scholarly journals Critical Layer Analysis of Stuart Vortices in a Plane Jet

2014 ◽  
Vol 2014 ◽  
pp. 1-12
Author(s):  
Ghada Alobaidi ◽  
Roland Mallier
Keyword(s):  
Steady State ◽  
Finite Amplitude ◽  
Critical Layer ◽  
Quasi Steady State ◽  
Two Dimensional ◽  
Layer Analysis ◽  
Plane Jet ◽  
Stuart Vortices

Asymptotic techniques are used to model quasi-steady-state vortices in the plane (Bickley) inviscid jet. A nonlinear critical layer analysis is used to find a family of steady-state finite amplitude two-dimensional vortices which are based on the Stuart vortex.

Buoyant Flow and Heat Transfer in a Conducting Baffle

2008 ◽  
Author(s):  
S. K. S. Boetcher ◽  
F. A. Kulacki
Keyword(s):  
Heat Transfer ◽  
Steady State ◽  
Quasi Steady State ◽  
Two Dimensional ◽  
Buoyant Flow ◽  
Transfer Rates ◽  
Flow And Heat Transfer ◽  
Rayleigh Numbers ◽  
Negatively Buoyant ◽  
Surrounding Fluid

A numerical simulation of transient two-dimensional negatively buoyant flow into a straight baffle situated below an isothermal circular cylinder is performed. Both an adiabatic and a highly conducting baffle are considered over a range of Rayleigh numbers, 106 < RaD < 107. During the quasi-steady-state period, the surrounding fluid is effectively considered infinite in extent and at constant temperature. It is found that in general, the conducting baffle is at a disadvantage in maintaining a short attachment length which is needed to optimally slow the flow to prevent mixing. Qualitative flow fields are shown and heat transfer rates to the cylinder are calculated at the quasi-steady state.

An investigation of transition to turbulence in bounded oscillatory Stokes flows Part 2. Numerical simulations

1991 ◽  
Vol 225 ◽  
pp. 423-444 ◽  
Author(s):  
R. Akhavan ◽  
R. D. Kamm ◽  
A. H. Shapiro
Keyword(s):  
Steady State ◽  
Numerical Simulations ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Finite Amplitude ◽  
Transition To Turbulence ◽  
Quasi Equilibrium ◽  
Two Dimensional ◽  
Spectral Techniques ◽  
Periodic Steady State

The stability of oscillatory channel flow to different classes of infinitesimal and finite-amplitude two- and three-dimensional disturbances has been investigated by direct numerical simulations of the Navier–Stokes equations using spectral techniques. All infinitesimal disturbances were found to decay monotonically to a periodic steady state, in agreement with earlier Floquet theory calculations. However, before reaching this periodic steady state an infinitesimal disturbance introduced in the boundary layer was seen to experience transient growth in accordance with the predictions of quasi-steady theories for the least stable eigenmodes of the Orr–Sommerfeld equation for instantaneous ‘frozen’ profiles. The reason why this growth is not sustained in the periodic steady state is explained. Two-dimensional infinitesimal disturbances reaching finite amplitudes were found to saturate in an ordered state of two-dimensional quasi-equilibrium waves that decayed on viscous timescales. No finite-amplitude equilibrium waves were found in our cursory study. The secondary instability of these two-dimensional finite-amplitude quasi-equilibrium states to infinitesimal three-dimensional perturbations predicts transitional Reynolds numbers and turbulent flow structures in agreement with experiments.

scholarly journals Optimal perturbation for two-dimensional vortex systems: route to non-axisymmetric state

2018 ◽  
Vol 855 ◽  
pp. 922-952 ◽  
Author(s):  
Navrose ◽  
H. G. Johnson ◽  
V. Brion ◽  
L. Jacquin ◽  
J. C. Robinet
Keyword(s):  
Steady State ◽  
Initial Perturbation ◽  
Vortex Pair ◽  
Vortex State ◽  
Quasi Steady State ◽  
Two Dimensional ◽  
Optimal Perturbation ◽  
Perturbation Energy ◽  
Counter Rotating Vortex Pair ◽  
Linear And Nonlinear

We investigate perturbations that maximize the gain of disturbance energy in a two-dimensional isolated vortex and a counter-rotating vortex pair. The optimization is carried out using the method of Lagrange multipliers. For low initial energy of the perturbation ( $E(0)$ ), the nonlinear optimal perturbation/gain is found to be the same as the linear optimal perturbation/gain. Beyond a certain threshold $E(0)$ , the optimal perturbation/gain obtained from linear and nonlinear computations are different. There exists a range of $E(0)$ for which the nonlinear optimal gain is higher than the linear optimal gain. For an isolated vortex, the higher value of nonlinear optimal gain is attributed to interaction among different azimuthal components, which is otherwise absent in a linearized system. Spiral dislocations are found in the nonlinear optimal perturbation at the radial location where the most dominant wavenumber changes. Long-time nonlinear evolution of linear and nonlinear optimal perturbations is studied. The evolution shows that, after the initial increment of perturbation energy, the vortex attains a quasi-steady state where the mean perturbation energy decreases on a slow time scale. The quasi-steady vortex state is non-axisymmetric and its shape depends on the initial perturbation. It is observed that the lifetime of a quasi-steady vortex state obtained using the nonlinear optimal perturbation is longer than that obtained using the linear optimal perturbation. For a counter-rotating vortex pair, the mechanism that maximizes the energy gain is found to be similar to that of the isolated vortex. Within the linear framework, the optimal perturbation for a vortex pair can be either symmetric or antisymmetric, whereas the structure of the nonlinear optimal perturbation, beyond the threshold $E(0)$ , is always asymmetric. No quasi-steady state for a counter-rotating vortex pair is observed.

Network reconstruction based on steady-state data

2008 ◽  
Vol 45 ◽  
pp. 161-176 ◽  
Author(s):  
Eduardo D. Sontag
Keyword(s):  
Steady State ◽  
Reverse Engineering ◽  
Theoretical Method ◽  
Network Reconstruction ◽  
Quasi Steady State ◽  
State Data

This paper discusses a theoretical method for the “reverse engineering” of networks based solely on steady-state (and quasi-steady-state) data.

Quasi-steady-state performance of a heat pipe subjected to transient acceleration loadings

10.2514/3.895 ◽  
1997 ◽  
Vol 11 ◽  
pp. 306-309 ◽  
Author(s):  
Edwin H. Olmstead ◽  
Edward S. Taylor ◽  
Meng Wang ◽  
Parviz Moin ◽  
Scott K. Thomas ◽  
...  
Keyword(s):  
Steady State ◽  
Heat Pipe ◽  
Quasi Steady State ◽  
Steady State Performance
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