A Novel Velocity–Vorticity Formulation of the Navier–Stokes Equations with Applications to Boundary Layer Disturbance Evolution

Davies, Christopher; Carpenter, Peter W.

doi:10.1006/jcph.2001.6817

Cited by 113 publications

(116 citation statements)

References 59 publications

(128 reference statements)

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“…It is the results for these flows that demonstrate the remarkably strong dependence of the linear stability critical conditions on the frequency and amplitude of the perturbation. These Floquet theory results are confirmed by a direct numerical solution of the governing linear equations, using the DNS approach developed by Davies & Carpenter (2001) and described in §2.2.…”

Section: Introductionsupporting

confidence: 56%

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The linear stability of a Stokes layer subjected to high-frequency perturbations

Thomas

Blennerhassett²,

Bassom³

et al. 2014

J. Fluid Mech.

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Quantitative results for the linear stability of planar Stokes layers subject to small, high frequency perturbations are obtained for both a narrow channel and a flow approximating the classical semi-infinite Stokes layer. Previous theoretical and experimental predictions of the critical Reynolds number for the classical flat Stokes layer have differed widely with the former exceeding the latter by a factor of two or three. Here it is demonstrated that only a one percent perturbation, at an appropriate frequency, to the nominal sinusoidal wall motion is enough to result in a reduction of the theoretical critical Reynolds number of as much as 60%, bringing the theoretical conditions much more in line with the experimentally reported values. Furthermore, within the various experimental observations there is a wide variation in reported critical conditions and the results presented here may provide a new explanation for this behaviour.

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Section: Introductionsupporting

confidence: 56%

“…The velocity-vorticity formulation described by Davies & Carpenter (2001) was employed where the velocity and vorticity fields are given as…”

Section: Linear Stability Via Direct Numerical Simulationmentioning

confidence: 99%

The linear stability of a Stokes layer subjected to high-frequency perturbations

Thomas

Blennerhassett²,

Bassom³

et al. 2014

J. Fluid Mech.

Self Cite

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“…Although larger (in y) grid resolutions were investigated, only marginal differences in the LNS and ALNS solutions arose, this was insufficient to affect the receptivity computations to the graphical accuracy presented in this paper. Although not published or included here, to confirm correctness of the codes, comparisons were made against solutions of the velocity-vorticity scheme developed by Davies & Carpenter 42 , for the idealised swept Hiemenz flow and excellent agreement was obtained for both stationary and non-stationary disturbances.…”

Section: A Base Flowmentioning

confidence: 99%

On predicting receptivity to surface roughness in a compressible infinite swept wing boundary layer

2017

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The receptivity of crossflow disturbances on an infinite swept wing is investigated using solutions of the adjoint linearised Navier-Stokes equations. The adjoint based method for predicting the magnitude of stationary disturbances generated by randomly distributed surface roughness is described, with the analysis extended to include both surface curvature and compressible flow effects. Receptivity is predicted for a broad spectrum of spanwise wavenumbers, variable freestream Reynolds numbers and subsonic Mach numbers. Curvature is found to play a significant role in the receptivity calculations, while compressible flow effects are only found to marginally affect the initial size of the crossflow instability. A Monte-Carlo type analysis is undertaken to establish the mean amplitude and variance of crossflow disturbances generated by the randomly distributed surface roughness. Mean amplitudes are determined for a range of flow parameters that are maximised for roughness distributions containing a broad spectrum of roughness wavelengths, including those that are most effective in generating stationary crossflow disturbances. A control mechanism is then developed where the short scale roughness wavelengths are damped, leading to significant reductions in the receptivity amplitude.

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“…Both the mathematical formulation and the discretization were similar to those deployed in a previously developed and extensively tested numerical scheme 5 . Great care was taken in the treatment of the artificial extremities of the computational domain, to avoid the production of numerical noise and spurious reflections.…”

Section: Simulation Results For the Family-tree Structure Of Wavepackmentioning

confidence: 99%

The linear impulse response for disturbances in an oscillatory stokes layer

Davies

Thomas

Bassom

et al. 2013

AIP Conference Proceedings

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A brief review is given of numerical simulation results for the evolution of disturbances in a flat oscillatory Stokes layer. A spatially localised form of impulsive forcing is applied to trigger the disturbances. For the linearized case, the disturbance development displays an intriguing family tree-like structure, which involves the birth of successive generations of wavepackets. Although some features of the wavepacket behaviour may be accounted for using a Floquet linear stability analysis, for Fourier modes with prescribed wavenumbers, the discovery of the tree-like structure was completely unexpected. Simulation results were also obtained for nonlinear disturbances, where highly localised spikes were found to develop.

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A Novel Velocity–Vorticity Formulation of the Navier–Stokes Equations with Applications to Boundary Layer Disturbance Evolution

Cited by 113 publications

References 59 publications

The linear stability of a Stokes layer subjected to high-frequency perturbations

The linear stability of a Stokes layer subjected to high-frequency perturbations

On predicting receptivity to surface roughness in a compressible infinite swept wing boundary layer

The linear impulse response for disturbances in an oscillatory stokes layer

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