Stability of unstably stratified shear flow in a channel under non-Boussinesq conditions

Vasilyev, Oleg V.; Paolucci, Samuel

doi:10.1007/bf01177477

Cited by 5 publications

(2 citation statements)

References 15 publications

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“…Particular emphasis has been placed on describing the stability characteristics of the flow as the level of shear, arising of use, available at https://www.cambridge.org/core/terms. https://doi.org/10.1017/S0334270000012418 142 James P. Denier and Andrew P. Bassom [20] from the Couette component of the flow, is increased. We have demonstrated that as this element grows the flow is stabilised to two-dimensional wave modes and these neutrally stable wave modes are driven to progressively shorter wavelengths.…”

Section: Discussionmentioning

confidence: 99%

“…Further work on the stability of stratified plane Poiseuille flow can be found in Tveitereid [19] who considered flows of arbitrary Prandtl number (thus extending the results of [10]); Schafer & Herwig [18], who considered the effect of temperature dependent viscosity on the flow stability, and Vasilyev & Paolucci [20], who removed the Boussinesq assumption employed in earlier studies. By considering fluids whose thermal conductivity and viscosity are governed by Sutherland's law they demonstrated that the dominant form of motion is still the longitudinal roll (aligned with the direction of the mean flow) and that the critical Rayleigh number increases as a function of the difference in the applied temperatures of the bounding plates.…”

Section: Introductionmentioning

confidence: 99%

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Neutrally stable wave motions in thermally stratified Poiseuille-Couette flow

Denier¹,

Bassom²

1998

J. Aust. Math. Soc. Series B, Appl. Math

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The influence of thermal buoyancy on neutral wave modes in Poiseuille-Couette flow is considered. We examine the modifications to the asymptotic structure first described by Mureithi, Denier & Stott [16], who demonstrated that neutral wave modes in a strongly thermally stratified boundary layer are localized at the position where the streamwise velocity attains its maximum value. The present work demonstrates that such a flow structure also holds for Poiseuille-Couette flow but that a new flow structure emerges as the position of maximum velocity approaches the wall (and which occurs as the level of shear, present as a consequence of the Couette component of the flow, is increased). The limiting behaviour of these wave modes is discussed thereby allowing us to identify the parameter regime appropriate to the eventual restabilization of the flow at moderate levels of shear.

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Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Neutrally stable wave motions in thermally stratified Poiseuille-Couette flow

Denier¹,

Bassom²

1998

J. Aust. Math. Soc. Series B, Appl. Math

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Conservative High-Order Finite-Difference Schemes for Low-Mach Number Flows

Nicoud¹

2000

Journal of Computational Physics

163

156

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Three finite-difference algorithms are proposed to solve a low-Mach number approximation for the Navier-Stokes equations. These algorithms exhibit fourth-order spatial and second-order temporal accuracy. They are dissipation-free, and thus well suited for DNS and LES of turbulent flows. The key ingredient common to each of the methods presented is a Poisson equation with variable coefficient that is solved for the hydrodynamic pressure. This feature ensures that the velocity field is constrained correctly. It is shown that this approach is needed to avoid violation of the conservation of kinetic energy in the inviscid limit which would otherwise arise through the pressure term in the momentum equation. An existing set of finite-difference formulae for incompressible flow is generalized to handle arbitrary large density fluctuations with no violation of conservation through the non-linear convective terms. An algorithm which conserves mass, momentum, and kinetic energy fully is obtained when an approximate equation of state is used instead of the exact one. Results from a model problem are used to show both spatial and temporal convergence rates and several test cases are presented to illustrate the performance of the algorithms.

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Stability of natural convection flow in a tall vertical enclosure under non-Boussinesq conditions

Suslov

Paolucci

1995

International Journal of Heat and Mass Transfer

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Stability of unstably stratified shear flow in a channel under non-Boussinesq conditions

Cited by 5 publications

References 15 publications

Neutrally stable wave motions in thermally stratified Poiseuille-Couette flow

Neutrally stable wave motions in thermally stratified Poiseuille-Couette flow

Conservative High-Order Finite-Difference Schemes for Low-Mach Number Flows

Stability of natural convection flow in a tall vertical enclosure under non-Boussinesq conditions

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