The stability of free boundary layers between two uniform streams

1960 ◽  
Vol 7 (3) ◽  
pp. 433-441 ◽  
Author(s):  
T. Tatsumi ◽  
K. Gotoh
Keyword(s):  
Boundary Layer ◽  
Free Boundary ◽  
Reynolds Numbers ◽  
Velocity Profiles ◽  
Point Of View ◽  
Boundary Layer Flows ◽  
Type Curves ◽  
Neutral Curves ◽  
Critical Reynolds Numbers ◽  
The Stability

Hydrodynamic stability of free boundary-layer flows is treated in general. It is found that the situations at low Reynolds numbers are universal for all velocity profiles of free boundary-layer type. Curves of constant amplification are calculated as far as O(R3). In particular, the asymptotic form of the neutral curves for R [eDot ] 0 is found to be α = R/(4√3), so that the critical Reynolds numbers of these flows are identically zero. The phase velocity of the disturbance is also found to be zero, for all disturbances, up to the second approximation.A method of normalizing the velocity profiles is suggested, and existing results for the stability of various profiles at large Reynolds numbers are discussed from a new point of view.

The Stability of a Free Boundary Layer at Large Reynolds Numbers

1964 ◽  
Vol 19 (10) ◽  
pp. 1966-1980 ◽  
Author(s):  
Tomomasa Tatsumi ◽  
Kanehfusa Gotoh ◽  
Kyôzô Ayukawa
Keyword(s):  
Boundary Layer ◽  
Free Boundary ◽  
Reynolds Numbers ◽  
The Stability

The Stability of Pipe Entrance Flows Subjected to Axisymmetric Disturbances

1994 ◽  
Vol 116 (1) ◽  
pp. 61-65 ◽  
Author(s):  
D. F. da Silva ◽  
E. A. Moss
Keyword(s):  
Boundary Layer ◽  
Reynolds Numbers ◽  
Finite Amplitude ◽  
Axial Distance ◽  
Displacement Thickness ◽  
Critical Reynolds Numbers ◽  
Equilibrium Profile ◽  
Stability Data ◽  
The Stability ◽  
Theoretical Results

This paper reexamines an important unresolved problem in fluid mechanics—the discrepancy between measurements and predictions of stability in pipe entrance flows. Whereas measured critical Reynolds numbers are relatively insensitive to velocity profile shape in the streamwise direction, the theoretical results indicate a rapid increase, both as the equilibrium profile is approached, and toward the inlet. The current work uses the displacement thickness based Reynolds number as a rational basis on which to compare new stability predictions obtained by means of the Q-Z algorithm, with existing theoretical results. Although the present data are shown to be the only that are consistent with the classical parallel boundary layer limit towards the inlet, they still deviate increasingly with axial distance from the only available experimental results. By examining pipe inlet stability data in relation to boundary layer measurements and predictions, the work effectively questions the commonly held belief that streamwise variations of flow alone are responsible for these deviations, suggesting that the finite amplitude nature of the applied disturbances is the most likely cause.

scholarly journals Non-modal stability analysis of the boundary layer under solitary waves

2017 ◽  
Vol 836 ◽  
pp. 740-772 ◽  
Author(s):  
Joris C. G. Verschaeve ◽  
Geir K. Pedersen ◽  
Cameron Tropea
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Stability Analysis ◽  
Solitary Waves ◽  
Reynolds Numbers ◽  
Two Dimensional ◽  
Modal Theory ◽  
Critical Reynolds Numbers ◽  
Streamwise Streaks ◽  
The Stability

In the present work, a stability analysis of the bottom boundary layer under solitary waves based on energy bounds and non-modal theory is performed. The instability mechanism of this flow consists of a competition between streamwise streaks and two-dimensional perturbations. For lower Reynolds numbers and early times, streamwise streaks display larger amplification due to their quadratic dependence on the Reynolds number, whereas two-dimensional perturbations become dominant for larger Reynolds numbers and later times in the deceleration region of this flow, as the maximum amplification of two-dimensional perturbations grows exponentially with the Reynolds number. By means of the present findings, we can give some indications on the physical mechanism and on the interpretation of the results by direct numerical simulation in Vittori & Blondeaux (J. Fluid Mech., vol. 615, 2008, pp. 433–443) and Özdemir et al. (J. Fluid Mech., vol. 731, 2013, pp. 545–578) and by experiments in Sumer et al. (J. Fluid Mech., vol. 646, 2010, pp. 207–231). In addition, three critical Reynolds numbers can be defined for which the stability properties of the flow change. In particular, it is shown that this boundary layer changes from a monotonically stable to a non-monotonically stable flow at a Reynolds number of $Re_{\unicode[STIX]{x1D6FF}}=18$.

scholarly journals Linear stability of boundary layers under solitary waves

2014 ◽  
Vol 761 ◽  
pp. 62-104 ◽  
Author(s):  
Joris C. G. Verschaeve ◽  
Geir K. Pedersen
Keyword(s):  
Linear Stability ◽  
Solitary Waves ◽  
Reynolds Numbers ◽  
Quantitative Agreement ◽  
Linear Instability ◽  
Navier Stokes ◽  
Acceleration Region ◽  
Critical Reynolds Numbers ◽  
Tollmien Schlichting ◽  
The Stability

AbstractIn the present treatise, the stability of the boundary layer under solitary waves is analysed by means of the parabolized stability equation. We investigate both surface solitary waves and internal solitary waves. The main result is that the stability of the flow is not of parametric nature as has been assumed in the literature so far. Not only does linear stability analysis highlight this misunderstanding, it also gives an explanation why Sumer et al. (J. Fluid Mech., vol. 646, 2010, pp. 207–231), Vittori & Blondeaux (Coastal Engng, vol. 58, 2011, pp. 206–213) and Ozdemir et al. (J. Fluid Mech., vol. 731, 2013, pp. 545–578) each obtained different critical Reynolds numbers in their experiments and simulations. We find that linear instability is possible in the acceleration region of the flow, leading to the question of how this relates to the observation of transition in the acceleration region in the experiments by Sumer et al. or to the conjecture of a nonlinear instability mechanism in this region by Ozdemir et al. The key concept for assessment of instabilities is the integrated amplification which has not been employed for this kind of flow before. In addition, the present analysis is not based on a uniformization of the flow but instead uses a fully nonlinear description including non-parallel effects, weakly or fully. This allows for an analysis of the sensitivity with respect to these effects. Thanks to this thorough analysis, quantitative agreement between model results and direct numerical simulation has been obtained for the problem in question. The use of a high-order accurate Navier–Stokes solver is primordial in order to obtain agreement for the accumulated amplifications of the Tollmien–Schlichting waves as revealed in this analysis. An elaborate discussion on the effects of amplitudes and water depths on the stability of the flow is presented.

Investigation of Boundary Layer Flows Over a Flat Plate With Different-Size Transverse Square Grooves at s/w = 10

2007 ◽  
Author(s):  
Redha Wahidi ◽  
Walid Chakroun ◽  
Sami Al-Fahad
Keyword(s):  
Boundary Layer ◽  
Flat Plate ◽  
Skin Friction ◽  
Turbulence Intensity ◽  
Viscous Sublayer ◽  
Velocity Profiles ◽  
Boundary Layer Flows ◽  
Mean Velocity ◽  
Uncertainty Range ◽  
The Mean

Turbulent boundary layer flows over a flat plate with multiple transverse square grooves spaced 10 element widths apart were investigated. Mean velocity profiles, turbulence intensity profiles, and the distributions of the skin-friction coefficients (Cf) and the integral parameters are presented for two grooved walls. The two transverse square groove sizes investigated are 5mm and 2.5mm. Laser-Doppler Anemometer (LDA) was used for the mean velocity and turbulence intensity measurements. The skin-friction coefficient was determined from the gradient of the mean velocity profiles in the viscous sublayer. Distribution of Cf in the first grooved-wall case (5mm) shows that Cf overshoots downstream of the groove and then oscillates within the uncertainty range and never shows the expected undershoot in Cf. The same overshoot is seen in the second grooved-wall case (2.5mm), however, Cf continues to oscillate above the uncertainty range and never returns to the smooth-wall value. The mean velocity profiles clearly represent the behavior of Cf where a downward shift is seen in the Cf overshoot region and no upward shift is seen in these profiles. The results show that the smaller grooves exhibit larger effects on Cf, however, the boundary layer responses to these effects in a slower rate than to those of the larger grooves.

Low-Reynolds-Number Turbulent Boundary Layers

1981 ◽  
Vol 103 (4) ◽  
pp. 624-630 ◽  
Author(s):  
B. R. White
Keyword(s):  
Boundary Layer ◽  
Shape Factor ◽  
Reynolds Numbers ◽  
Viscous Sublayer ◽  
Factor H ◽  
Boundary Layer Flows ◽  
Viscous Effects ◽  
Boundary Layer Height ◽  
Wind Tunnel Data ◽  
Logarithmic Velocity Profile

This paper presents experimental wind-tunnel data that show the universal logarithmic velocity profile for zero-pressure-gradient turbulent boundary layer flows is valid for values of momentum-deficit Reynolds numbers Rθ as low as 600. However, for values of Rθ between 425 and 600, the von Ka´rma´n and additive constants vary and are shown to be functions of Rθ and shape factor H. Furthermore, the viscous sublayer in the range 425<Rθ<600 can no longer maintain its characteristically small size. It is forced to grow, due to viscous effects, into a super sublayer (6-9 percent of the boundary layer height) that greatly exceeds conventional predictions of sublayer heights.

The stability of the decaying flow in a suddenly blocked channel

1976 ◽  
Vol 75 (2) ◽  
pp. 305-314 ◽  
Author(s):  
P. Hall ◽  
K. H. Parker
Keyword(s):  
Velocity Field ◽  
Laminar Flow ◽  
Differential System ◽  
Reynolds Numbers ◽  
Velocity Profiles ◽  
Partial Differential ◽  
Partial Differential System ◽  
Small Reynolds Numbers ◽  
The Stability ◽  
Wkb Expansion

The stability of the decaying laminar flow in a suddenly blocked channel is investigated. The partial differential system governing the stability of the flow is solved using a WKB type of approach. It is shown that the first term of the WKB expansion of the disturbance velocity field is just that obtained by a quasi-steady approach. The flow is found to be unstable at quite small Reynolds numbers. This instability is associated with the inflexional nature of the velocity profiles of the decaying flow.

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