the deep ocean and through remineralization within the upper ocean. The model is tuned using genetic algorithms to simulate the atmospheric CO2 time series for the last four glacial-interglacial cycles. The fit to the data is very good, with correlations above 0.8, as the upper ocean responds to shifts in (1) the intensity of the meridional overturning circulation, from off to on during the glacial-interglacial transition, and (2) the size and sign of net primary production, with respiration greatly exceeding primary production during interglacial periods and production larger than respiration during the glacial phase. The glacial-interglacial transitions are interpreted as shifts between two distinct metabolic states of the Earth system, with high/low supply of dissolved inorganic carbon and nutrients to the productive upper ocean during interglacial/glacial periods.