# American Institute of Mathematical Sciences

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

 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.
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 and 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 and Heterogeneous Media, 2006, 1 (1) : 1-40. doi: 10.3934/nhm.2006.1.1 [4] Yat Tin Chow, Ali Pakzad. On the zeroth law of turbulence for the stochastically forced Navier-Stokes equations. Discrete and Continuous Dynamical Systems - B, 2021  doi: 10.3934/dcdsb.2021270 [5] Eric Falcon. Laboratory experiments on wave turbulence. Discrete and Continuous Dynamical Systems - B, 2010, 13 (4) : 819-840. doi: 10.3934/dcdsb.2010.13.819 [6] Hugo Beirão da Veiga. Turbulence models, $p-$fluid flows, and $W^{2, L}$ regularity of solutions. Communications on Pure and Applied Analysis, 2009, 8 (2) : 769-783. doi: 10.3934/cpaa.2009.8.769 [7] Luigi C. Berselli, Argus Adrian Dunca, Roger Lewandowski, Dinh Duong Nguyen. Modeling error of $\alpha$-models of turbulence on a two-dimensional torus. Discrete and Continuous Dynamical Systems - B, 2021, 26 (9) : 4613-4643. doi: 10.3934/dcdsb.2020305 [8] W. Layton, R. Lewandowski. On a well-posed turbulence model. Discrete and 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 and Imaging, 2013, 7 (3) : 839-861. doi: 10.3934/ipi.2013.7.839 [10] Mimi Dai. Phenomenologies of intermittent Hall MHD turbulence. Discrete and Continuous Dynamical Systems - B, 2021  doi: 10.3934/dcdsb.2021285 [11] 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 [12] Baoquan Yuan, Guoquan Qin. A blowup criterion for the 2D $k$-$\varepsilon$ model equations for turbulent flows. Kinetic and Related Models, 2016, 9 (4) : 777-796. doi: 10.3934/krm.2016016 [13] Alexandre Boritchev. Decaying turbulence for the fractional subcritical Burgers equation. Discrete and Continuous Dynamical Systems, 2018, 38 (5) : 2229-2249. doi: 10.3934/dcds.2018092 [14] Ka Kit Tung, Wendell Welch Orlando. On the differences between 2D and QG turbulence. Discrete and Continuous Dynamical Systems - B, 2003, 3 (2) : 145-162. doi: 10.3934/dcdsb.2003.3.145 [15] Alexey Cheskidov, Susan Friedlander, Nataša Pavlović. An inviscid dyadic model of turbulence: The global attractor. Discrete and Continuous Dynamical Systems, 2010, 26 (3) : 781-794. doi: 10.3934/dcds.2010.26.781 [16] Nusret Balci, Ciprian Foias, M. S Jolly, Ricardo Rosa. On universal relations in 2-D turbulence. Discrete and Continuous Dynamical Systems, 2010, 27 (4) : 1327-1351. doi: 10.3934/dcds.2010.27.1327 [17] John V. Shebalin. Theory and simulation of real and ideal magnetohydrodynamic turbulence. Discrete and Continuous Dynamical Systems - B, 2005, 5 (1) : 153-174. doi: 10.3934/dcdsb.2005.5.153 [18] Chjan C. Lim, Ka Kit Tung. Introduction: Recent advances in vortex dynamics and turbulence. Discrete and Continuous Dynamical Systems - B, 2005, 5 (1) : i-i. doi: 10.3934/dcdsb.2005.5.1i [19] Björn Birnir. The Kolmogorov-Obukhov-She-Leveque scaling in turbulence. Communications on Pure and Applied Analysis, 2014, 13 (5) : 1737-1757. doi: 10.3934/cpaa.2014.13.1737 [20] 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

Impact Factor: