A 2D model for hydrodynamics and biology coupling applied to algae growth simulations

Cultivating oleaginous microalgae in specific culturing devices such as raceways is seen as a future way to produce biofuel. The complexity of this process coupling non linear biological activity to hydrodynamics makes the optimization problem very delicate. The large amount of parameters to be taken into account paves the way for a useful mathematical modeling. Due to the heterogeneity of raceways along the depth dimension regarding temperature, light intensity or nutrients availability, we adopt a multilayer approach for hydrodynamics and biology. For free surface hydrodynamics, we use a multilayer Saint-Venant model that allows mass exchanges, forced by a simplified representation of the paddlewheel. Then, starting from an improved Droop model that includes light effect on algae growth, we derive a similar multilayer system for the biological part. A kinetic interpretation of the whole system results in an efficient numerical scheme. We show through numerical simulations in two dimensions that our approach is capable of discriminating between situations of mixed water or calm and heterogeneous pond. Moreover, we exhibit that a posteriori treatment of our velocity fields can provide lagrangian trajectories which are of great interest to assess the actual light pattern perceived by the algal cells and therefore understand its impact on the photosynthesis process.Comment: 27 pages, 11 figure

Ontogenetic shifts in natural diet during benthic stages of American lobster (Homarus americanus), off the Magdalen Islands

The natural diet of 506 American lobsters (Homarus americanus) ranging from instar V (4 mm cephalothorax length, CL) to the adult stage (112 mm CL) was determined by stomach content analysis for a site in the Magdalen Islands, Gulf of St. Lawrence, eastern Canada. Cluster and factor analyses determined four size groupings of lobsters based on their diet: <7.5 mm, 7.5 to <22.5 mm, 22.5 to <62.5 mm, and ≥62.5 mm CL. The ontogenetic shift in diet with increasing size of lobsters was especially apparent for the three dominant food items: the contribution of bivalves and animal tissue (flesh) to volume of stomach contents decreased from the smallest lobsters (28% and 39%, respectively) to the largest lobsters (2% and 11%, respectively), whereas the reverse trend was seen for rock crab Cancer irroratus (7% in smallest lobsters to 53% in largest lobsters). Large lobsters also ate larger rock crabs than did small lobsters

Layer-averaged Euler and Navier-Stokes equations

In this paper we propose a strategy to approximate incompressible hydrostatic free surface Euler and Navier-Stokes models. The main advantage of the proposed models is that the water depth is a dynamical variable of the system and hence the model is formulated over a fixed domain.The proposed strategy extends previous works approximating the Euler and Navier-Stokes systems using a multilayer description. Here, the needed closure relations are obtained using an energy-based optimality criterion instead of an asymptotic expansion. Moreover, the layer-averaged description is successfully applied to the Navier-Stokes system with a general form of the Cauchy stress tensor

Hydrodynamics-Biology Coupling for Algae Culture and Biofuel Production

International audienceBiofuel production from microalgae represents an acute optimization problem for industry. There is a wide range of parameters that must be taken into account in the development of this technology. Here, mathematical modelling has a vital role to play. The potential of microalgae as a source of biofuel and as a technological solution for CO2 fixation is the subject of intense academic and industrial research. Large-scale production of microalgae has potential for biofuel applications owing to the high productivity that can be attained in high-rate raceway ponds. We show, through 3D numerical simulations, that our approach is capable of discriminating between situations where the paddle wheel is rapidly moving water or slowly agitating the process. Moreover, the simulated velocity fields can provide lagrangian trajectories of the algae. The resulting light pattern to which each cell is submitted when travelling from light (surface) to dark (bottom) can then be derived. It will then be reproduced in lab experiments to study photosynthesis under realistic light patterns

Hyperbolicity of a semi-Lagrangian formulation of the hydrostatic free-surface Euler system

By a semi-Lagrangian change of coordinates, the hydrostatic Euler equations describing free-surface sheared flows is rewritten as a system of quasilinear equations, where stability conditions can be determined by the analysis of its hyperbolic structure. This new system can be written as a quasi linear system in time and horizontal variables and involves no more vertical derivatives. However, the coefficients in front of the horizontal derivatives include an integral operator acting on the new vertical variable. The spectrum of these operators is studied in detail, in particular it includes a continuous part. Riemann invariants are then determined as conserved quantities along the characteristic curves. Examples of solutions are provided, in particular stationary solutions and solutions blowing-up in finite time. Eventually, we propose an exact multi-layer $\mathbb{P}_0$-discretization, which could be used to solve numerically this semi-Lagrangian system, and analyze the eigenvalues of the corresponding discretized operator to investigate the hyperbolic nature of the approximated system.Comment: 35 pages, 7 figure

Solutions quasi-analytiques d’ondes propagatives dans les équations d’Euler à surface libre

International audienceThis note describes some quasi-analytical solutions for wave propagation in free surface Euler equations and linearized Euler equations. The obtained solutions vary from a sinusoidal form to a form with singularities. They allow a numerical validation of the free-surface Euler codes.Cette note décrit des solutions quasi analytiques correspondant à la propagation d'ondes dans les équations d'Euler et d'Euler linéarisées à surface libre. Les solutions obtenues varient d'une forme sinusoïdale à une forme présentant des singularités. Elles permettent de valider numériquement les codes de simulation des équations d'Euler à surface libre

Artificial Intelligence, Machine Learning and Modeling for Understanding the Oceans and Climate Change

International audienceThe ongoing transformation of climate and biodiversity will have a drastic impact on almost all forms of life in the ocean with further consequences on food security, ecosystem services in coastal and inland communities. Despite these impacts, scientific data and infrastructures are still lacking to understand and quantify the consequences of these perturbations on the marine ecosystem. Understanding this phenomenon is not only an urgent but also a scientifically demanding task. Consequently, it is a problem that must be addressed with a tific cohort approach, where multi-disciplinary teams collaborate to bring the best of different scientific areas. In this proposal paper, we describe our newly launched four-years project focusedon developing new artificial intelligence, machine learning, and mathematical modeling tools to contribute to the understanding of the structure, functioning, and underlying mechanisms and dynamics of the global ocean symbiome and its relation with climate change. These actions should enable the understanding of our oceans and predict and mitigate the consequences of climate and biodiversity changes

Variable Mate-Guarding Time and Sperm Allocation by Male Snow Crabs (Chionoecetes opilio) in Response to Sexual Competition, and their Impact on the Mating Success of Females

Volume: 201Start Page: 204End Page: 21