The energy balance in modulated plane Poiseuille flow

Herbert, D. M.

doi:10.1017/s0022112072002186

Cited by 11 publications

(9 citation statements)

References 2 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…We note that a complete set of dimensionless parameters for the basic flow is provided by G, R 1 and R 2 . Studies relevant to the current investigation include those of Grosch & Salwen (1968) based on numerical time integration of a Galerkin approximation to the governing equations; Herbert (1972), who employed energy methods; Hall (1975), who used perturbation methods based on Floquet theory and von Kerczek (1982), where numerical techniques also based on Floquet theory were implemented. These authors looked at the stability of oscillatory plane Poiseuille flow from the standpoint that the oscillatory component could be thought of as a perturbation of the underlying steady flow.…”

Section: Introductionmentioning

confidence: 99%

“…For relatively large values of G time-modulation appeared to have a stabilizing effect but when G is less than roughly 10 destabilization occurred. Herbert (1972) provided further qualitative information by examining the disturbance energy balance in modulated plane Poiseuille flow. He concluded that the oscillatory component of the basic flow inhibited energy transfer in some parameter regions and thus had a stabilizing effect on perturbations.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

The linear stability of oscillatory Poiseuille flow in channels and pipes

Thomas¹,

Bassom²,

Blennerhassett

et al. 2011

Proc. R. Soc. A.

View full text Add to dashboard Cite

The linear stability of confined, periodic, parallel fluid flows is examined. The flow fields considered consist of a steady pressure gradient-driven velocity field combined with a purely oscillatory component generated by either an oscillatory pressure gradient or by harmonically oscillating bounding surfaces. Plane channel and circular pipe geometries are studied and all possible combinations of the steady and oscillatory flow components investigated. Neutral stability curves and critical conditions for instability are computed for a selection of steady-unsteady velocity ratios, channel half-widths and pipe radii. The results obtained confirm previous investigations into the effects of small amounts of periodic modulation on the linear stability of the underlying steady flow, but provide much more comprehensive information on the linear stability regions of unsteady parallel flows in channels and pipes.

show abstract

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

The linear stability of oscillatory Poiseuille flow in channels and pipes

Thomas¹,

Bassom²,

Blennerhassett

et al. 2011

Proc. R. Soc. A.

View full text Add to dashboard Cite

show abstract

“…The oscillatory velocity profile consists of Stokes layers a t the channel walls matched to an oscillating slug flow in the core of the channel. The linear stability theory of this OPP flow has been examined by Grosch & Salwen (1968), Herbert (1972) and Hall (1975). These three studies contain certain conclusions concerning the stability characteristics of this flow that are not entirely in obvious accord.…”

Section: Introductionmentioning

confidence: 99%

The instability of oscillatory plane Poiseuille flow

Kerczek

1982

J. Fluid Mech.

View full text Add to dashboard Cite

The instability of oscillatory plane Poiseuille flow, in which the pressure gradient is time-periodically modulated, is investigated by a perturbation technique. The Floquet exponents (i.e. the complex growth rates of the disturbances to the oscillatory flow) are computed by series expansions, in powers of the oscillatory to steady flow velocity amplitude ratio, about the values of the growth rates of the disturbances of the steady flow. It is shown that the oscillatory flow is more stable than the steady flow for values of Reynolds number and disturbance wave number in the vicinity of the steady flow critical point and for values of frequencies of imposed oscillation greater than about one tenth of the frequency of the steady flow neutral disturbance. At very high and low values of imposed oscillation frequency, the unsteady flow is slightly less stable than the steady flow. These results hold for the values of the velocity amplitude ratio at least up to 0·25.

show abstract

“…On the other hand, the plane Poiseuille flow with longitudinal wall oscillation is also investigated by many researchers because this flow is basically twodimensional and it seems that the analytical approach is more suitable [8][9][10][11][12]. Most general way to deal this flow is to assume as a combination of the plane Poiseuille flow with the Stokes layer.…”

Section: Introductionmentioning

confidence: 99%

The influence of longitudinal wall-oscillation on the plane Poiseuille flow

Atobe¹

2014

Advances in Fluid Mechanics X

View full text Add to dashboard Cite

Influence of wall oscillation on laminar-turbulent transition of the plane Poiseuille flow is investigated analytically and numerically. For the analytical approach, the Floquet theory using a time-dependent Orr-Sommerfeld equation is employed to estimate the fundamental aspect of this flow. The velocity profiles for the analysis are assumed as the superposition of the plane Poiseuille flow and the Stokes layer. Also the collocation method is used in the wallnormal direction for making the monodromy matrix. Depending on the parameters, namely frequencyΩand amplitude U w of the wall-oscillation, there is the stable region inΩ-U w plane even though the Reynolds number is of supercritical. Direct numerical simulation (DNS) based on the Fourier spectral method is also employed to confirm the analytical results and to clear the flow structures. The results by DNS show good agreement with the Floquet analysis and also reveal that the vortex structures in the vicinity of the walls are strongly affected by the wall oscillation.

show abstract

The energy balance in modulated plane Poiseuille flow

Cited by 11 publications

References 2 publications

The linear stability of oscillatory Poiseuille flow in channels and pipes

The linear stability of oscillatory Poiseuille flow in channels and pipes

The instability of oscillatory plane Poiseuille flow

The influence of longitudinal wall-oscillation on the plane Poiseuille flow

Contact Info

Product

Resources

About