Application to Geophysical Flows: Some Recent Research Studies
In this chapter are presented few recent research studies led by the author and his collaborators (or in the reverse way !, see the citations in the slides). These studies may come from PhD students work in applied mathematics (M. Honnorat, N. Martin), postdoctoral researchers in applied mathematics (X. Lai), postdoctoral researchers in fluid mechanics (P.-A. Garambois), and in close collaboration with colleagues researchers in river hydraulics (D. Dartus et al. IMFT) or in glaciology (Legos, Lgge).
Fondamental : River hydraulic & flood plain flows - some studies
River hydraulics if flooding and glaciers flows are complex multi-scale geophysical thinflows. Data are uncertain (if existing !), sparse and heterogeneous in nature, time and space. Variational data assimilation is well suited for such flows since it aims at ”fusing at best” all the knowledge of the flow: mathematical models (law conservations, eg shallow water model or Stokes non-linear free surface flow model here) and in-situ measurements and/or remote sensed date (eg satellite images).
First, few research studies in river hydraulic are considered. We present the assimilation of lagrangian data into eulerian shallow water flows, the superposition of 1D model over a finer 2D model, sensitivity analysis helping both at understanding the model and the flow (feedback to the modeling process), the estimate of un certain parameters (identification process).
Next, are presented current researches aiming at identifying discharge of rivers from the forthcoming spatial mission SWOT data (NASA-CNES, launch planned in 2020).
Download the slides :
Fondamental : Forthcoming SWOT spatial mission (Nasa-Cnes) : towards river discharge estimates ?
Download a general poster (NASA-CNES) :
Download a 2nd poster (studies led at IMT - INSA, in collaboration with IMFT and LEGOS):
Download the slides :
Fondamental : Glaciology & Viscoplastic flows
Below are presented few studies involving viscoplastic free surface flows (eg pastes, blood, many industrial fluids, dense snow, mud, ice) and with a special focus on glaciers flows. The slides downable come from Nathan Martin's PhD defence (IMT - Insa Toulouse july 2013), see [20], and from a conference in glaciology given by O. Gagliardini et al (LGGE Grenoble, IMT Toulouse).
Glaciers flows : context and model
Viscoplastic flows : Towards virtual rheometry ?
Numerical experiments on a glacier of Greenland
