### Abstract

The large-scale organized structures of turbulent flow can be characterized quantitatively by a conditional eddy, given the local kinematic state of the flow as specified by the conditional average of u(x‘, t) given the velocity and the deformation tensor at a point x:(u(x‘, t)u(x, t), d(xt)}. By means of linear mean-square stochastic estimation, (u‘u, £/ is approximated in terms of the two-point spatial correlation tensor, and the conditional eddy is evaluated for arbitrary values of u(x, t) and d(x, t), permitting study of the turbulent field for a wide range of local kinematic states. The linear estimate is applied to homogeneous turbulent shear flow data generated by direct numerical simulation. The joint velocity-deformation probability density function is used to obtain conditions corresponding to those events that contribute most to the Reynolds shear stress. The primary contributions to the second-quadrant and fourth-quadrant Reynolds-stress events in homogeneous shear flow come from flow induced through the’legs’ and close to the ‘heads’ of upright and inverted ‘hairpins’, respectively. The equation governing the joint probability density function of f_{u} _{d}(u, d) is derived. It is shown that this equation contains u’ 1 u, f and that the equations for second-order closure can be derived from it.

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

Pages (from-to) | 531-559 |

Number of pages | 29 |

Journal | Journal of Fluid Mechanics |

Volume | 190 |

DOIs | |

State | Published - 1988 |

Externally published | Yes |

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### ASJC Scopus subject areas

- Mechanical Engineering
- Mechanics of Materials
- Condensed Matter Physics

### Cite this

**Stochastic estimation of organized turbulent structure : Homogeneous shear flow.** / Adrian, Ronald.

Research output: Contribution to journal › Article

}

TY - JOUR

T1 - Stochastic estimation of organized turbulent structure

T2 - Homogeneous shear flow

AU - Adrian, Ronald

PY - 1988

Y1 - 1988

N2 - The large-scale organized structures of turbulent flow can be characterized quantitatively by a conditional eddy, given the local kinematic state of the flow as specified by the conditional average of u(x‘, t) given the velocity and the deformation tensor at a point x:(u(x‘, t)u(x, t), d(xt)}. By means of linear mean-square stochastic estimation, (u‘u, £/ is approximated in terms of the two-point spatial correlation tensor, and the conditional eddy is evaluated for arbitrary values of u(x, t) and d(x, t), permitting study of the turbulent field for a wide range of local kinematic states. The linear estimate is applied to homogeneous turbulent shear flow data generated by direct numerical simulation. The joint velocity-deformation probability density function is used to obtain conditions corresponding to those events that contribute most to the Reynolds shear stress. The primary contributions to the second-quadrant and fourth-quadrant Reynolds-stress events in homogeneous shear flow come from flow induced through the’legs’ and close to the ‘heads’ of upright and inverted ‘hairpins’, respectively. The equation governing the joint probability density function of fu d(u, d) is derived. It is shown that this equation contains u’ 1 u, f and that the equations for second-order closure can be derived from it.

AB - The large-scale organized structures of turbulent flow can be characterized quantitatively by a conditional eddy, given the local kinematic state of the flow as specified by the conditional average of u(x‘, t) given the velocity and the deformation tensor at a point x:(u(x‘, t)u(x, t), d(xt)}. By means of linear mean-square stochastic estimation, (u‘u, £/ is approximated in terms of the two-point spatial correlation tensor, and the conditional eddy is evaluated for arbitrary values of u(x, t) and d(x, t), permitting study of the turbulent field for a wide range of local kinematic states. The linear estimate is applied to homogeneous turbulent shear flow data generated by direct numerical simulation. The joint velocity-deformation probability density function is used to obtain conditions corresponding to those events that contribute most to the Reynolds shear stress. The primary contributions to the second-quadrant and fourth-quadrant Reynolds-stress events in homogeneous shear flow come from flow induced through the’legs’ and close to the ‘heads’ of upright and inverted ‘hairpins’, respectively. The equation governing the joint probability density function of fu d(u, d) is derived. It is shown that this equation contains u’ 1 u, f and that the equations for second-order closure can be derived from it.

UR - http://www.scopus.com/inward/record.url?scp=84974505978&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84974505978&partnerID=8YFLogxK

U2 - 10.1017/S0022112088001442

DO - 10.1017/S0022112088001442

M3 - Article

VL - 190

SP - 531

EP - 559

JO - Journal of Fluid Mechanics

JF - Journal of Fluid Mechanics

SN - 0022-1120

ER -