Topic

# Secondary flow

About: Secondary flow is a research topic. Over the lifetime, 4957 publications have been published within this topic receiving 82021 citations.

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TL;DR: In this paper, the secondary circulation of a hurricane-like vortice is modeled as a two-dimensional stream function dipole response of Eliassen's diagnostic technique, modified by both the spatial variations of the vortex structure and the influences of boundary conditions.

Abstract: Eliassen's (1951) diagnostic technique is used to calculate the secondary circulation induced by point sources of heat and momentum in balanced, hurricane-like vortices. Scale analysis reveals that such responses are independent of the horizontal scale of the vortex. Analytic solutions for the secondary circulation are readily obtained in idealized barotropic vortices, but numerical methods are required for more realistic barotropic and baroclinic vortices. For sources near the radius of maximum wind, the local, two-dimensional, streamfunction dipole response of Eliassen is modified by both the spatial variations of the vortex structure and the influences of boundary conditions. The secondary flow advects mean-flow buoyancy and angular momentum and thus leads to a slow evolution of the vortex structure. In weak systems (maximum tangential wind <35 m s−1), the restraining influences of structure and boundaries lengthen the time scale of the vortex evolution. In stronger vortices, the horizontal sc...

535 citations

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TL;DR: Numerical calculations of the 2-D steady incompressible driven cavity flow are presented and comparisons are made with benchmark solutions found in the literature.

Abstract: SUMMARY Numerical calculations of the 2-D steady incompressible driven cavity flow are presented. The NavierStokes equations in streamfunction and vorticity formulation are solved numerically using a fine uniform grid mesh of 601 × 601. The steady driven cavity solutions are computed for Re ≤ 21,000 with a maximum absolute residuals of the governing equations that were less than 10 −10 . A new quaternary vortex at the bottom left corner and a new tertiary vortex at the top left corner of the cavity are observed in the flow field as the Reynolds number increases. Detailed results are presented and comparisons are made with benchmark solutions found in the literature.

531 citations

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TL;DR: In this article, a sphere is placed in a weak shear flow of an inviscid fluid and the secondary velocity resulting from advection of vorticity by the irrotational component of the flow is computed on the sphere surface, and on the upstream axis.

Abstract: This paper concerns the flow about a sphere placed in a weak shear flow of an inviscid fluid. The secondary velocity resulting from advection of vorticity by the irrotational component of the flow is computed on the sphere surface, and on the upstream axis. The resulting lift force on the sphere is evaluated, and the result is confirmed by an analytical far-field calculation. The displacement of the stagnation streamline, far upstream of the sphere, is calculated more accurately than in previous papers.

508 citations

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TL;DR: In this article, the authors consider the way in which the state of rigid rotation of a contained viscous fluid is established, and they find that the motion consists of three distinct phases, namely, the development of the Ekman layer, the inviscid fluid spin-up, and the viscous decay of residual oscillations.

Abstract: We consider here the manner in which the state of rigid rotation of a contained viscous fluid is established. It is found that the motion consists of three distinct phases, namely, the development of the Ekman layer, the inviscid fluid spin-up, and the viscous decay of residual oscillations. The Ekman layer plays the significant role in the transient process by inducing a small circulatory secondary flow. Low angular momentum fluid entering the layer from the geostrophic interior is replaced by fluid with greater angular momentum convected inward to conserve mass. The rotational velocity in the interior increases as a consequence of conservation of angular momentum, and the vorticity is increased through the stretching of vortex lines. The spin-up time is Boundary-layer theory is used to study the phenomenon in the case of general axially symmetric container configuration and explicit formulas are deduced which exhibit the effect of geometry in spin-up. The special case of cylindrical side walls is also investigated by this method. The results of very simple experiments confirm the theoretical predictions.

442 citations

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TL;DR: The mean flow and turbulent statistics obtained from the numerical simulation of the fully developed turbulent flow through a straight duct of square cross-section are reported in this paper, and the Reynolds number based on the bulk velocity and hydraulic diameter is 4410.

Abstract: The mean flow and turbulent statistics obtained from the numerical simulation of the fully developed turbulent flow through a straight duct of square cross-section are reported. The Reynolds number based on the bulk velocity and hydraulic diameter is 4410. Spatial and temporal approximations of the equations of motion were derived from standard finite-difference techniques. To achieve sufficient spatial resolution 16.1 × 106 grid nodes were employed. Turbulent statistics along the wall bisectors show good agreement with plane channel data despite the influence of the sidewalls in the former flow. The mean secondary flow field consists of two counter-rotating cells symmetrically placed about the corner bisectors with their common flow towards each corner with strong evidence for the existence of a smaller and much weaker pair situated about the wall bisectors. The mean streamwise vorticity of each corner cell is found to be associated with a stronger vorticity distribution of the opposite sign having an absolute maximum on the nearest duct wall.

441 citations