G. Artana, A. Cammilleri, J. Carlier, and E. Mémin, Strong and weak constraint variational assimilations for reduced order fluid flow modeling, Journal of Computational Physics, vol.231, issue.8, pp.3264-3288, 2012.
DOI : 10.1016/j.jcp.2012.01.010

URL : https://hal.archives-ouvertes.fr/hal-00772297

A. Bensoussan and R. Temam, Equations stochastiques du type Navier-Stokes, Journal of Functional Analysis, vol.13, issue.2, pp.195-222, 1973.
DOI : 10.1016/0022-1236(73)90045-1

URL : http://doi.org/10.1016/0022-1236(73)90045-1

M. Bergmann and L. Cordier, Optimal control of the cylinder wake in the laminar regime by trust-region methods and POD reduced-order models, Journal of Computational Physics, vol.227, issue.16, pp.7813-7840, 2008.
DOI : 10.1016/j.jcp.2008.04.034

URL : https://hal.archives-ouvertes.fr/hal-00368500

S. Beyou, A. Cuzol, S. Gorthi, and E. Mémin, Weighted ensemble transform Kalman filter for image asssimilation, pp.1-17, 2013.

J. Boussinesq, Essai sur la théorie des eaux courantes. Mémoires présentés par divers savantsàsavantsà l, Académie des Sciences, vol.1877, issue.231, pp.1-680

Z. Brze´zniakbrze´zniak, M. Capi´nskicapi´nski, and F. Flandoli, STOCHASTIC PARTIAL DIFFERENTIAL EQUATIONS AND TURBULENCE, Mathematical Models and Methods in Applied Sciences, vol.01, issue.01, pp.41-59, 1991.
DOI : 10.1142/S0218202591000046

P. Constantin and G. Iyer, A stochastic Lagrangian representation of the three-dimensionnal incompressible Navier-Stokes equations, Comm. Pure Appl. Math, pp.61-330, 2008.

P. Constantin and G. Iyer, A stochastic-Lagrangian approach to the Navier???Stokes equations in domains with boundary, The Annals of Applied Probability, vol.21, issue.4, pp.1466-1492, 2011.
DOI : 10.1214/10-AAP731

A. Deane, I. Kevrekidis, G. Karniadakis, and S. Orszag, Low???dimensional models for complex geometry flows: Application to grooved channels and circular cylinders, Physics of Fluids A: Fluid Dynamics, vol.3, issue.10, pp.2337-2354, 1991.
DOI : 10.1063/1.857881

G. Evensen, Data assimilation: The ensemble Kalman filter, 2006.
DOI : 10.1007/978-3-642-03711-5

M. Farge, G. Pellegrino, and K. Schneider, Coherent Vortex Extraction in 3D Turbulent Flows Using Orthogonal Wavelets, Physical Review Letters, vol.87, issue.5, p.54501, 2001.
DOI : 10.1103/PhysRevLett.87.054501

M. Farge, K. Schneider, and N. Kevlahan, Non-Gaussianity and coherent vortex simulation for two-dimensional turbulence using an adaptive orthogonal wavelet basis, Physics of Fluids, vol.11, issue.8, pp.2187-2201, 1999.
DOI : 10.1063/1.870080

F. Flandoli, Lecture Notes in Math, An intoduction to 3D stochastic Navier Stokes, SPDE in hydrodynamics, pp.51-150, 1942.

C. Franzke and A. Majda, Low-Order Stochastic Mode Reduction for a Prototype Atmospheric GCM, Journal of the Atmospheric Sciences, vol.63, issue.2, pp.457-479, 2005.
DOI : 10.1175/JAS3633.1

J. Frederiksen, Subgrid-Scale Parameterizations of Eddy-Topographic Force, Eddy Viscosity, and Stochastic Backscatter for Flow over Topography, Journal of the Atmospheric Sciences, vol.56, issue.11, pp.1481-1494, 1999.
DOI : 10.1175/1520-0469(1999)056<1481:SSPOET>2.0.CO;2

J. Frederiksen, Statistical Dynamical Closures and Subgrid Modeling for Inhomogeneous QG and 3D Turbulence, Entropy, vol.14, issue.12, pp.32-57
DOI : 10.3390/e14010032

J. Frederiksen, T. O-'kane, and M. Zidikheri, Subgrid modelling for geophysical flows, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, vol.55, issue.1910, pp.371-20120166, 1982.
DOI : 10.1098/rsta.2009.0192

K. Gawedzky and A. Kupiainen, Anomalous Scaling of the Passive Scalar, Physical Review Letters, vol.75, issue.21, pp.3834-3837, 1995.
DOI : 10.1103/PhysRevLett.75.3834

P. Gent and J. Mcwilliams, Isopycnal Mixing in Ocean Circulation Models, Journal of Physical Oceanography, vol.20, issue.1, pp.150-155, 1990.
DOI : 10.1175/1520-0485(1990)020<0150:IMIOCM>2.0.CO;2

N. Gordon, A. Doucet, and J. D. Freitas, Sequential Monte Carlo methods in practice, 2001.

P. Holmes, J. Lumley, and G. Berkooz, Turbulence, coherence structures, dynamical systems and symetry, 1996.
DOI : 10.1017/cbo9780511622700

G. Karamanos and G. Karniadakis, A Spectral Vanishing Viscosity Method for Large-Eddy Simulations, Journal of Computational Physics, vol.163, issue.1, pp.22-50, 2000.
DOI : 10.1006/jcph.2000.6552

R. Kraichnan, The structure of isotropic turbulence at very high Reynolds numbers, Journal of Fluid Mechanics, vol.1, issue.04, pp.477-543, 1959.
DOI : 10.1103/PhysRev.107.1485

R. Kraichnan, Small-scale structure of a randomly advected passive scalar, Phys. Rev. Lett, vol.11, pp.945-963, 1968.

R. Kraichnan, Convergents to turbulence functions, Journal of Fluid Mechanics, vol.2, issue.01, pp.189-217, 1970.
DOI : 10.1063/1.1761185

R. Kraichnan, Eddy viscosity and diffusivity: exact formulas and approximations, Complex Systems, vol.1, pp.805-820, 1987.

H. Kunita, Stochastic flows and stochastic differential equations, 1990.

C. Leith, Atmospheric Predictability and Two-Dimensional Turbulence, Journal of the Atmospheric Sciences, vol.28, issue.2, pp.145-161, 1971.
DOI : 10.1175/1520-0469(1971)028<0145:APATDT>2.0.CO;2

M. Lesieur and O. Métais, New Trends in Large-Eddy Simulations of Turbulence, Annual Review of Fluid Mechanics, vol.28, issue.1, pp.45-82, 1996.
DOI : 10.1146/annurev.fl.28.010196.000401

D. Lilly, On the Application of the Eddy Viscosity Concept in the Inertial Subrange of Turbulence, 1966.

A. Majda and P. Kramer, Simplified models for turbulent diffusion:Theory, numerical modelling, and physical phenomena, pp.314-237, 1999.

A. Majda, I. Timofeyev, and E. Vanden-eijnden, Models for stochastic climate prediction, Proceedings of the National Academy of Sciences, vol.96, issue.26, pp.96-14687, 1999.
DOI : 10.1073/pnas.96.26.14687

C. Meneveau and J. Katz, Scale-Invariance and Turbulence Models for Large-Eddy Simulation, Annual Review of Fluid Mechanics, vol.32, issue.1, pp.1-32, 2000.
DOI : 10.1146/annurev.fluid.32.1.1

R. Mikulevicius and B. Rozovskii, Stochastic Navier--Stokes Equations for Turbulent Flows, SIAM Journal on Mathematical Analysis, vol.35, issue.5, pp.1250-1310, 2004.
DOI : 10.1137/S0036141002409167

B. Noack, K. Afanasiev, M. Morzynski, G. Tadmor, and F. Thiele, A hierarchy of low-dimensional models for the transient and post-transient cylinder wake, Journal of Fluid Mechanics, vol.497, pp.335-363, 2003.
DOI : 10.1017/S0022112003006694

B. Noack, M. Morzynski, and G. Tadmor, Reduced-Order Modelling for Flow Control, CISM Courses and Lectures, vol.528, 2010.
DOI : 10.1007/978-3-7091-0758-4

B. Noack, P. Papas, and P. Monkevitz, The need for a pressure-term representation in empirical Galerkin models of incompressible shear flows, Journal of Fluid Mechanics, vol.523, pp.339-365, 2005.
DOI : 10.1017/S0022112004002149

T. Palmer and P. Williams, Theme Issue 'Stochastic physics and climate modelling, Phil. Trans. R. Soc. A, p.366, 2008.

R. Pasquetti, Spectral Vanishing Viscosity Method for Large-Eddy Simulation of Turbulent Flows, Journal of Scientific Computing, vol.196, issue.2, pp.365-375, 2006.
DOI : 10.1007/s10915-005-9029-9

D. Rempfer, Investigations of boundary layer transition via Galerkin projections on empirical eigenfunctions, Physics of Fluids, vol.8, issue.1, pp.175-188, 1996.
DOI : 10.1063/1.868825

D. Rempfer and H. Fasel, Evolution of three-dimensional coherent structures in a flat-plate boundary layer, Journal of Fluid Mechanics, vol.104, issue.-1, pp.351-375, 1994.
DOI : 10.1063/1.857573

P. Sagaut, Large Eddy Simulation for Incompressible Flows. An Introduction, Measurement Science and Technology, vol.12, issue.10, 2005.
DOI : 10.1088/0957-0233/12/10/707

F. M. Selten, An Efficient Description of the Dynamics of Barotropic Flow, Journal of the Atmospheric Sciences, vol.52, issue.7, pp.915-936, 1995.
DOI : 10.1175/1520-0469(1995)052<0915:AEDOTD>2.0.CO;2

L. Sirovich, Turbulence and the dynamics of coherent structures. I. Coherent structures, Quarterly of Applied Mathematics, vol.45, issue.3, pp.561-590, 1987.
DOI : 10.1090/qam/910462

J. Slingo and T. Palmer, Uncertainty in weather and climate prediction, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, vol.50, issue.7024, pp.4751-4767, 2011.
DOI : 10.1038/nature03301

J. Smagorinsky, GENERAL CIRCULATION EXPERIMENTS WITH THE PRIMITIVE EQUATIONS, Monthly Weather Review, vol.91, issue.3, pp.99-165, 1963.
DOI : 10.1175/1520-0493(1963)091<0099:GCEWTP>2.3.CO;2

E. Tadmor, Convergence of Spectral Methods for Nonlinear Conservation Laws, SIAM Journal on Numerical Analysis, vol.26, issue.1, pp.30-44, 1989.
DOI : 10.1137/0726003