<p>Reynolds stress budgets computed from a direct numerical simulation of the spanwise-periodic flow over a Gaussian bump are analyzed to gain insight into turbulence modification under different pressure-gradient regimes in three subregions. The four nonzero Reynolds stress components are defined in the local orthogonal coordinate system at a given location on the bump surface. The first subregion starts upstream of the bump under a mild adverse pressure gradient (APG) that becomes progressively stronger toward the bump. The second subregion succeeds the first subregion near the bump foot and contains a strong favorable pressure gradient (FPG) until very near the bump apex. The third subregion is the strong APG section that begins near the apex and lasts until the flow separation point. The mild/strong APG reduces the mean shear rate near the wall, which has a dampening effect on turbulence production while the strong FPG leads to an order of magnitude increase in near-wall turbulence production as a result of the much-enhanced mean shear rate. The mean shear rate of the buffer zone between inner and outer parts of the decelerated flow past the apex also gives way to enhanced production. The turbulent kinetic energy (TKE) gets redistributed internally among the normal stress components via the pressure-strain correlation. For the shear stress, pressure strain is generally a consuming term. The reduction in near-wall TKE production in the APG sections leads to decreases in pressure-strain amplitudes for all normal stresses. For the shear stress, a similar correlation between production and pressure strain also exists in the mild APG section, but a more intricate behavior is found in the strong APG section. In the strong FPG region, the much-amplified near-wall production of turbulence leads to substantial enhancements of the pressure-strain correlation for all components. As the flow goes through different pressure-gradient regimes, the decreasing/increasing deficits or surpluses between energizing (production and/or pressure strain) and consuming (dissipation and/or pressure strain) terms near the wall are balanced by the relevant spatially-redistributive terms that proportionally either diminish or amplify in magnitude. The budget surpluses resulting from the much-amplified near-wall turbulence production in the strong FPG section lead to the formation of an internal layer beneath the accelerated boundary layer, where new near-wall peaks emerge for the wall-normal and shear stresses as the original peaks of the other components strengthen substantially. The paper describes the rather complex flow dynamics that eventually leads to boundary-layer separation.</p>

Turbulence Modification Under the Influence of Pressure Gradients

期刊论文
发表日期：

2026年7月22日

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Ali Uzun,
Mujeeb R. Malik

摘要

Reynolds stress budgets computed from a direct numerical simulation of the spanwise-periodic flow over a Gaussian bump are analyzed to gain insight into turbulence modification under different pressure-gradient regimes in three subregions. The four nonzero Reynolds stress components are defined in the local orthogonal coordinate system at a given location on the bump surface. The first subregion starts upstream of the bump under a mild adverse pressure gradient (APG) that becomes progressively stronger toward the bump. The second subregion succeeds the first subregion near the bump foot and contains a strong favorable pressure gradient (FPG) until very near the bump apex. The third subregion is the strong APG section that begins near the apex and lasts until the flow separation point. The mild/strong APG reduces the mean shear rate near the wall, which has a dampening effect on turbulence production while the strong FPG leads to an order of magnitude increase in near-wall turbulence production as a result of the much-enhanced mean shear rate. The mean shear rate of the buffer zone between inner and outer parts of the decelerated flow past the apex also gives way to enhanced production. The turbulent kinetic energy (TKE) gets redistributed internally among the normal stress components via the pressure-strain correlation. For the shear stress, pressure strain is generally a consuming term. The reduction in near-wall TKE production in the APG sections leads to decreases in pressure-strain amplitudes for all normal stresses. For the shear stress, a similar correlation between production and pressure strain also exists in the mild APG section, but a more intricate behavior is found in the strong APG section. In the strong FPG region, the much-amplified near-wall production of turbulence leads to substantial enhancements of the pressure-strain correlation for all components. As the flow goes through different pressure-gradient regimes, the decreasing/increasing deficits or surpluses between energizing (production and/or pressure strain) and consuming (dissipation and/or pressure strain) terms near the wall are balanced by the relevant spatially-redistributive terms that proportionally either diminish or amplify in magnitude. The budget surpluses resulting from the much-amplified near-wall turbulence production in the strong FPG section lead to the formation of an internal layer beneath the accelerated boundary layer, where new near-wall peaks emerge for the wall-normal and shear stresses as the original peaks of the other components strengthen substantially. The paper describes the rather complex flow dynamics that eventually leads to boundary-layer separation.