American Institute of Mathematical Sciences

Advanced
2011, 2011(Special): 794-802. doi: 10.3934/proc.2011.2011.794

Reduction of three-dimensional model of the far turbulent wake to one-dimensional problem

Oleg V. Kaptsov 1, and  Alexey V. Schmidt 1,

1. 

Institute of Computational Modeling SB RAS, Akademgorodok, 66036, Krasnoyarsk, Russian Federation, Russian Federation

Received  July 2010 Revised  March 2011 Published  October 2011

Semi-empirical three-dimensional model of turbulence in the approximation of the far turbulent wake behind a self-propelled body in a passively strati ed medium is considered. The sought quantities are the kinetic turbulent energy, kinetic energy dissipation rate, averaged density defect and density uctuation variance. The full group of transformations admitted by this model is found. The governing equations are reduced into ordinary differential equations by similarity reduction and method of the B-determining equations (BDEs). This system of ordinary di erential equations satisfying natural boundary conditions was solved numerically. The obtained solutions agree with experimental data.
Keywords: B-determining equations method., far turbulent wake, $k-\epsilon$ models of turbulence, Turbulence.
Mathematics Subject Classification: Primary: 76F60, 35Q3.
Citation: Oleg V. Kaptsov, Alexey V. Schmidt. Reduction of three-dimensional model of the far turbulent wake to one-dimensional problem. Conference Publications, 2011, 2011 (Special) : 794-802. doi: 10.3934/proc.2011.2011.794
[1]

Joachim Naumann, Jörg Wolf. On Prandtl's turbulence model: Existence of weak solutions to the equations of stationary turbulent pipe-flow. Discrete & Continuous Dynamical Systems - S, 2013, 6 (5) : 1371-1390. doi: 10.3934/dcdss.2013.6.1371
[2]

D.J. Georgiev, A. J. Roberts, D. V. Strunin. Nonlinear dynamics on centre manifolds describing turbulent floods: k-$\omega$ model. Conference Publications, 2007, 2007 (Special) : 419-428. doi: 10.3934/proc.2007.2007.419
[3]

François Baccelli, Augustin Chaintreau, Danny De Vleeschauwer, David R. McDonald. HTTP turbulence. Networks & Heterogeneous Media, 2006, 1 (1) : 1-40. doi: 10.3934/nhm.2006.1.1
[4]

Eric Falcon. Laboratory experiments on wave turbulence. Discrete & Continuous Dynamical Systems - B, 2010, 13 (4) : 819-840. doi: 10.3934/dcdsb.2010.13.819
[5]

Hugo Beirão da Veiga. Turbulence models, $p-$fluid flows, and $W^{2, L}$ regularity of solutions. Communications on Pure & Applied Analysis, 2009, 8 (2) : 769-783. doi: 10.3934/cpaa.2009.8.769
[6]

Luigi C. Berselli, Argus Adrian Dunca, Roger Lewandowski, Dinh Duong Nguyen. Modeling error of $ \alpha $-models of turbulence on a two-dimensional torus. Discrete & Continuous Dynamical Systems - B, 2020  doi: 10.3934/dcdsb.2020305
[7]

Chui-Jie Wu, Hongliang Zhao. Generalized HWD-POD method and coupling low-dimensional dynamical system of turbulence. Conference Publications, 2001, 2001 (Special) : 371-379. doi: 10.3934/proc.2001.2001.371
[8]

W. Layton, R. Lewandowski. On a well-posed turbulence model. Discrete & Continuous Dynamical Systems - B, 2006, 6 (1) : 111-128. doi: 10.3934/dcdsb.2006.6.111
[9]

Yifei Lou, Sung Ha Kang, Stefano Soatto, Andrea L. Bertozzi. Video stabilization of atmospheric turbulence distortion. Inverse Problems & Imaging, 2013, 7 (3) : 839-861. doi: 10.3934/ipi.2013.7.839
[10]

Baoquan Yuan, Guoquan Qin. A blowup criterion for the 2D $k$-$\varepsilon$ model equations for turbulent flows. Kinetic & Related Models, 2016, 9 (4) : 777-796. doi: 10.3934/krm.2016016
[11]

Alexandre Boritchev. Decaying turbulence for the fractional subcritical Burgers equation. Discrete & Continuous Dynamical Systems - A, 2018, 38 (5) : 2229-2249. doi: 10.3934/dcds.2018092
[12]

Ka Kit Tung, Wendell Welch Orlando. On the differences between 2D and QG turbulence. Discrete & Continuous Dynamical Systems - B, 2003, 3 (2) : 145-162. doi: 10.3934/dcdsb.2003.3.145
[13]

Alexey Cheskidov, Susan Friedlander, Nataša Pavlović. An inviscid dyadic model of turbulence: The global attractor. Discrete & Continuous Dynamical Systems - A, 2010, 26 (3) : 781-794. doi: 10.3934/dcds.2010.26.781
[14]

Nusret Balci, Ciprian Foias, M. S Jolly, Ricardo Rosa. On universal relations in 2-D turbulence. Discrete & Continuous Dynamical Systems - A, 2010, 27 (4) : 1327-1351. doi: 10.3934/dcds.2010.27.1327
[15]

John V. Shebalin. Theory and simulation of real and ideal magnetohydrodynamic turbulence. Discrete & Continuous Dynamical Systems - B, 2005, 5 (1) : 153-174. doi: 10.3934/dcdsb.2005.5.153
[16]

Chjan C. Lim, Ka Kit Tung. Introduction: Recent advances in vortex dynamics and turbulence. Discrete & Continuous Dynamical Systems - B, 2005, 5 (1) : i-i. doi: 10.3934/dcdsb.2005.5.1i
[17]

Björn Birnir. The Kolmogorov-Obukhov-She-Leveque scaling in turbulence. Communications on Pure & Applied Analysis, 2014, 13 (5) : 1737-1757. doi: 10.3934/cpaa.2014.13.1737
[18]

Peter R. Kramer, Joseph A. Biello, Yuri Lvov. Application of weak turbulence theory to FPU model. Conference Publications, 2003, 2003 (Special) : 482-491. doi: 10.3934/proc.2003.2003.482
[19]

Marcel Lesieur. Two-point closure based large-eddy simulations in turbulence, Part 1: Isotropic turbulence. Discrete & Continuous Dynamical Systems - S, 2011, 4 (1) : 155-168. doi: 10.3934/dcdss.2011.4.155
[20]

Qi Wang, Yanren Hou. Determining an obstacle by far-field data measured at a few spots. Inverse Problems & Imaging, 2015, 9 (2) : 591-600. doi: 10.3934/ipi.2015.9.591

 Impact Factor: 

Tools

Metrics

  • PDF downloads (15)
  • HTML views (0)
  • Cited by (0)

Other articles
by authors

[Back to Top]

Copyright © 2020 American Institute of Mathematical Sciences