533.6.011.6 Numerical simulation of supersonic flow around a parachute with a head body

Fortova S. V. (Institute for Computer Aided Design of the Russian Academy of Sciences), Ermakov A. D. (Institute for Computer Aided Design of the Russian Academy of Sciences)

QUASI-TWO-DIMENSIONAL TURBULENCE, DIRECT NUMERICAL MODELING, CFD PACKAGES, ROTATING LIQUID


doi: 10.18698/2309-3684-2024-4-7892


Many atmospheric and oceanic phenomena demonstrate the features of quasi-two-dimensional turbulence that occurs in the presence of rotational force. The study of vortex formation processes in such systems is conditioned by the need to develop qualitative forecasting of the occurrence of cyclones and anticyclones. These weather phenomena are geostrophic flows that can be described within the framework of quasi-two-dimensional turbulence. In this paper, based on numerical modeling of the Navier-Stokes system of equations, the problem of forming coherent vertical structures in a cubic cell in the presence of rotation (Coriolis force) and a constantly acting external force (pumping) is investigated. In the course of numerical experiments, depending on the values of the rotational force and the pumping force, several types of flows were obtained — a chaotic mode, the mode of occurrence of several cyclone vortices and the mode of occurrence of one large cyclone with an anticyclone inside a cyclonic region (“cyclone-anticyclone”).


[1] Frisch U. Turbulence: The Legacy of A. N. Kolmogorov. Journal of Fluid Mechanics, 1996, vol. 317, pp. 407–410.
[2] Pope S.B. Turbulent flows. Cambridge University Press, 2000, 812 p.
[3] Davidson P.A. Turbulence in Rotating, Stratified and Electrically Conducting Fluids. Cambridge University Press, 2013, 695 p.
[4] Godeferd F.S., Moisy F. Structure and dynamics of rotating turbulence: a review of recent experimental and numerical results. Applied Mechanics, 2015, vol. 67, art. no. 030802.
[5] Kolmogorov A.N. Lokal'naya struktura turbulentnosti v neszhimaemoj vyazkoj zhidkosti pri ochen' bol'shih chislah Rejnol'dsa [Local structure of turbulence in an incompressible viscous fluid at very high reynolds numbers]. Doklady Akademii Nauk, 1968, vol. 30, no. 4, pp. 734–746.
[6] Boffetta G., Ecke R.E. Two-Dimensional Turbulence. Annual Review of Fluid
Mechanics, 2012, vol. 44, pp. 427-451.
[7] Sommeria J. Experimental Study of the Two-Dimensional Inverse Energy Cascade in a Square Box. Journal of Fluid Mechanics, 1986, vol. 170, pp. 139-168.
[8] Moiseev S.S., Sagdeev R.Z., Tur A.V., Khomenko G.A., Yanovsky V.V. Teoriya vozniknoveniya krupnomasshtabnyh struktur v gidrodinamicheskoj turbulentnosti [Theory of the Origin of Large-Scale Structures in Hydrodynamic Turbulence]. Journal of Experimental and Theoretical Physics, 1983, vol. 85, No. 6, pp. 549-553.
[9] Alexakis A., Biferale L. Cascades and transitions in turbulent flows. Physics Reports, 2018, vol. 767-769, pp. 1-101.
[10] Campagne A., Gallet B., Moisy F., Cortet P.-P. Disentangling inertial waves from eddy turbulence in a forced rotating-turbulence experiment. Physical Review E, 2015, vol. 91, art. no. 043016.
[11] Levina G.V., Moiseev S.S., Rutkevich P.B. Hydrodynamic Alpha-Effect in a Convective System. Non-Linear Instability, Chaos and Turbulence, Series Advances in Fluid Mechanics, 2000, pp. 110-161.
[12] Arnol’d V.I., Meshalkin A. D. A.N. Kolmogorov’s seminar on selected problems in analysis (1958–1959) [Kolmogorov on selected questions of analysis (1958–1959)]. Russian Mathematical Surveys, 1960, vol. 15, part 1, pp. 247–250.
[13] Bondarenko N.F., Gak M.Z., Dolzhansky F.V. Laboratornaya i teoreticheskaya modeli ploskogo periodicheskogo techeniya [Laboratory and theoretical models of flat periodic flow]. Izvestiya. Atmospheric and Oceanic Physics, 1979, pp. 1017-1026.
[14] Doludenko A.N., Fortova S.V., Kolokolov I.V., Lebedev V.V. Coherent vortex versus chaotic state in two-dimension turbulence. Annals of Physics, 2022, vol. 447, part 2, art. no. 169072.
[15] Tumachev D.D., Filatov S.V., Vergeles S.S. and Levchenko A.A. Dva rezhima dinamiki kogerentnyh stolbovyh vihrej vo vrashchayushchejsya zhidkosti [Two Dynamical Regimes of Coherent Columnar Vortices in a Rotating Fluid]. Pis'ma v Zhurnal Èksperimental'noi i Teoreticheskoi Fiziki [Letters to the Journal of Experimental and Theoretical Physics], 2023, vol. 118, iss. 6, pp. 430-437.
[16] [Electronic resource]. URL: https://www.openfoam.com
[17] Marshall J., Adcroft A., Hill C. A finite-volume, incompressible Navier Stokes model for studies of the ocean on parallel computers. Journal of Geophysical Research: Oceans, 1997, vol. 102, pp. 5753—5766.
[18] Tumachev D., Filatov S., Vergeles S., Levchenko A. Two dynamical regimes of coherent columnar vortices in rotating fluid. JETP Letters, 2023, vol. 118, pp. 426–432.
[19] Yue-Kin Tsang. Nonuniversal velocity probability densities in two-dimensional turbulence: The effect of large-scale dissipation. Physics of Fluids, 2010, vol. 22, art. no. 115102.
[20] M. Chertkov, C. Connaughton, I. Kolokolov, V. Lebedev. Dynamics of Energy Condensation in Two-Dimensional Turbulence. Physisal Reiew Letters, 2007, vol. 99, art. no. 084501.


Фортова С.В., Ермаков А.Д. Численное моделирование квази-двумерных турбулентных течений в замкнутой кубической ячейке. Математическое моделирование и численные методы, 2024, № 4, с. 78–92.


Работа выполнена при финансовой поддержке Министерства науки и высшего образования РФ (госзадание 124022400174-3).


Download article

Количество скачиваний: 248