TY - JOUR

T1 - Dynamical eigenfunction decomposition of turbulent pipe flow

AU - Duggleby, Andrew

AU - Ball, Kenneth S.

AU - Paul, Mark

AU - Fischer, Paul

N1 - Funding Information:
This research was supported in part by the National Science Foundation through TeraGrid resources provided by the San Diego Supercomputing Center, and by Virginia Tech through their Terascale Computing Facility, System X.

PY - 2007

Y1 - 2007

N2 - The results of an analysis of turbulent pipe flow based on a Karhunen-Loeve decomposition are presented. The turbulent flow is generated by a direct numerical simulation of the Navier-Stokes equations using a spectral element algorithm at a Reynolds number Reπ = 150. This simulation yields a set of basis functions that captures 90% of the energy after 2763 modes. The eigenfunctions are categorized into two classes and six subclasses based on their wavenumber and coherent vorticity structure. Of the total energy, 81% is in the propagating class, characterized by constant phase speeds; the remaining energy is found in the non-propagating subclasses, the shear and roll modes. The four subclasses of the propagating modes are the wall, lift, asymmetric and ring modes. The wall modes display coherent vorticity structures near the wall, the lift modes display coherent vorticity structures that lift away from the wall, the asymmetric modes break the symmetry about the axis, and the ring modes display rings of coherent vorticity. Together, the propagating modes form a wave packet, as found from a circular normal speed locus. The energy transfer mechanism in the flow is a four-step process. The process begins with energy being transferred from mean flow to the shear modes, then to the roll modes. Energy is then transferred from the roll modes to the wall modes, and then eventually to the lift modes. The ring and asymmetric modes act as catalysts that aid in this four-step energy transfer. Physically, this mechanism shows how the energy in the flow starts at the wall and then propagates into the outer layer.

AB - The results of an analysis of turbulent pipe flow based on a Karhunen-Loeve decomposition are presented. The turbulent flow is generated by a direct numerical simulation of the Navier-Stokes equations using a spectral element algorithm at a Reynolds number Reπ = 150. This simulation yields a set of basis functions that captures 90% of the energy after 2763 modes. The eigenfunctions are categorized into two classes and six subclasses based on their wavenumber and coherent vorticity structure. Of the total energy, 81% is in the propagating class, characterized by constant phase speeds; the remaining energy is found in the non-propagating subclasses, the shear and roll modes. The four subclasses of the propagating modes are the wall, lift, asymmetric and ring modes. The wall modes display coherent vorticity structures near the wall, the lift modes display coherent vorticity structures that lift away from the wall, the asymmetric modes break the symmetry about the axis, and the ring modes display rings of coherent vorticity. Together, the propagating modes form a wave packet, as found from a circular normal speed locus. The energy transfer mechanism in the flow is a four-step process. The process begins with energy being transferred from mean flow to the shear modes, then to the roll modes. Energy is then transferred from the roll modes to the wall modes, and then eventually to the lift modes. The ring and asymmetric modes act as catalysts that aid in this four-step energy transfer. Physically, this mechanism shows how the energy in the flow starts at the wall and then propagates into the outer layer.

KW - Direct numerical simulation

KW - Karhunen-Loeve decomposition

KW - Mechanism

KW - Pipe flow

KW - Turbulence

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U2 - 10.1080/14685240701376316

DO - 10.1080/14685240701376316

M3 - Article

AN - SCOPUS:38049053008

SN - 1468-5248

VL - 8

SP - 1

EP - 24

JO - Journal of Turbulence

JF - Journal of Turbulence

ER -