### Abstract

We explore the effects of a quadratic drag, similar to that used in bulk aerodynamic formulas, on the inverse cascade of homogeneous two-dimensional turbulence. If a two-dimensional fluid is forced at a relatively small scale, then an inverse cascade of energy will be generated that may then be arrested by such a drag at large scales. Both scaling arguments and numerical experiments support the idea that in a statistically steady state the length scale of energy-containing eddies will not then depend on the energy input to the system; rather, the only external parameter that defines this scale is the quadratic drag coefficient itself. A universal form of the spectrum is suggested, and numerical experiments are in good agreement. Further, the turbulent transfer of a passive tracer in the presence of a uniform gradient is well predicted by scaling arguments based solely on the energy cascade rate and the nonlinear drag coefficient.

Original language | English (US) |
---|---|

Pages (from-to) | 73-78 |

Number of pages | 6 |

Journal | Physics of Fluids |

Volume | 16 |

Issue number | 1 |

DOIs | |

State | Published - Jan 2004 |

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### ASJC Scopus subject areas

- Mechanics of Materials
- Computational Mechanics
- Physics and Astronomy(all)
- Fluid Flow and Transfer Processes
- Condensed Matter Physics

### Cite this

*Physics of Fluids*,

*16*(1), 73-78. https://doi.org/10.1063/1.1630054

**The effects of quadratic drag on the inverse cascade of two-dimensional turbulence.** / Grianik, N.; Held, I. M.; Smith, K. S.; Vallis, G. K.

Research output: Contribution to journal › Article

*Physics of Fluids*, vol. 16, no. 1, pp. 73-78. https://doi.org/10.1063/1.1630054

}

TY - JOUR

T1 - The effects of quadratic drag on the inverse cascade of two-dimensional turbulence

AU - Grianik, N.

AU - Held, I. M.

AU - Smith, K. S.

AU - Vallis, G. K.

PY - 2004/1

Y1 - 2004/1

N2 - We explore the effects of a quadratic drag, similar to that used in bulk aerodynamic formulas, on the inverse cascade of homogeneous two-dimensional turbulence. If a two-dimensional fluid is forced at a relatively small scale, then an inverse cascade of energy will be generated that may then be arrested by such a drag at large scales. Both scaling arguments and numerical experiments support the idea that in a statistically steady state the length scale of energy-containing eddies will not then depend on the energy input to the system; rather, the only external parameter that defines this scale is the quadratic drag coefficient itself. A universal form of the spectrum is suggested, and numerical experiments are in good agreement. Further, the turbulent transfer of a passive tracer in the presence of a uniform gradient is well predicted by scaling arguments based solely on the energy cascade rate and the nonlinear drag coefficient.

AB - We explore the effects of a quadratic drag, similar to that used in bulk aerodynamic formulas, on the inverse cascade of homogeneous two-dimensional turbulence. If a two-dimensional fluid is forced at a relatively small scale, then an inverse cascade of energy will be generated that may then be arrested by such a drag at large scales. Both scaling arguments and numerical experiments support the idea that in a statistically steady state the length scale of energy-containing eddies will not then depend on the energy input to the system; rather, the only external parameter that defines this scale is the quadratic drag coefficient itself. A universal form of the spectrum is suggested, and numerical experiments are in good agreement. Further, the turbulent transfer of a passive tracer in the presence of a uniform gradient is well predicted by scaling arguments based solely on the energy cascade rate and the nonlinear drag coefficient.

UR - http://www.scopus.com/inward/record.url?scp=0942267333&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0942267333&partnerID=8YFLogxK

U2 - 10.1063/1.1630054

DO - 10.1063/1.1630054

M3 - Article

AN - SCOPUS:0942267333

VL - 16

SP - 73

EP - 78

JO - Physics of Fluids

JF - Physics of Fluids

SN - 1070-6631

IS - 1

ER -