On the Stability of Oscillatory Pipe Flows
Bibliographic record
Abstract
The linear stability of pure oscillatory pipe flow is investigated by solving the linearized disturbance equations as an initial value problem. The importance of the initial conditions on transient dynamics of the flow is analyzed. It is shown that transient growth can play an important role in the development of flow instability. The accuracy of the quasi-steady assumption is assessed. It is shown that the growth rates obtained with this assumption deviate considerably from the results obtained with a direct numerical solution of the linearized initial value problem. Linear stability of unsteady flows is a relatively new topic in hydrodynamic stability theory. Oscillatory flows represent an important subset of unsteady flows and often occur in engineering applications as well as in the field of physiological fluid mechanics. Grosch and Salwen (1968) studied linear stability of oscillatory flow superimposed on a steady plane Poiseuille flow (such a flow is known as a pulsatile flow in the hydrodynamic stability literature). They found that modulation of the pressure gradient has an important effect on the stability characteristics of the flow. In particular, for large modulation amplitude the flow is destabilized at lower mean Reynolds number. The results of Grosch and Salwen (1968) are re-examined by von Kerczek (1982). He found that the oscillating plane Poiseuille flow is more stable than the steady plane Poiseuille flow for a wide range of frequencies. However, the results of von Kerczek (1982) differ substantially from those of Grosch and Salwen (1968) for certain values of the parameters of the problem. A similar problem was recently solved by Straatman et al. (1998) for the range of parameter values which are of interest in physiological fluid mechanics. Modulated plane Poiseuille flow for high modulation frequencies is analyzed asymptotically by Hall (1975). It was shown that modulation destabilized the flow. Note that the Floquet theory is used in their stability analyses. It should be pointed out that the Floquet exponents (which are used to determine whether the given time-periodic flow is linearly unstable) are measures of the average long-term growth or decay of perturbations. The magnitudes of the Floquet exponents cannot be used to determine the transient behavior of a perturbation during one cycle of the imposed oscillation. An exact unsteady solution of the Navier‐Stokes equations for the case of a rigid wall oscillating transversely in a viscous fluid was found by Stokes and is known as the Stokes layer. The linear stability of the Stokes layer was investigated by von Kerczek and Davis (1974), Hall (1978), Cowley (1987), Blennerhassett and Bassom (2002) and Hall (2003). Von Kerczek and Davis (1974) introduced a second boundary away from the oscillating wall and found no unstable modes for Reynolds numbers up to 400. Hall (1978) presented an improved model without an upper boundary but he also could not find unstable modes for Reynolds numbers up to 160. Cowley (1987) used the method of multiple scales to demonstrate that, for sufficiently large Reynolds numbers, disturbances can experience a significant growth over a part of the oscillating cycle. The analysis by Blennerhassett and Bassom (2002) showed that the Stokes layer becomes unstable at Reynolds numbers about 708. Since this result is inconsistent with the previous studies, in a recent paper Hall (2003) tried to resolve this inconsistency. He found that there are no unstable Floquet modes at high Reynolds numbers. The instability of a pure oscillatory flow in a pipe (which is the most interesting flow geometry from a practical point of view) has been analyzed by Sergeev (1966) and Hino et al. (1976). Three types of flow regimes were analyzed in their experiments: laminar flow, weakly turbulent flow and conditionally turbulent flow. It was found that, in the conditionally turbulent flow, turbulence is generated in the decelerating phase but the flow returns to laminar in the accelerating phase. Thus, the experiments by Hino et al. (1976) confirmed that some oscillatory pipe flows can be unstable only over part of the oscillating cycle.
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.003 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.000 | 0.001 |
| Research integrity | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.001 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".