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<p>A new vortex-dominated flow problem was defined to reveal some flow physics and to aid the design and assessment of turbulence models. The case is rich in turbulence and vorticity and physically complex although two-dimensional in the mean and free of solid boundaries. The <i>z</i> direction is homogeneous, and used for averages in the DNS so that the turbulence quantities are functions of (<i>x</i>,&#xa0;<i>y</i>,&#xa0;<i>t</i>). The flow is periodic in the <i>x</i> direction. The initial condition is a thin shear layer straddling the (<i>x</i>,&#xa0;<i>z</i>) plane and given a slight wave in the (<i>x</i>,&#xa0;<i>y</i>) plane. It is seeded with random perturbations, and turbulence develops before the Kelvin-Helmholtz instability creates two primary vortices. Each vortex entrains the shear layer into spiral sheets around itself, like vortices do over wings. Most RANS models are inaccurate in these situations, which is confirmed in the present case; they miss how the turbulence rapidly decays in and near the young vortex. The two vortices later collide and merge. The flow is driven by concurrent inviscid and turbulent phenomena, and RANS is more accurate for the former than the latter. A variety of measures of the numerical quality of the DNS are presented. We seek evidence that the vorticity exceeds the bounds of its initial condition. This cannot happen in (2D) laminar flow, but is common in RANS: vorticity of the sign opposite to the initial condition is generated by many models. We see strong evidence that this is not meaningfully present in the DNS, and attribute the small opposite excursions to the finite spatial-averaging interval and residual numerical errors. This matches our intuition, although we know of no theorem stating that opposite vorticity is unphysical. Part&#xa0;II contains comparisons with models, including eddy viscosity with and without rotation corrections and Reynolds-stress transport.</p>

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Study of a system of turbulent shear layers and vortices. Part I: direct numerical simulation and theoretical considerations

  • 期刊论文

  • 发表日期：

    2026年7月23日

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  • David J. Lusher,
  • Andrea Sansica,
  • Gary N. Coleman,
  • Philippe R. Spalart

摘要

A new vortex-dominated flow problem was defined to reveal some flow physics and to aid the design and assessment of turbulence models. The case is rich in turbulence and vorticity and physically complex although two-dimensional in the mean and free of solid boundaries. The z direction is homogeneous, and used for averages in the DNS so that the turbulence quantities are functions of (x, y, t). The flow is periodic in the x direction. The initial condition is a thin shear layer straddling the (x, z) plane and given a slight wave in the (x, y) plane. It is seeded with random perturbations, and turbulence develops before the Kelvin-Helmholtz instability creates two primary vortices. Each vortex entrains the shear layer into spiral sheets around itself, like vortices do over wings. Most RANS models are inaccurate in these situations, which is confirmed in the present case; they miss how the turbulence rapidly decays in and near the young vortex. The two vortices later collide and merge. The flow is driven by concurrent inviscid and turbulent phenomena, and RANS is more accurate for the former than the latter. A variety of measures of the numerical quality of the DNS are presented. We seek evidence that the vorticity exceeds the bounds of its initial condition. This cannot happen in (2D) laminar flow, but is common in RANS: vorticity of the sign opposite to the initial condition is generated by many models. We see strong evidence that this is not meaningfully present in the DNS, and attribute the small opposite excursions to the finite spatial-averaging interval and residual numerical errors. This matches our intuition, although we know of no theorem stating that opposite vorticity is unphysical. Part II contains comparisons with models, including eddy viscosity with and without rotation corrections and Reynolds-stress transport.