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Finite-amplitude effects on steady lee-wave patterns in subcritical stratified flow over topography
ANNUAL LITERATURE SURVEY 1996
105
Axisymmetric pressure-driven flow of rigid pellets through a cylindrical tube lined with a deformable porous wall layer Damiano E.R., Duling B.R., Ley K. & Skalak T.C., Journal of Fluid Mechanics, 1996, 314/- (163-189). In English. A closed-form analytic solution for the motion ofaxisymmetric rigid pellets suspended in a Ncwtonian fluid and driven under a pressure gradient through a rigid impermeable cylindrical tube lined with a porous deformable biphasic wall layer is derived using mixture and lubrication theories. The analysis details the velocity distributions in the lubrication and wall layers as well as the solid-phase displacement field in the wall layer. Expressions for the shear stress and pressure gradient are obtained throughout the lubrication and wall layers. Results are presented in terms of resistance, volume flow, and driving pressure relative to smooth-walled tubes for cases both with and without rigid spheres flowing in the free lumen. (from Authors) Turbulence, similarity scaling and vortex geometry in the wake of a towed sphere in a stably stratified fluid Spedding G.R., Browand F.K. & Fincham A.M., Journal of Fluid Mechanics, 1996, 314/- (53-103). In English. Late wakes of towed spheres in a stably stratified fluid were analysed in a plane using a reliable, customized DPIV technique that provides sufficient spatial and temporal resolution to cover allimportant scales of motion in this freely decaying geophysical flow. Individual vortex cross-sections appear to be well approximated by G aussian distributions of all Re, F and Nt studied here. The scaling behaviour o findividual vortices mimics that of the statistical, wake-averaged quantities, and differs measurably from a simple two-dimensional viscous diffusion model. The importance of formulating a realistic three-dimensional model is discussed, and some limited steps in this direction point to future useful experiments and modelling efforts. (from Authors) Linear dynamics of wind waves in coupled turbulent air-water flow. Part 2. Numerical model Harris J.A., Belcher S.E. & Street R.L., Journal of Fluid Mechanics, 1996, 308/- (219-254). In English. We develop a numerical model of the interaction between wind and a small-amplitude water wave. The model first calculates the turbulent flows in both the air and water that would be obtained with a flat interface, and then calculates linear perturbations to this base flow caused by a travelling surface wave. The damped eddy viscosity model has a free constant that is calibrated by comparing with results from a second-order closure model. The new model is then used to calculate the variation of form drag on a stationary rigid wave with Reynolds number, R. Results from the numerical model show reasonable agreement with profiles measured over travelling water waves by Hsu & Hsu (1983), particularly for slower moving waves. The model suggests that the wave-induced flow in the water is irrotational except in an extremely thin interface layer, where viscous stresses are as likely to be important as turbulent stresses. (from Authors) Stability of two-layer stratified flow in inclined channels: applications to air entrainment in coating systems Severtson Y.C. & Aidun C.K., Journal of Fluid Mechanics, 1996, 312/- (173-200). In English. To understand the physics of air entrainment in thin-film liquid coating and other applications, the stability characteristics of general stratified two-layer Poiseuille-Couette flow are examined in inclined channels. The generalized eigenvalue problem, formed by spectral decomposition and solution of the general two-layer OrrSommerfeld equation, is solved to obtain all of the critical modes. Analysis of the air/liquid interface corresponding to experiments reveals that because of the large density variation between the two layers, the interfacial mode is the only mode of instability in air entrainment. (from Authors) Finite-amplitude effects on steady lee-wave patterns in subcritical stratified flow over topography Yang T.-S. & Akylas T.R., Journal of Fluid Mechanics, 1996, 308/- (147-170). In English. The flow of a continuously stratified fluid over a smooth bottom bump in a channel o f finite depth is considered. Comparison with numerical results indicates that the asymptotic theory often remains reasonably accurate even for moderately small values of mu and epsilon, in which case the (formally exponentially small) lee-wave amplitude is greatly enhanced by nonlinearity and can be quite substantial. Moreover, these findings reveal that the range of validity of the classical linear lee-wave theory (A 1) is rather limited. (from Authors) Surfactant dynamics and rectified diffusion of microbubbles Fyrillas M.M. & Szeri A.J., Journal of Fluid Mechanics, 1996, 311/- (361-378). In English. Surfactant transport dynamics and the consequences for rectified diffusion of microbubbles are treated for bubbles undergoing arbitrarily large-amplitude periodic radial oscillations. A perturbation technique is used to reveal averaged equations for the slow convection-enhanced diffusive transport of surfactant molecules. Bubble oscillations are shown to drive an increased number ofsurfactant molecules to the interface, if it is lightly populated, but to reduce the maximum possible population of surfactants on the interface. These effects have important consequences for rectified diffusion, in which the interfacial resistance to gas transfer ofa surfactant monolayer is a strong function of the surface excess population. (from Authors) The effect of eentreline particle concentration in a wave tube Vainshtein P., Fichman M., Shuster K. & Gutfinger C., Journal of Fluid Mechanics, 1996, 306/- (31-42). In English. The interaction of sound waves with an aqueous suspension o f solid particles was analysed experimentally and theoretically. A heretofore unreported effect of particle concentration in the vicinity of a wave-tube centreline was observed. The phenomenon is related to the combined effect of Rayleigh-type acoustic streaming, jet-like streaming (quartz wind) and drift forces occurring in the presence of a sonic wave in the suspension-filled tube. (Authors) Stability of two-layer stratified flow in inclined channels: applications to air entrainment in coating systems Severtson Y.C. & Aidun C.K., Journal of Fluid Mechanics, 1996, 312/- (173-200). In English.
105
Axisymmetric pressure-driven flow of rigid pellets through a cylindrical tube lined with a deformable porous wall layer Damiano E.R., Duling B.R., Ley K. & Skalak T.C., Journal of Fluid Mechanics, 1996, 314/- (163-189). In English. A closed-form analytic solution for the motion ofaxisymmetric rigid pellets suspended in a Ncwtonian fluid and driven under a pressure gradient through a rigid impermeable cylindrical tube lined with a porous deformable biphasic wall layer is derived using mixture and lubrication theories. The analysis details the velocity distributions in the lubrication and wall layers as well as the solid-phase displacement field in the wall layer. Expressions for the shear stress and pressure gradient are obtained throughout the lubrication and wall layers. Results are presented in terms of resistance, volume flow, and driving pressure relative to smooth-walled tubes for cases both with and without rigid spheres flowing in the free lumen. (from Authors) Turbulence, similarity scaling and vortex geometry in the wake of a towed sphere in a stably stratified fluid Spedding G.R., Browand F.K. & Fincham A.M., Journal of Fluid Mechanics, 1996, 314/- (53-103). In English. Late wakes of towed spheres in a stably stratified fluid were analysed in a plane using a reliable, customized DPIV technique that provides sufficient spatial and temporal resolution to cover allimportant scales of motion in this freely decaying geophysical flow. Individual vortex cross-sections appear to be well approximated by G aussian distributions of all Re, F and Nt studied here. The scaling behaviour o findividual vortices mimics that of the statistical, wake-averaged quantities, and differs measurably from a simple two-dimensional viscous diffusion model. The importance of formulating a realistic three-dimensional model is discussed, and some limited steps in this direction point to future useful experiments and modelling efforts. (from Authors) Linear dynamics of wind waves in coupled turbulent air-water flow. Part 2. Numerical model Harris J.A., Belcher S.E. & Street R.L., Journal of Fluid Mechanics, 1996, 308/- (219-254). In English. We develop a numerical model of the interaction between wind and a small-amplitude water wave. The model first calculates the turbulent flows in both the air and water that would be obtained with a flat interface, and then calculates linear perturbations to this base flow caused by a travelling surface wave. The damped eddy viscosity model has a free constant that is calibrated by comparing with results from a second-order closure model. The new model is then used to calculate the variation of form drag on a stationary rigid wave with Reynolds number, R. Results from the numerical model show reasonable agreement with profiles measured over travelling water waves by Hsu & Hsu (1983), particularly for slower moving waves. The model suggests that the wave-induced flow in the water is irrotational except in an extremely thin interface layer, where viscous stresses are as likely to be important as turbulent stresses. (from Authors) Stability of two-layer stratified flow in inclined channels: applications to air entrainment in coating systems Severtson Y.C. & Aidun C.K., Journal of Fluid Mechanics, 1996, 312/- (173-200). In English. To understand the physics of air entrainment in thin-film liquid coating and other applications, the stability characteristics of general stratified two-layer Poiseuille-Couette flow are examined in inclined channels. The generalized eigenvalue problem, formed by spectral decomposition and solution of the general two-layer OrrSommerfeld equation, is solved to obtain all of the critical modes. Analysis of the air/liquid interface corresponding to experiments reveals that because of the large density variation between the two layers, the interfacial mode is the only mode of instability in air entrainment. (from Authors) Finite-amplitude effects on steady lee-wave patterns in subcritical stratified flow over topography Yang T.-S. & Akylas T.R., Journal of Fluid Mechanics, 1996, 308/- (147-170). In English. The flow of a continuously stratified fluid over a smooth bottom bump in a channel o f finite depth is considered. Comparison with numerical results indicates that the asymptotic theory often remains reasonably accurate even for moderately small values of mu and epsilon, in which case the (formally exponentially small) lee-wave amplitude is greatly enhanced by nonlinearity and can be quite substantial. Moreover, these findings reveal that the range of validity of the classical linear lee-wave theory (A 1) is rather limited. (from Authors) Surfactant dynamics and rectified diffusion of microbubbles Fyrillas M.M. & Szeri A.J., Journal of Fluid Mechanics, 1996, 311/- (361-378). In English. Surfactant transport dynamics and the consequences for rectified diffusion of microbubbles are treated for bubbles undergoing arbitrarily large-amplitude periodic radial oscillations. A perturbation technique is used to reveal averaged equations for the slow convection-enhanced diffusive transport of surfactant molecules. Bubble oscillations are shown to drive an increased number ofsurfactant molecules to the interface, if it is lightly populated, but to reduce the maximum possible population of surfactants on the interface. These effects have important consequences for rectified diffusion, in which the interfacial resistance to gas transfer ofa surfactant monolayer is a strong function of the surface excess population. (from Authors) The effect of eentreline particle concentration in a wave tube Vainshtein P., Fichman M., Shuster K. & Gutfinger C., Journal of Fluid Mechanics, 1996, 306/- (31-42). In English. The interaction of sound waves with an aqueous suspension o f solid particles was analysed experimentally and theoretically. A heretofore unreported effect of particle concentration in the vicinity of a wave-tube centreline was observed. The phenomenon is related to the combined effect of Rayleigh-type acoustic streaming, jet-like streaming (quartz wind) and drift forces occurring in the presence of a sonic wave in the suspension-filled tube. (Authors) Stability of two-layer stratified flow in inclined channels: applications to air entrainment in coating systems Severtson Y.C. & Aidun C.K., Journal of Fluid Mechanics, 1996, 312/- (173-200). In English.