M. Andrejczuk, F. Cooper, S. Juricke, T. Palmer, A. Weisheimer et al., Oceanic stochastic parameterization in a seasonal forecast system, Month. Weath. R, vol.144, pp.1867-1875, 2016.

D. Andrews and M. Mcintyre, An exact theory of nonlinear waves on a Lagrangian-mean flow, J. Fluid. Mech, vol.89, issue.4, pp.609-646, 1978.

A. Arakawa and V. Lamb, Computational design of the basic dynamical process of the UCLA general circulation mode, Methods Computational Physics, vol.17, pp.173-265, 1977.

F. Ardhuin, N. Rascle, and K. Belibassakis, Explicit wave-averaged primitive equations using a generalized Lagrangian mean, Ocean Modell, vol.20, issue.1, pp.35-60, 2008.
URL : https://hal.archives-ouvertes.fr/hal-00129588

J. Boussinesq, 1877: Mémoires présentés par divers savantsà l'Académie des Sciences, vol.23, pp.1-680

R. Buizza, M. Miller, and T. Palmer, Stochastic representation of model uncertainties in the ECMWF ensemble prediction system, Quarterly Journal Royal Meteorological Society, vol.125, pp.2887-2908, 1999.

P. Chandramouli, D. Heitz, S. Laizet, and E. Mémin, Coarse large-eddy simulations in a transitional wake flow with flow models under location uncertainty, Comp. & Fluids, vol.168, pp.170-189, 2018.
URL : https://hal.archives-ouvertes.fr/hal-01764616

B. Chapron, P. Dérian, E. Mémin, and V. Resseguier, Large-scale flows under location uncertainty: a consistent stochastic framework, QJRMS, vol.144, issue.710, pp.251-260, 2018.
URL : https://hal.archives-ouvertes.fr/hal-01629898

A. Craik and S. Leibovich, Rational model for langmuir circulations, J. Fluid Mech, vol.73, pp.401-426, 1976.

C. Franzke and A. Majda, Low-order stochastic mode reduction for a prototype atmospheric gcm, J. Atmos. Sci, vol.63, pp.457-479, 2005.

A. Glazunov, On the effect that the direction of geostrophic wind has on turbulence and quasiordered large-scale structures in the atmospheric boundary layer, Izvestiya, Atmospheric and Oceanic Physics, vol.46, issue.6, pp.727-747, 2010.

S. Gottlieb, On high order strong stability preserving runge-kutta and multi step time discretizations, J. Sci. Comput, vol.25, issue.1, pp.105-128, 2005.

F. Gugole and C. Franzke, Numerical development and evaluation of an energy conserving conceptual stochastic climate model. Mathematics of climate and weather forecasting, vol.5, pp.45-64, 2019.

S. Haney and W. Young, Radiation of internal waves from groups of surface gravity waves, J. Fluid Mech, vol.829, pp.280-303, 2017.

R. Harcourt, 2015: An improved second-moment closure model of langmuir turbulence, J. Phys. Oceanogr, vol.45, pp.84-103

R. Harcourt and E. D'asaro, Large-eddy simulation of langmuir turbulence in pure wind seas, J. Phys. Oceanogr, vol.38, issue.7, pp.1542-1562, 2008.

K. Hasselmann, On the mass and momentum transfer between short gravity waves and larger-scale motions, J. Fluid Mech, vol.50, pp.189-201, 1971.

K. Hasselmann, Stochastic climate models part I theory, Tellus, vol.28, pp.473-485, 1976.

D. Haworth and S. Pope, A generalized Langevin model for turbulent flows, Phys. Fluids, vol.29, pp.387-405, 1986.

D. Holm, 2015: Variational principles for stochastic fluid dynamics, Proc. R. Soc. A, p.471, 20140963.

D. Holm, Stochastic closures for wave-current interaction dynamics, 2019.

D. D. Holm, The ideal craik-leibovich equations, Physica-D, vol.98, pp.415-441, 1996.

S. Kadri-harouna and E. Mémin, Stochastic representation of the Reynolds transport theorem: revisiting large-scale modeling, Computers & Fluids, vol.156, pp.456-469, 2017.
URL : https://hal.archives-ouvertes.fr/hal-01394780

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

E. Lane, J. Restrepo, and J. Mcwilliams, Wave-current interaction: A comparison of radiation-stress and vortex-force representations, J. Phys. Oceanogr, vol.37, issue.5, pp.1122-1141, 2007.

S. Leibovich, On wave-current interaction theories of langmuir circulations, J. Fluid Mech, vol.99, issue.4, pp.715-724, 1980.

C. Leith, Stochastic backscatter in a subgrid-scale model: plane shear mixing layer, Phys. of Fluids, vol.2, issue.3, pp.1521-1530, 1990.

J. Liu, J. Liang, J. Mcwilliams, P. Sullivan, Y. Fan et al., Effect of planetary rotation on oceanic surface boundary layer turbulence, Journ of phys. Oceanogr, vol.48, pp.2057-2080, 2018.

M. Longuet-higgins and R. Stewart, Radiation stresses in water waves: A physical discussion, with applications, Deep Sea Res. Oceanogr. Abstr, vol.11, pp.529-562, 1964.

J. Mcwilliams, The emergence of isolated coherent vortices in turbulent flow, J. Fluid Mech, vol.146, issue.1, p.21, 1984.

J. Mcwilliams, J. Restrepo, and E. Lane, An asymptotic theory for the interaction of waves and currents in coastal waters, J. of Fluid Mech, vol.511, pp.135-178, 2004.

J. Mcwilliams, P. Sullivan, and C. Moeng, Langmuir turbulence in the ocean, J. Fluid Mech, vol.334, pp.1-30, 1997.

G. Mellor, The three-dimensional current and surface wave equations, J. Phys. Oceanogr, vol.33, issue.9, pp.1978-1989, 2003.

G. Mellor, On theories dealing with the interaction of surface waves and ocean circulation, J. Geophys. Res, vol.121, pp.4474-4486, 2016.

E. Mémin, Fluid flow dynamics under location uncertainty, Geophys. & Astro. Fluid Dyn, vol.108, issue.2, pp.119-146, 2014.

C. Meneveau and J. Katz, Scale-invariance and turbulence models for large-eddy simulation, Annu. Rev. Fluid. Mech, vol.32, pp.1-32, 2000.

G. Pavliotis and A. Stuart, Multiscale methods: averaging and homogenization. Science & Business Media, 2008.

J. Pedlosky, Geophysical Fluid Dynamics, 1992.

O. M. Phillips, The Dynamics of the Upper Ocean, 1977.

B. Pinier, E. Mémin, S. Laizet, and R. Lewandowski, Stochastic flow approach to model the mean velocity profile of wall-bounded flows, Phys. Rev. E, vol.063, issue.6, p.101, 2019.
URL : https://hal.archives-ouvertes.fr/hal-01947662

S. Pope, Lagrangian pdf methods for turbulent flows, Annu. Rev. Fluid Mech, 1994.

S. Pope, Turbulent flows, 2000.
URL : https://hal.archives-ouvertes.fr/hal-00712179

P. Porta-mana and L. Zanna, Toward a stochastic parametrization of ocean mesoscale eddies, vol.79, pp.1-20, 2014.

W. Press, S. Teukolsky, W. Vetterling, and B. Flannery, Numerical Recipes 3rd Edition: The Art of Scientific Computing, 2007.

M. Reeks, The transport of discrete particles in inhomogeneous turbulence, J. Aerosol Sci, vol.14, issue.6, pp.729-739, 1983.

V. Resseguier, E. Mémin, and B. Chapron, Geophysical flows under location uncertainty, Part I Random transport and general models, Geophys. & Astro. Fluid Dyn, vol.111, issue.3, pp.149-176, 2017.
URL : https://hal.archives-ouvertes.fr/hal-01391420

V. Resseguier, E. Mémin, and B. Chapron, Geophysical flows under location uncertainty, Part II Quasi-geostrophy and efficient ensemble spreading, Geophys. & Astro. Fluid Dyn, vol.111, issue.3, pp.177-208, 2017.
URL : https://hal.archives-ouvertes.fr/hal-01391476

V. Resseguier, E. Mémin, and B. Chapron, Geophysical flows under location uncertainty, Part III SQG and frontal dynamics under strong turbulence conditions, Geophys. & Astro. Fluid Dyn, vol.111, issue.3, pp.209-227, 2017.
URL : https://hal.archives-ouvertes.fr/hal-01391484

V. Resseguier, E. Mémin, D. Heitz, and B. Chapron, Stochastic modelling and diffusion modes for proper orthogonal decomposition models and small-scale flow analysis, J. Fluid Mech, vol.828, p.29, 2017.
URL : https://hal.archives-ouvertes.fr/hal-01400119

B. Sawford, Generalized random forcing in random-walk models of turbulent dispersion model, Phys. Fluids, vol.29, pp.3582-3585, 1986.

G. Shutts, A kinetic energy backscatter algorithm for use in ensemble prediction systems, Quarterly Journal of the Royal Meteorological Society, vol.612, pp.3079-3012, 2005.

N. Suzuki and B. Fox-kemper, Understanding stokes forces in the wave-averaged equations, J. Geophys. Res. Oceans, vol.121, pp.3579-3596, 2016.

M. Teixeira and S. Belcher, On the structure of langmuir turbulence, Ocean Modell, vol.31, issue.3, pp.105-119, 2010.

J. Weiss, The dynamics of enstrophy transfer in two-dimensional hydrodynamics, Physica D, vol.48, issue.2-3, pp.273-294, 1991.

Y. Yang and E. Mémin, Estimation of physical parameters under location uncertainty using an ensemble 2 -expectation-maximization algorithm, QJRMS, vol.145, issue.719, pp.418-433, 2019.
URL : https://hal.archives-ouvertes.fr/hal-01944730