Geodesic
On the statistical properties of the hydro dynamic models based on solutions to the Boussinesq equations
Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 1 (1998) no. 2, pp. 135-142.

Voir la notice de l'article provenant de la source Math-Net.Ru

Using simplified Boussinesq equations as an example, we show that their solutions describing vortex structures (convective cells) are unstable perturbations of finite-amplitude. This property of the solutions makes it possible to advance a hypothesis concerning the mechanism of formation of the spectrum of the ensemble of convective cells and go from the hydrodynamic model to a statistical model. The results obtained earlier for the adiabatic atmosphere are generalized to a more general case of a polytropic atmosphere. This case includes the spontaneous convection that leads to formation of mesoscale convective ensembles. Such ensembles consisting of thermals and convective clouds play an important role in formation of the weather and climate of the planet. 
@article{SJVM_1998_1_2_a2,
     author = {V. M. Malbackov},
     title = {On the statistical properties of the hydro dynamic models based on solutions to the {Boussinesq} equations},
     journal = {Sibirskij \v{z}urnal vy\v{c}islitelʹnoj matematiki},
     pages = {135--142},
     publisher = {mathdoc},
     volume = {1},
     number = {2},
     year = {1998},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SJVM_1998_1_2_a2/}
}
TY  - JOUR
AU  - V. M. Malbackov
TI  - On the statistical properties of the hydro dynamic models based on solutions to the Boussinesq equations
JO  - Sibirskij žurnal vyčislitelʹnoj matematiki
PY  - 1998
SP  - 135
EP  - 142
VL  - 1
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SJVM_1998_1_2_a2/
LA  - ru
ID  - SJVM_1998_1_2_a2
ER  - 
%0 Journal Article
%A V. M. Malbackov
%T On the statistical properties of the hydro dynamic models based on solutions to the Boussinesq equations
%J Sibirskij žurnal vyčislitelʹnoj matematiki
%D 1998
%P 135-142
%V 1
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SJVM_1998_1_2_a2/
%G ru
%F SJVM_1998_1_2_a2
V. M. Malbackov. On the statistical properties of the hydro dynamic models based on solutions to the Boussinesq equations. Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 1 (1998) no. 2, pp. 135-142. http://geodesic.mathdoc.fr/item/SJVM_1998_1_2_a2/

[1] Davaile A. and Jampart C., “Transient high-Rayleigh-number thermal convection with large viscosity variations”, J. Fluid Mech., 253 (1993), 141–146 | DOI

[2] Deardorff J. W., “Three-dimensional numerical study of turbulence in an entraining mixed layer”, Bound.-Layer Meteor., 7 (1974), 199–226

[3] Decker W., Petch W., and Weber A., “Spiral defect chaos in Rayleigh–Benard convection”, Phys. Rev. Let., 73 (1994), 648–651 | DOI

[4] Ebert E. E., Shuman U., and Stul R. B., “Nonlocal turbulent mixing in the convective boundary layer evaluated from large eddy simulation”, J. Atmos. Sci., 46 (1989), 2178–2207 | 2.0.CO;2 class='badge bg-secondary rounded-pill ref-badge extid-badge'>DOI

[5] Pushistov P. Yu., Vaskevich L. A., “Chislennoe modelirovanie konvektivnogo pogranichnogo sloya atmosfery”, Izv. AN SSSR. Fizika atmosfery i okeana, 24:11 (1988), 1142–1154

[6] Gutman L. N., Vvedenie v nelineinuyu teoriyu mezometeorologicheskikh protsessov, Gidrometeoizdat, L., 1969

[7] Malbakhov V. M., “Uproschennaya model ansamblya konvektivnykh yacheek i postroenie protsedur parametrizatsii vlazhnoi konvektsii”, Izv. AN SSSR. Fizika atmosfery i okeana, 28:6 (1992), 631–640

[8] Malbakhov V. M., Perov V. L., “Parametrizatsiya konvektsii v modelyakh krupnomasshtabnoi tsirkulyatsii atmosfery”, Vychislitelnye protsessy i sistemy, 10, ed. G. I. Marchuk, Fizmatlit, M., 1993, 96–136

[9] Moeng C.-H., Lenshow D. H., and Rendal D. A., “Numerical investigations of the roles of radiative and evaporative feedbacks in stratocumulus entrainment and breakup”, J. Atmos. Sci., 52 (1995), 2869–2883 | 2.0.CO;2 class='badge bg-secondary rounded-pill ref-badge extid-badge'>DOI

[10] Noto K., Yamamoto Y., and Nakajima T., “Three-dimensional natural convection from a square plate with uniform surface heat flux”, Proc. 10-th. Int. Heat Trasfer Conf. (Brighton, 1994), 531–536

[11] Zeldovich Ya. B., “Predelnye zakony svobodno voskhodyaschikh turbulentnykh potokov”, Zhurnal teoreticheskoi i eksperimentalnoi fiziki, 7:12 (1937), 29