TY - JOUR

T1 - Absolute linear instability in laminar and turbulent gas-liquid two-layer channel flow

AU - Náraigh, L. Ó

AU - Spelt, P. D.M.

AU - Shaw, S. J.

PY - 2013/1/10

Y1 - 2013/1/10

N2 - We study two-phase stratified flow where the bottom layer is a thin laminar liquid and the upper layer is a fully developed gas flow. The gas flow can be laminar or turbulent. To determine the boundary between convective and absolute instability, we use Orr-Sommerfeld stability theory, and a combination of linear modal analysis and ray analysis. For turbulent gas flow, and for the density ratio r= 1000, we find large regions of parameter space that produce absolute instability. These parameter regimes involve viscosity ratios of direct relevance to oil and gas flows. If, instead, the gas layer is laminar, absolute instability persists for the density ratio r= 1000, although the convective/absolute stability boundary occurs at a viscosity ratio that is an order of magnitude smaller than in the turbulent case. Two further unstable temporal modes exist in both the laminar and the turbulent cases, one of which can exclude absolute instability. We compare our results with an experimentally determined flow-regime map, and discuss the potential application of the present method to nonlinear analyses.

AB - We study two-phase stratified flow where the bottom layer is a thin laminar liquid and the upper layer is a fully developed gas flow. The gas flow can be laminar or turbulent. To determine the boundary between convective and absolute instability, we use Orr-Sommerfeld stability theory, and a combination of linear modal analysis and ray analysis. For turbulent gas flow, and for the density ratio r= 1000, we find large regions of parameter space that produce absolute instability. These parameter regimes involve viscosity ratios of direct relevance to oil and gas flows. If, instead, the gas layer is laminar, absolute instability persists for the density ratio r= 1000, although the convective/absolute stability boundary occurs at a viscosity ratio that is an order of magnitude smaller than in the turbulent case. Two further unstable temporal modes exist in both the laminar and the turbulent cases, one of which can exclude absolute instability. We compare our results with an experimentally determined flow-regime map, and discuss the potential application of the present method to nonlinear analyses.

KW - absolute/convective instability

KW - instability

KW - interfacial flows (free surface)

UR - http://www.scopus.com/inward/record.url?scp=84871882883&partnerID=8YFLogxK

U2 - 10.1017/jfm.2012.452

DO - 10.1017/jfm.2012.452

M3 - Article

AN - SCOPUS:84871882883

SN - 0022-1120

VL - 714

SP - 58

EP - 94

JO - Journal of Fluid Mechanics

JF - Journal of Fluid Mechanics

ER -