American Institute of Mathematical Sciences

Advanced
  • Previous Article
    The Dirichlet quotient of point vortex interactions on the surface of the sphere examined by Monte Carlo experiments
  • DCDS-B Home
  • This Issue
  • Next Article
    On the double cascades of energy and enstrophy in two dimensional turbulence. Part 1. Theoretical formulation
February  2005, 5(1): 103-124. doi: 10.3934/dcdsb.2005.5.103

On the double cascades of energy and enstrophy in two dimensional turbulence. Part 2. Approach to the KLB limit and interpretation of experimental evidence

Eleftherios Gkioulekas 1, and  Ka Kit Tung 2,

1. 

Department of Applied Mathematics, Box 352420, University of Washington, Seattle, WA, 98195-2420
2. 

University of Washington, Department of Applied Mathematics, Box 352420, Seattle, WA 98195-2420

Received  October 2003 Revised  July 2004 Published  November 2004

This paper is concerned with three interrelated issues on our proposal of double cascades intended to serve as a more realistic theory of two-dimensional turbulence. We begin by examining the approach to the KLB limit. We present improved proofs of the result by Fjortoft. We also explain why in that limit the subleading downscale energy cascade and upscale enstrophy cascade are hidden in the energy spectrum. Then we review the experimental evidence from numerical simulations concerning the realizability of the energy and enstrophy cascade. The inverse energy cascade is found to be affected by the presense of a particular solution, and the downscale enstrophy cascade is not robust. In particular, while it is possible to have either the upscale range or the downscale range with suitable choice of dissipations, the dual cascade of KLB does not appear to be realizable, not even approximately. Finally, we amplify the hypothesis that the energy spectrum of the atmosphere reflects a combined downscale cascade of energy and enstrophy. The possibility of the downscale helicity cascade is also considered.
Keywords: energy, QG turbulence., 2d turbulence, enstrophy.
Mathematics Subject Classification: 76FXX, 60G6.
Citation: Eleftherios Gkioulekas, Ka Kit Tung. On the double cascades of energy and enstrophy in two dimensional turbulence. Part 2. Approach to the KLB limit and interpretation of experimental evidence. Discrete and Continuous Dynamical Systems - B, 2005, 5 (1) : 103-124. doi: 10.3934/dcdsb.2005.5.103
[1]

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
[2]

S. Danilov. Non-universal features of forced 2D turbulence in the energy and enstrophy ranges. Discrete and Continuous Dynamical Systems - B, 2005, 5 (1) : 67-78. doi: 10.3934/dcdsb.2005.5.67
[3]

Patrick Fischer, Charles-Henri Bruneau, Hamid Kellay. Multiresolution analysis for 2D turbulence. part 2: A physical interpretation. Discrete and Continuous Dynamical Systems - B, 2007, 7 (4) : 717-734. doi: 10.3934/dcdsb.2007.7.717
[4]

Patrick Fischer. Multiresolution analysis for 2D turbulence. Part 1: Wavelets vs cosine packets, a comparative study. Discrete and Continuous Dynamical Systems - B, 2005, 5 (3) : 659-686. doi: 10.3934/dcdsb.2005.5.659
[5]

Eleftherios Gkioulekas, Ka Kit Tung. On the double cascades of energy and enstrophy in two dimensional turbulence. Part 1. Theoretical formulation. Discrete and Continuous Dynamical Systems - B, 2005, 5 (1) : 79-102. doi: 10.3934/dcdsb.2005.5.79
[6]

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
[7]

Marcel Lesieur. Two-point closure based large-eddy simulations in turbulence. Part 2: Inhomogeneous cases. Discrete and Continuous Dynamical Systems, 2010, 28 (1) : 227-241. doi: 10.3934/dcds.2010.28.227
[8]

Leonardo Kosloff, Tomas Schonbek. Existence and decay of solutions of the 2D QG equation in the presence of an obstacle. Discrete and Continuous Dynamical Systems - S, 2014, 7 (5) : 1025-1043. doi: 10.3934/dcdss.2014.7.1025
[9]

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
[10]

Eleftherios Gkioulekas, Ka Kit Tung. Is the subdominant part of the energy spectrum due to downscale energy cascade hidden in quasi-geostrophic turbulence?. Discrete and Continuous Dynamical Systems - B, 2007, 7 (2) : 293-314. doi: 10.3934/dcdsb.2007.7.293
[11]

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
[12]

Tianwen Luo, Tao Tao, Liqun Zhang. Finite energy weak solutions of 2d Boussinesq equations with diffusive temperature. Discrete and Continuous Dynamical Systems, 2020, 40 (6) : 3737-3765. doi: 10.3934/dcds.2019230
[13]

Aseel Farhat, M. S Jolly, Evelyn Lunasin. Bounds on energy and enstrophy for the 3D Navier-Stokes-$\alpha$ and Leray-$\alpha$ models. Communications on Pure and Applied Analysis, 2014, 13 (5) : 2127-2140. doi: 10.3934/cpaa.2014.13.2127
[14]

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
[15]

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
[16]

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
[17]

Mimi Dai. Phenomenologies of intermittent Hall MHD turbulence. Discrete and Continuous Dynamical Systems - B, 2021  doi: 10.3934/dcdsb.2021285
[18]

Gianluca Crippa, Elizaveta Semenova, Stefano Spirito. Strong continuity for the 2D Euler equations. Kinetic and Related Models, 2015, 8 (4) : 685-689. doi: 10.3934/krm.2015.8.685
[19]

Bernd Kawohl, Guido Sweers. On a formula for sets of constant width in 2d. Communications on Pure and Applied Analysis, 2019, 18 (4) : 2117-2131. doi: 10.3934/cpaa.2019095
[20]

Julien Cividini. Pattern formation in 2D traffic flows. Discrete and Continuous Dynamical Systems - S, 2014, 7 (3) : 395-409. doi: 10.3934/dcdss.2014.7.395

2021 Impact Factor: 1.497

Tools

Metrics

  • PDF downloads (56)
  • HTML views (0)
  • Cited by (17)

Other articles
by authors

[Back to Top]

Copyright © 2022 American Institute of Mathematical Sciences | Privacy Policy