Hydrodynamic stability of the Ekman boundary layer including interaction with a compliant surface: a numerical framework

Allen, Leanne; Bridges, Thomas J.

doi:10.1016/s0997-7546(03)00036-0

Cited by 16 publications

(22 citation statements)

References 25 publications

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“…For plane Poiseuille flow, in [26] both stable and unstable spurious eigenvalues with large distinguishable magnitude have been reported. According to [27], such spurious eigenvalues are created due to fracturing of the continuous spectrum for problems in infinite domain. In [28], a QR algorithm based on Chebyshev polynomials have been used for the spatio-temporal study of mixed convection boundary layers developing over a vertical plate.…”

Section: Introductionmentioning

confidence: 99%

Spatial Stability for Mixed Convection Boundary Layer over a Heated Horizontal Plate

Sengupta

Subbaiah

2006

Stud Appl Math

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The spatial stability properties of a mixed convection boundary layer developing over a heated horizontal plate is studied here under linear and quasi-parallel flow assumption. The main aim of the present work is to find out if there is a critical buoyancy parameter that would indicate the importance of heat transfer in destabilizing mixed convection boundary layers, when the buoyancy effect is given by Boussinesq approximation. The undisturbed flow used here is that given by the similarity solution of [1] that implies the wall temperature to vary as the inverse square root of the distance from the leading edge of the plate. The stability of this flow has been investigated by using the compound matrix method (CMM)-that allows finding all the modes in the chosen range in the complex wave number plane for spatial stability analysis. Presented neutral curves for mixed convection boundary layer show the existence of two types of disturbances present simultaneously, for large buoyancy parameter. One notices very unstable high-frequency mode when the buoyancy parameter exceeds the above-mentioned critical value. This unstable thermal mode is in addition to the hydrodynamic mode of isothermal flow given by corresponding similarity profile. The calculated critical buoyancy parameter is shown to qualitatively match with experimental results.

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Section: Introductionmentioning

confidence: 99%

Spatial Stability for Mixed Convection Boundary Layer over a Heated Horizontal Plate

Sengupta

Subbaiah

2006

Stud Appl Math

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“…For continuation of the curves we used the Matlab package MatCont, which uses pseudo-arclength continuation (Dhooge, Govaerts and Kuznetsov [29]). Figures 15 and 16 show the neutral curves which match those in Allen and Bridges [6] and Allen [4]. The integration of the Riccati system has been done with the Matlab ODE-solver ode23s from z = 10 to z * = 0 (as in Allen and Bridges) with absolute and relative tolerances 10 −6 and 10 −4 .…”

Section: Provided Neither Riccati Flow Becomes Singular This Evans Fmentioning

confidence: 95%

“…The third test system is a boundary layer flow over a flat plate which is infinitely extended in the x and y directions and rotates around the half infinite z-axis with a given rotational speed. Linear stability of the Ekman boundary layer has been investigated in Allen and Bridges [6] and Allen [4] using the compound matrix method. The flow is governed by the continuity equation u x + v y + w z = 0 and by the Navier-Stokes equations in a co-rotating frame,…”

Section: Provided Neither Riccati Flow Becomes Singular This Evans Fmentioning

confidence: 99%

Grassmannian spectral shooting

2010

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Abstract. We present a new numerical method for computing the pure-point spectrum associated with the linear stability of coherent structures. In the context of the Evans function shooting and matching approach, all the relevant information is carried by the flow projected onto the underlying Grassmann manifold. We show how to numerically construct this projected flow in a stable and robust manner. In particular, the method avoids representation singularities by, in practice, choosing the best coordinate patch representation for the flow as it evolves. The method is analytic in the spectral parameter and of complexity bounded by the order of the spectral problem cubed. For large systems it represents a competitive method to those recently developed that are based on continuous orthogonalization. We demonstrate this by comparing the two methods in three applications: Boussinesq solitary waves, autocatalytic travelling waves and the Ekman boundary layer.

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“…Namely, the study by Koga and Nagata (described in [48]) of the effects of wall compliance on the stability of Taylor-Couette flow. And also, the study of Allen and Bridges [49] on the hydrodynamic stability of the Ekman boundary layer over a compliant wall.…”

Section: Flow Stability Theory For Compliant Rotating-disk Flowsmentioning

confidence: 99%

Flow over compliant rotating disks

Carpenter

Thomas

2006

J Eng Math

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Flow over compliant materials and compliant coatings has been studied for decades because of the potential of using such materials for laminar-flow control. Since boundary layers in most flows of engineering interest are three-dimensional the classic rotating-disk flow geometry, the paradigm for studying three-dimensional boundary layers, has been adapted to investigate flow over compliant rotating disks. This paper reviews the literature on the existing experimental and theoretical research on flow over compliant rotating disks. The article concludes by evaluating the status of the available results and their implications as regards future research routes to investigate the capabilities of compliant materials for laminar-flow control.

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Hydrodynamic stability of the Ekman boundary layer including interaction with a compliant surface: a numerical framework

Cited by 16 publications

References 25 publications

Spatial Stability for Mixed Convection Boundary Layer over a Heated Horizontal Plate

Spatial Stability for Mixed Convection Boundary Layer over a Heated Horizontal Plate

Grassmannian spectral shooting

Flow over compliant rotating disks

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