Numerical simulation of phytoplankton transport in turbulent flows by means of kinematic and LES models
Doctorat Doctorat complet, Doctorat co-tutelle, Programme Doctoral
Terre & Univers
EA (en cours d'enregistrement) Unité de Mécanique de Lille
Institution d'accueil
Université de Lille
Ecole doctorale
Sciences pour l'ingénieur (SPI) - ED 72


Reaction transport systems emerge in many areas of research and applications. While the dynamics of reacting species have been widely studied in homogeneous media, their understanding in heterogeneous environments, relevant for ecological problems, is still limited. In this project we propose to elucidate, by means of numerical simulations of Advection-Reaction-Diffusion (ARD) systems, the complex interplay between environmental heterogeneity (due to resource limitations) and transport by a fluid flow, which controls the appearance of phytoplankton blooms in aquatic environments. The focus is on the role of spatially structured flows and turbulent mixing on growth, persistence and distribution of algal populations. To investigate these issues, turbulent flows arising from Navier-Stokes based Large-Eddy-Simulations (LES) or kinematic models will be considered. This approach is expected to allow access to the details at different scales of the interacting mechanisms that determine phytoplankton dynamics. Due to the wide range of spatial and temporal scales involved, this represents a highly challenging task and it constitutes the main original aspect of the project. Analysing temporal behaviours of the adopted models it will be possible to explore the mechanisms controlling the onset of conditions acting as precursors of algal blooms. This study is expected to provide insights on how to better account for the complexity of fluid motions, with respect to the population dynamics models typically used in fundamental and applied studies at scales larger than the spatial (turbulent) structures of the flow. Results will be useful to establish new constraints for improving food web models in marine ecology. Ameliorating the possibility to predict and control phytoplankton blooms also has major societal impacts, as for the management of the anthropogenically induced eutrophication (enhanced algal growth due to excess nutrients) of freshwater and coastal marine ecosystems.


Context and Motivation


Phytoplankton are unicellular algae (of different types) that transform inorganic materials and light into living matter in aquatic ecosystems. Hence, they are the main responsible for primary production in oceans and lakes and they are at the base of virtually any aquatic food web; it is estimated that they contribute about half of the global primary production. Owing to their role in photosynthesis, i.e. the capability of removing carbon dioxide from the atmosphere to release oxygen, such microorganisms have a deep impact on the climatic system and their distribution is an important variable in climate models. Due to the complex interplay of biological and physical processes, phytoplankton dynamics display considerable (large and small-scale) spatiotemporal variability. Biological growth is mainly limited by the availability of light and that of nutrients. While light decreases with depth due to absorption by the fluid medium, the opposite is true for nutrients due to remineralisation in deep layers. Moreover, being heavier than water, practically all species tend to sink. Sinking can have dramatic consequences on population survival, since it transports the algae from the well-lit, euphotic, upper layer to the regions underneath, where growth is inhibited. Finally, mechanical forcing at the surface (by the wind) produces a thin intensely mixed fluid layer just below. Here turbulent motions, depending on their intensity, may either help keeping the algae in the favorable upper layer or bring them outside of it. Predicting how phytoplankton organize in space under the action of such biophysical mechanisms in generic conditions is a formidable challenge. The problem clearly raises important fundamental questions. From an applied perspective, it is unavoidable to provide sound physical basis for model upscaling. Understanding the underlying basic processes is then critical. In this project we will address the role of turbulence by means of numerical simulations. Scientific Objectives We will carry out small-scale extensive numerical studies to explore how hydrodynamics couples with environmental heterogeneity (associated with light/nutrient limitations) using ARD equations. The latter are today considered classical in theoretical ecology. However, due to the difficulty of representing the wide range of scales taking part in the dynamics, turbulent mixing is typically only accounted for by simple parameterizations. Moreover, the modeling of interactions between different components involves often poorly constrained parameters estimated from data. Within this conceptual framework, we aim at better representing the complexity of fluid motions. Besides algal gravitational sinking, we will then consider fluid transport arising from multiscale turbulent flows. Light limitation will be taken into account via Lambert-Beer’s law, nutrient dynamics (possibly) by adding a similar, coupled, equation for their concentration. Our setup is expected to provide a good description for non-swimming algae, like diatoms. We will focus on population persistence and distribution, for a range of parameter values close to the realistic ones. By examining biological indicators like the total biomass and its vertical profile versus turbulent intensity, our analysis could contribute to assessing the validity of some simplifying assumptions adopted in analytical and numerical models. We further aim at characterizing the successive phases of algal blooms and at measuring, when appropriate, the mean extinction time, which are relevant to the dynamics of invasive species. We remark that fully dynamical simulations in completely realistic conditions can in this case easily reach the limits of feasibility due to resolution and computational time requirements. Hence, we will consider kinematic-flow models and LES. Despite simplified, these models retain some of the essential turbulence features and should allow extending the range of parameter values that can be explored.


Methodology and Planning


Task 1 - Eutrophic environments (year 1) In the first phase of the project we will focus on light-limited growth in the presence of homogeneous isotropic flows. Previous results from the literature seem to support the simplified (eddy-diffusivity) hypothesis used to develop idealized theories, in the special conditions of no nutrient limitations (i.e. in eutrophic environments) and turbulence uniformly extending over the well-lit upper (euphotic) layer. However, they are still preliminary and the conclusions tentative. It then seems necessary to reconsider this case, to gather robust quantitative information about phytoplankton vertical distribution and the conditions allowing for its survival (versus mixing intensity and water depth). The coupling between biological and fluid dynamics can present some numerically delicate points. A careful testing work will then be required here, when adapting the numerical codes already available in the research team (pseudo-spectral for turbulence; pseudo-Lagrangian for population density). Task 2 - Oligotrophic environments (from year 2 to year 3-3.5) The previous configuration is based on the assumption of saturated nutrient limitation. Aiming at increasing the biological realism, the main modeling extension we plan is to consider oligotrophic (as opposed to eutrophic) habitats, to explicitly take into account the dynamics of nutrient concentration. Richer dynamics are expected since now turbulence also creates environmental heterogeneities by spreading nutrients. Due to the complexity of the system, analytical results are particularly difficult to obtain in this case and the numerical approach becomes even more valuable. The numerical implementations needed in this task are of the same type of those described in Task 1 and will benefit from the work performed there. Besides exploring how the picture is modified in this case, we aim at studying how different assumptions on the recycling of dead biomass into nutrients affect the results. To improve the biogeochemical realism of models an interaction with LOG laboratory is envisaged, which represents a strong opportunity to bridge the gap between the dynamics that can be reproduced in-silico and field observations. Task 3 - Non-uniform turbulence intensity (year 3) A further interesting question that we plan to study, depending on time, concerns the hypothesis of uniform intensity of turbulent mixing across the entire fluid layer. This simplifying assumption is not always met in the reality, e.g. due to seasonal variations (which affect stratification conditions). The width of the region over which turbulence decays, relative to the depth of the euphotic layer, may play a key role on phytoplankton distribution. Let us add that, since the relative population of different types of algae is typically a function of turbulence intensity, addressing this issue could broaden the perspective to new developments on multi-species models.


Joint PhD Advisor : Stefano Berti / Université de Lille

Compétences requises

Candidate having good knowledge of fluid mechanics or dynamical systems and an interest for numerical methods and/or theoretical ecology and/or oceanography; education: Master in Fluid Mechanics, Physics, Applied Mathematics. Good knowledge of oral and written English is required. Knowing Fortran, C or Python would be a plus

Your profile is eligible to apply for the PhD/Doctorate program "Make Our Planet Great Again" if:

- You have a Master's degree or you will pass a Master's degree before August 31, 2018
- You have lived in France for less than 90 days since April 1, 2016
- You are exclusively a foreign national

How to APPLY?

Please send your CV and a letter of motivation to the following contact :

Mots clés

Reaction transport systems; Fluid dynamics; Turbulence; Models of complex systems; Ecology; Numerical simulations

Offre financée

Type de financement
Contrat de travail
Montant du financement
1350 € Net / mois


Date limite de candidature 04/05/18

Durée36 mois

Date de démarrage01/09/18

Date de création06/04/18


Niveau de français requisAucun

Niveau d'anglais requisB2 (intermédiaire)

Possibilité de faire sa thèse en anglais


Frais de scolarité annuels400 € / an


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