. Kf-=-np, zeros(mm0.shape, float) for i, mmi in enumerate(mm0): sol = worster_leitch_solve(xi_end

R. J. Adrian, Particle-Imaging Techniques for Experimental Fluid Mechanics, Annual Review of Fluid Mechanics, vol.23, issue.1, pp.261-304, 1991.
DOI : 10.1146/annurev.fl.23.010191.001401

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.57.5404

G. Ahlers, S. Grossmann, and D. Lohse, Heat transfer and large scale dynamics in turbulent Rayleigh-B??nard convection, Reviews of Modern Physics, vol.81, issue.2, pp.503-537, 2009.
DOI : 10.1103/RevModPhys.81.503

P. G. Baines, Two-dimensional plumes in stratified environments, Journal of Fluid Mechanics, vol.471, pp.315-337, 2002.
DOI : 10.1017/S0022112002002215

W. D. Baines and J. S. Turner, Turbulent buoyant convection from a source in a confined region, Journal of Fluid Mechanics, vol.5, issue.01, pp.51-80, 1969.
DOI : 10.1175/1520-0469(1964)021 2.0.CO;2

A. Bejan and J. L. Lage, The Prandtl Number Effect on the Transition in Natural Convection Along a Vertical Surface, Journal of Heat Transfer, vol.112, issue.3, pp.787-790, 1990.
DOI : 10.1115/1.2910457

E. Bodenschatz, W. Pesch, and G. Ahlers, Recent Developments in Rayleigh-B??nard Convection, Annual Review of Fluid Mechanics, vol.32, issue.1, pp.709-778, 2000.
DOI : 10.1146/annurev.fluid.32.1.709

M. Bruchhausen, F. Guillard, and F. Lemoine, Instantaneous measurement of two-dimensional temperature distributions by means of two-color planar laser induced fluorescence (PLIF), Experiments in Fluids, vol.16, issue.5, pp.123-131, 2005.
DOI : 10.1007/s00348-004-0911-2

T. Caudwell, 2015 Convection et stratification induites par une paroi chauffante : mesures expérimentales et modélisations

F. Chillà and J. Schumacher, 2012 New perspectives in turbulent Rayleigh- Bénard convection, Eur. Phys. J. E, vol.35, issue.7

X. Chunyan and C. Xiaoshu, Measuring the Water Temperature via Two- Band Planer Laser Induced Fluorescence, Photonics and Optoelectronics, pp.1-4, 2009.

M. Coolen, R. Kieft, C. Rindt, and A. Van-steenhoven, Application of 2-D LIF temperature measurements in water using a Nd : YAG laser, Experiments in Fluids, vol.27, issue.5, pp.420-426, 1999.
DOI : 10.1007/s003480050367

P. Cooper and G. R. Hunt, The ventilated filling box containing a vertically distributed source of buoyancy, Journal of Fluid Mechanics, vol.91, pp.39-58, 2010.
DOI : 10.1017/S0022112002002215

J. Coppeta and C. Rogers, Dual emission laser induced fluorescence for direct planar scalar behavior measurements, Experiments in Fluids, vol.25, issue.1, pp.1-15, 1998.
DOI : 10.1007/s003480050202

T. H. Ellison and J. S. Turner, Turbulent entrainment in stratified flows, Journal of Fluid Mechanics, vol.3, issue.03, pp.423-448, 1959.
DOI : 10.1007/BF02021146

H. J. Fernando, Turbulent Mixing in Stratified Fluids, Annual Review of Fluid Mechanics, vol.23, issue.1, pp.455-493, 1991.
DOI : 10.1146/annurev.fl.23.010191.002323

N. Fujisawa and S. Funatani, Simultaneous measurement of temperature and velocity in a turbulent thermal convection by the extended range scanning liquid crystal visualization technique, Experiments in Fluids, vol.29, issue.7, pp.158-165, 2000.
DOI : 10.1007/s003480070017

S. Funatani, N. Fujisawa, and H. Ikeda, Simultaneous measurement of temperature and velocity using two-colour LIF combined with PIV with a colour CCD camera and its application to the turbulent buoyant plume, Measurement Science and Technology, vol.15, issue.5, p.983, 2004.
DOI : 10.1088/0957-0233/15/5/030

A. E. Germeles, Forced plumes and mixing of liquids in tanks, Journal of Fluid Mechanics, vol.37, issue.03, pp.601-623, 1975.
DOI : 10.1017/S0022112075002765

G. G. Guilbault, fluorescence ; theory, methods, and techniques, Practical, 1973.
DOI : 10.1063/1.3068881

K. Hishida and J. Sakakibara, Combined planar laser-induced fluorescence-particle image velocimetry technique for velocity and temperature fields, Experiments in Fluids, vol.29, issue.7, pp.129-140, 2000.
DOI : 10.1007/s003480070015

G. R. Hunt and T. S. Van-den-bremer, Classical plume theory: 1937-2010 and beyond, IMA Journal of Applied Mathematics, vol.76, issue.3, pp.424-448, 2011.
DOI : 10.1093/imamat/hxq056

E. Kaminski, S. Tait, and G. Carazzo, Turbulent entrainment in jets with arbitrary buoyancy, Journal of Fluid Mechanics, vol.526, pp.361-376, 2005.
DOI : 10.1017/S0022112004003209

N. B. Kaye, Turbulent Plumes in Stratified Environments: A Review of Recent Work, ATMOSPHERE-OCEAN, vol.46, issue.4, pp.433-441, 2008.
DOI : 10.3137/ao.460404

N. B. Kaye and G. R. Hunt, Overturning in a filling box, Journal of Fluid Mechanics, vol.576, pp.297-323, 2007.
DOI : 10.1017/S0022112006004435

R. D. Keane and R. J. Adrian, Theory of cross-correlation analysis of PIV images, Applied Scientific Research, vol.23, issue.3, pp.191-215, 1992.
DOI : 10.1007/BF00384623

H. J. Kim and K. D. Khim, Application of a two-color laser induced fluorescence (LIF) technique for temperature mapping, Proc. of 2001 ASME International Mechanical Engineering Congress and Exposition. ASME, 2001.

K. Kohse-höinghaus, Laser techniques for the quantitative detection of reactive intermediates in combustion systems, Progress in Energy and Combustion Science, vol.20, issue.3, pp.203-279, 1994.
DOI : 10.1016/0360-1285(94)90015-9

L. Larsen and J. Crimaldi, The effect of photobleaching on PLIF, Experiments in Fluids, vol.31, issue.10, pp.803-812, 2006.
DOI : 10.1007/s00348-006-0205-y

P. Lavieille, A. Delconte, D. Blondel, M. Lebouche, and F. Lemoine, Non-intrusive temperature measurements using three-color laser-induced fluorescence, Experiments in Fluids, vol.36, issue.5, pp.706-716, 2004.
DOI : 10.1007/s00348-003-0748-0

P. Lavieille, F. Lemoine, G. Lavergne, and M. Lebouche, Evaporating and combusting droplet temperature measurements using two-color laser-induced fluorescence, Experiments in Fluids, vol.31, issue.1, pp.45-55, 2001.
DOI : 10.1007/s003480000257

F. Lemoine, Y. Antoine, M. Wolff, and M. Lebouche, Simultaneous temperature and 2D velocity measurements in a turbulent heated jet using combined laser-induced fluorescence and LDA, Experiments in Fluids, vol.26, issue.4, pp.315-323, 1999.
DOI : 10.1007/s003480050294

F. Lemoine and F. Grisch, 2012 Métrologie laser pour la mécanique des fluides : Granulométrie et techniques spectroscopiques, chap. 7 -Fluorescence induite par laser. Mécanique et ingénierie des matériaux, Géomécanique

F. Lemoine and B. Leporcq, An efficient optical pressure measurement in compressible flows: Laser-induced iodine fluorescence, Experiments in Fluids, vol.19, issue.3, pp.150-158, 1995.
DOI : 10.1007/BF00189703

F. Lemoine, M. Wolff, and M. Lebouche, Simultaneous concentration and velocity measurements using combined laser-induced fluorescence and laser Doppler velocimetry: Application to turbulent transport, Experiments in Fluids, vol.20, issue.5, pp.319-327, 1996.
DOI : 10.1007/BF00191013

P. F. Linden, THE FLUID MECHANICS OF NATURAL VENTILATION, Annual Review of Fluid Mechanics, vol.31, issue.1, pp.201-238, 1999.
DOI : 10.1146/annurev.fluid.31.1.201

A. Matulka, P. López, J. M. Redondo, and A. Tarquis, On the entrainment coefficient in a forced plume: quantitative effects of source parameters, Nonlinear Processes in Geophysics, vol.21, issue.1, pp.269-278
DOI : 10.5194/npg-21-269-2014

B. R. Morton, G. Taylor, and J. S. Turner, Turbulent Gravitational Convection from Maintained and Instantaneous Sources, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, vol.234, issue.1196, pp.1-23, 1196.
DOI : 10.1098/rspa.1956.0011

T. Nakajima, M. Utsunomiya, and Y. Ikeda, Simultaneous measurement of velocity and temperature of water using LDV and fluorescence technique, Applications of Laser Techniques to Fluid Mechanics, pp.34-53, 1991.

S. Paillat and E. Kaminski, 2014 Entrainment in plane turbulent pure plumes, J. Fluid Mech, vol.755

J. Partridge and P. Linden, 2013 Validity of thermally-driven small-scale ventilated filling box models, Exp. Fluids, vol.54, issue.11

J. Patterson and J. Imberger, Unsteady natural convection in a rectangular cavity, Journal of Fluid Mechanics, vol.65, issue.01, pp.65-86, 1980.
DOI : 10.1016/0017-9310(74)90079-9

A. Petracci, R. Delfos, and J. Westerweel, Combined PIV/LIF measurements in a Rayleigh-Bénard convection cell, 13th Int. Symp. on Application of Laser Techniques to Fluid Mechanics, 2006.

H. Phelippeau and . Paris, Méthodes et algorithmes de dématriçage et de filtrage du bruit pour la photographie numérique, 2009.

M. Riethmuller, L. David, and B. Lecordier, 2012 Vélocimétrie laser pour la mécanique des fluides, chap. 6 -Vélocimétrie par images de particules PIV. Mécanique et ingénierie des matériaux, Géomécanique

J. Sakakibara and R. J. Adrian, Whole field measurement of temperature in water using two-color laser induced fluorescence, Experiments in Fluids, vol.26, issue.1-2, pp.7-15, 1999.
DOI : 10.1007/s003480050260

J. Sakakibara, K. Hishida, and M. Maeda, Measurements of thermally stratified pipe flow using image-processing techniques, Experiments in Fluids, vol.3, issue.No. 10, pp.82-96, 1993.
DOI : 10.1007/BF00944910

S. D. Sandbach and G. Lane-serff, Transient buoyancy-driven ventilation: Part 1. Modelling advection, Building and Environment, vol.46, issue.8, pp.1578-1588
DOI : 10.1016/j.buildenv.2011.01.020

URL : https://www.escholar.manchester.ac.uk/api/datastream?publicationPid=uk-ac-man-scw:146026&datastreamId=POST-PEER-REVIEW-PUBLISHERS.PDF

R. De-socio, Lagrangian investigation of the temperature of a fluid with a LIF technique, 2010.

C. Spaccapaniccia, P. Planquart, M. R. Vetrano, and J. M. Buchlin, 2012 Mesure simultanée de la température et de la vitesse par les techniques LIF et PIV dans une cavité rectangulaire, Actes 13 e Congrès Francophone de Techniques Laser. AFVL

T. Tsuji and Y. Nagano, Characteristics of a turbulent natural convection boundary layer along a vertical flat plate, International Journal of Heat and Mass Transfer, vol.31, issue.8, pp.31-1723, 1988.
DOI : 10.1016/0017-9310(88)90284-0

B. Valeur, Invitation à la fluorescence moléculaire, 2004.

D. A. Walker, A fluorescence technique for measurement of concentration in mixing liquids, Journal of Physics E: Scientific Instruments, vol.20, issue.2, pp.217-224
DOI : 10.1088/0022-3735/20/2/019

A. J. Wells and M. G. Worster, A geophysical-scale model of vertical natural convection boundary layers, Journal of Fluid Mechanics, vol.234, pp.111-137, 2008.
DOI : 10.1017/S0022112005006300

M. G. Wells, R. W. Griffiths, and J. S. Turner, Competition between distributed and localized buoyancy fluxes in a confined volume, Journal of Fluid Mechanics, vol.391, pp.319-336, 1999.
DOI : 10.1017/S0022112099005248

J. Westerweel, Digital particle image velocimetry : Theory and application, 1993.

A. W. Woods, Turbulent Plumes in Nature, Annual Review of Fluid Mechanics, vol.42, issue.1, pp.391-412
DOI : 10.1146/annurev-fluid-121108-145430

URL : http://eprints.esc.cam.ac.uk/1471/1/Woods_annurev-fluid-121108-145430.pdf

M. G. Worster and H. E. Huppert, Time-dependent density profiles in a filling box, Journal of Fluid Mechanics, vol.71, issue.-1, pp.457-466, 1983.
DOI : 10.1017/S0022112069000413

M. G. Worster and A. M. Leitch, Laminar free convection in confined regions, Journal of Fluid Mechanics, vol.36, issue.-1, pp.301-319, 1985.
DOI : 10.1017/S0022112066001368