Spin-down in rotating Hagen–Poiseuille flow: a simple criterion to detect the onset of absolute instabilities

2016 ◽  
Vol 793 ◽  
pp. 316-334 ◽  
Author(s):  
A. Miranda-Barea ◽  
C. Fabrellas-García ◽  
L. Parras ◽  
C. del Pino
Keyword(s):  
Poiseuille Flow ◽  
Wave Packets ◽  
Reynolds Numbers ◽  
Finite Amplitude ◽  
Gradual Transition ◽  
Initial State ◽  
Mode Shift ◽  
Through Flow ◽  
Reliable Procedure ◽  
Swirl Parameter

We conduct experiments in a circular pipe with rotating Hagen–Poiseuille flow (RHPF) to which we apply spin-down or impulsive spin-down to rest, in order to analyse the threshold between convective and absolute instabilities through flow visualisations in the inlet region of the pipe. For a constant value of the Reynolds number,$Re$, the finite-amplitude wave packets generated by the arbitrary perturbation that results by reducing the swirl parameter, propagate upstream or downstream depending on the initial value of the swirl parameter,$L_{0}$. In fact, the main characteristic of the flow is that the velocity front of these wave packets changes from negative to positive when absolutely unstable modes are present in the initial state. The experimental results show that spin-down becomes a precise, reliable procedure to detect the onset of absolute instabilities. In addition, we give evidence of a gradual transition for Reynolds numbers ranging from 300 to 500 where a mode shift from$n=-1$to$n=-2$appears in the absolutely unstable region.

The effect of external forcing on the stability of plane Poiseuille flow

1978 ◽  
Vol 359 (1699) ◽  
pp. 453-478 ◽  
Keyword(s):  
Reynolds Number ◽  
Poiseuille Flow ◽  
Critical Reynolds Number ◽  
Stable Solution ◽  
Reynolds Numbers ◽  
Finite Amplitude ◽  
Plane Poiseuille Flow ◽  
Critical Reynolds Numbers ◽  
Threshold Amplitude ◽  
The Stability

The stability of plane Poiseuille flow in a channel forced by a wavelike motion on one of the channel walls is investigated. The amplitude Є of this forcing is taken to be small. The most dangerous modes of forcing are identified and it is found in general the critical Reynolds number is changed by O (Є) 2 . However, we identify two particular modes of forcing which give rise to decrements of order Є 2/3 and Є in the critical Reynolds number. Some types of forcing are found to generate sub critical stable finite amplitude perturbations to plane Poiseuille flow. This contrasts with the unforced case where the only stable solution is the zero amplitude solution. The forcing also deforms the unstable subcritical limit cycle solution from its usual circular shape into a more complicated shape. This has an effect on the threshold amplitude ideas suggested by, for example, Meksyn & Stuart (1951). It is found that the phase of disturbances must also be considered when finding the amplitude dependent critical Reynolds numbers.

Experimental evidence of convective and absolute instabilities in rotating Hagen–Poiseuille flow

2013 ◽  
Vol 716 ◽  
Author(s):  
K. Shrestha ◽  
L. Parras ◽  
C. Del Pino ◽  
E. Sanmiguel-Rojas ◽  
R. Fernandez-Feria
Keyword(s):  
Experimental Evidence ◽  
Poiseuille Flow ◽  
Pipe Flow ◽  
Reynolds Numbers ◽  
Hydrodynamic Instabilities ◽  
Theoretical Predictions ◽  
Rotating Pipe Flow ◽  
Theoretical Results ◽  
Good Agreement ◽  
Swirl Parameter

AbstractExperimental results for instabilities present in a rotating Hagen–Poiseuille flow are reported in this study through fluid flow visualization. First, we found a very good agreement between the experimental and the theoretical predictions for the onset of convective hydrodynamic instabilities. Our analysis in a space–time domain is able to obtain quantitative data, so the wavelengths and the frequencies are also estimated. The comparison of the predicted theoretical frequencies with the experimental ones shows the suitability of the parallel, spatial and linear stability analysis, even though the problem is spatially developing. Special attention is focused on the transition from convective to absolute instabilities, where we observe that the entire pipe presents wavy patterns, and the experimental frequencies collapse with the theoretical results for the absolute frequencies. Thus, we provide experimental evidence of absolute instabilities in a pipe flow, confirming that the rotating pipe flow may be absolutely unstable for moderate values of Reynolds numbers and low values of the swirl parameter.

Finite-amplitude instability of parallel shear flows

1967 ◽  
Vol 27 (3) ◽  
pp. 465-492 ◽  
Author(s):  
W. C. Reynolds ◽  
Merle C. Potter
Keyword(s):  
Poiseuille Flow ◽  
Critical Reynolds Number ◽  
Expansion Method ◽  
Reynolds Numbers ◽  
Finite Amplitude ◽  
Plane Couette Flow ◽  
Plane Poiseuille Flow ◽  
Combined Flow ◽  
Formal Expansion ◽  
Parallel Shear Flows

A formal expansion method for analysis of the non-linear development of an oblique wave in a parallel flow is presented. The present approach constitutes an extension and modification of the method of Stuart and Watson. Results are obtained for plane Poiseuille flow, and for a combination of plane Poiseuille and plane Couette flow. The Poiseuille flow exhibits finite-amplitude subcritical instability, and relatively weak but finite disturbances markedly reduce the critical Reynolds number. The combined flow, which becomes stable to infinitesimal disturbances at all Reynolds numbers when the Couette component is sufficiently great, remains unstable to finite disturbances.

Stability of Hagen-Poiseuille flow with superimposed rigid rotation

1976 ◽  
Vol 73 (1) ◽  
pp. 153-164 ◽  
Author(s):  
P.-A. Mackrodt
Keyword(s):  
Poiseuille Flow ◽  
Pipe Flow ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Reynolds Numbers ◽  
Neutral Curve ◽  
Rigid Rotation ◽  
Transition To Turbulence ◽  
Navier Stokes ◽  
Navier Stokes Equations

The linear stability of Hagen-Poiseuille flow (Poiseuille pipe flow) with superimposed rigid rotation against small three-dimensional disturbances is examined at finite and infinite axial Reynolds numbers. The neutral curve, which is obtained by numerical solution of the system of perturbation equations (derived from the Navier-Stokes equations), has been confirmed for finite axial Reynolds numbers by a few simple experiments. The results suggest that, at high axial Reynolds numbers, the amount of rotation required for destabilization could be small enough to have escaped notice in experiments on the transition to turbulence in (nominally) non-rotating pipe flow.

scholarly journals Finite-amplitude steady waves in plane viscous shear flows

1985 ◽  
Vol 160 ◽  
pp. 281-295 ◽  
Author(s):  
F. A. Milinazzo ◽  
P. G. Saffman
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Stokes Equations ◽  
Reynolds Numbers ◽  
Finite Amplitude ◽  
Linear Instability ◽  
Navier Stokes ◽  
Unidirectional Flow ◽  
Viscous Shear ◽  
Finite Amplitude Waves

Computations of two-dimensional solutions of the Navier–Stokes equations are carried out for finite-amplitude waves on steady unidirectional flow. Several cases are considered. The numerical method employs pseudospectral techniques in the streamwise direction and finite differences on a stretched grid in the transverse direction, with matching to asymptotic solutions when unbounded. Earlier results for Poiseuille flow in a channel are re-obtained, except that attention is drawn to the dependence of the minimum Reynolds number on the physical constraint of constant flux or constant pressure gradient. Attempts to calculate waves in Couette flow by continuation in the velocity of a channel wall fail. The asymptotic suction boundary layer is shown to possess finite-amplitude waves at Reynolds numbers orders of magnitude less than the critical Reynolds number for linear instability. Waves in the Blasius boundary layer and unsteady Rayleigh profile are calculated by employing the artifice of adding a body force to cancel the spatial or temporal growth. The results are verified by comparison with perturbation analysis in the vicinity of the linear-instability critical Reynolds numbers.

Local Finite-Amplitude Wave Activity as a Diagnostic for Rossby Wave Packets

2018 ◽  
Vol 146 (12) ◽  
pp. 4099-4114 ◽  
Author(s):  
Paolo Ghinassi ◽  
Georgios Fragkoulidis ◽  
Volkmar Wirth
Keyword(s):  
Rossby Wave ◽  
Model Simulation ◽  
Wave Packets ◽  
Meridional Wind ◽  
Finite Amplitude ◽  
Wave Activity ◽  
Amplitude Wave ◽  
High Impact Weather ◽  
Finite Amplitude Wave Activity ◽  
Isentropic Coordinates

AbstractUpper-tropospheric Rossby wave packets (RWPs) are important dynamical features, because they are often associated with weather systems and sometimes act as precursors to high-impact weather. The present work introduces a novel diagnostic to identify RWPs and to quantify their amplitude. It is based on the local finite-amplitude wave activity (LWA) of Huang and Nakamura, which is generalized to the primitive equations in isentropic coordinates. The new diagnostic is applied to a specific episode containing large-amplitude RWPs and compared with a more traditional diagnostic based on the envelope of the meridional wind. In this case, LWA provides a more coherent picture of the RWPs and their zonal propagation. This difference in performance is demonstrated more explicitly in the framework of an idealized barotropic model simulation, where LWA is able to follow an RWP into its fully nonlinear stage, including cutoff formation and wave breaking, while the envelope diagnostic yields reduced amplitudes in such situations.

Turbulent Annular Pipe Flow in Subcritical Transition Regime: Direct Numerical Simulation of a Large Domain

2015 ◽  
Author(s):  
Takahiro Ishida ◽  
Takahiro Tsukahara
Keyword(s):  
Reynolds Number ◽  
Poiseuille Flow ◽  
Reynolds Numbers ◽  
Radius Ratio ◽  
Transition Regime ◽  
Transitional Regime ◽  
Large Domain ◽  
High Reynolds ◽  
Annular Pipe ◽  
Transition Scenario

We performed direct numerical simulations of annular Poiseuille flow (APF) with a radius ratio of η (= rin/rout) = 0.8, in order to investigate the subcritical transition scenario from the developed turbulent state to the laminar state. In previous studies on annular Poiseuille flow, the flows at high Reynolds numbers were well examined and various turbulence statistics were obtained for several η, because of their dependence on η. Since the transitional APF is still unclear, we investigate annular Poiseuille flows in the transitional regime through the large-domain simulations in a range of the friction Reynolds number from Reτ = 150 down to 56. At a transitional Reynolds number, weak-fluctuation regions occur intermittently and regularly in the flow field, and the localized turbulence appears in the form of banded patterns same as in plane Poiseuille flow (PPF). The flow system of APF with a high radius ratio η ≈ 1 can be regarded as PPF and, hence, the transition regime in high radius-ratio of APF and in PPF should be analogous. However, in APF, the banded structure takes on helical shape around the inner cylinder, since APF is a closed system in the spanwise (azimuthal) direction. In this paper, the (dis-)similarity between APF and PPF is discussed.

Formation and recurrence of ion wave solitons

1975 ◽  
Vol 13 (2) ◽  
pp. 217-230 ◽  
Author(s):  
S. Watanabe
Keyword(s):  
Exact Solution ◽  
Numerical Analysis ◽  
Nonlinear Wave ◽  
Vries Equation ◽  
Dispersive Medium ◽  
Second Harmonic ◽  
Sine Wave ◽  
Finite Amplitude ◽  
Initial State ◽  
Coupled Mode

The interaction between an ion wave and its second harmonic is discussed theoretically, on the basis of coupled-mode equations derived from the Korteweg–de Vries equation. Using an exact solution of the coupled-mode equations, we give a numerical analysis of the properties of the solutions; and we show that superposition of two waves can describe the formation of two solitons, the interaction between them, and the recurrence of an initial state. Our theory can explain completely recent experimental results on ion wave solitons excited by a continuous sine wave.The propagation of a nonlinear wave in a dispersive medium has been extensively studied in the last decade. In a plasma, a finite-amplitude ion wave can form solitons in the course of its evolution, if wave damping is neglected.

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