Numerical investigation of a swirling flow under the optimal perturbation Journal of Hydrodynamics, Ser. B, DE Sun. Numerical investigation of a swirling flow under the optimal perturbation. The global optimal perturbation is considered as the highly sensitive to small perturbations, estimating the initial perturbation.
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In axisymmetric cases, three flow regimes extent of transient growth; however, the physical are found: 1 the linear growth; 2 the decay of perturbation mechanisms of growth was not investigated. Transient energy; 3 secondary energy growth. The development of the vortex structure is also investigated for non-symmetric flows. Furthermore, these transient growth called bypass transition to turbulence of parallel shear mechanisms were explained in terms of the combined flows and the linear transient growth of small effects of the strain and vorticity components of the disturbances is generally thought to be the starting mean flow, which play counteractive roles.
Thus, the point for bypass transition mechanisms. Different from the eigenmodes.
Namely, in a non-normal linear system study of Delbende et al. Physically, a lift-up present work concentrates on this problem by direct mechanism that spanwise vorticity in basic flow numerical simulation of the dynamics of the global transfers energy to streamwise velocity has been optimal perturbation obtained by solving the transient universally accepted to explain this short-term growth growth problem with given azimuthal and axial in asymptotically stable flow regimes.
More recently, transient growth has also been applied The remainder of the paper is organized as follows. In to swirling flows widely. Numerical like geophysical vortices. Final conclusions are given in the last Fig. The detailed numerical procedure is given in Ref. A periodic condition is imposed in z-direction as the optimal perturbation studied is Fourier-decomposed along z.
For fixed Re and a wavenumber pair n, k , structures on the fully three-dimensional flow fields, in transient growth analysis, G t is the transient we consider the axisymmetric case as the first step of energy growth function - enveloping all energy addressing the nonlinear evolution of the global growth curves E t - its maximum value optimal perturbation.
Special care is taken for the radial achieves the maximum value of Gmax. The initial resolution in the short wave case, and we use grid conditions for numerical simulations are obtained by points. The influences of axial wavenumber k will adding disturbances to the mean state. Here, we use also be documented in this section.
The maximum, minimum, and increment are a 0. The pursuit of Following Refs.
It is denoted by CP, shows that energy of disturbances decreases with time. Meanwhile, the outward motion of the position of the maximum azimuthal vorticity is observed Fig.
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Afterwards, a new maximum value exceeds the origin one Fig. The vortex ring surrounding the new maximum interacts with the Oseen vortex core, which transports energy to the vortex ring. It is the energy transport that renders an increase of the perturbation energy again. The maximum, minimum, and number of levels are a 0. Similar to the axisymmetric case, the flow evolution has three stages Fig. In The development trend of the flow field is obviously the linear stage, the radial perturbation still plays a similar for all three values of k considered.
However, key role, although the ratio of which to those in the growth of perturbations decreases with increasing k other directions is relatively small Fig. As the azimuthal perturbation velocity grows to high levels, as well as the length of the linear stage, due to the it is necessary to investigate the effect of its damping effect of viscosity. More computational time development on the vortex dynamics.
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Initially the dynamics of a single normal mode to better illustrate vorticity contribution lies in a wide range of the radial the effects of the transient growth characteristics on coordinate r Fig. This could result from the fact the nonlinear evolution of the Oseen vortex. Energy growth of three-dimensional remarkable fact that the vortex shape remains nearly disturbances in plane Poiseuille flow [J].
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