Stabilization mechanisms of short waves in stratified gas–liquid flow

Interfacial waves grow in a cocurrent, stratified gas–liquid flow by extracting energy from the main flow. The most unstable mode typically has a wavelength comparable to or less than the liquid depth. Experiments show that these short waves can saturate at small amplitude with no generation of long-wave or transverse modes. By decomposing the typical Stuart–Landau analysis into three components, it is found that saturation usually occurs by cubic self-interaction of the fundamental mode but quadratic resonant interaction with the first overtone is also possible. Interaction with mean flow modes is usually much less important. Experiments confirm the predictions of weakly nonlinear theory. The measured overtone is found to be O(|A1|2) and is phase-locked with the fundamental except near a 1–2 resonance point where the fundamental and the overtone have comparable speeds. Near this resonance, the amplitudes are of the same order and the phase angle between them is observed to jump irregularly as predicted b...

[1]  Yuriko Renardy,et al.  Weakly nonlinear behavior of periodic disturbances in two‐layer Couette–Poiseuille flow , 1989 .

[2]  Hsueh-Chia Chang,et al.  Subharmonic instabilities of finite‐amplitude monochromatic waves , 1992 .

[3]  R. W. Douglass,et al.  A modified tau spectral method that eliminated spurious eigenvalues , 1989 .

[4]  Gallagher,et al.  Finite-amplitude waves at the interface between fluids with different viscosity: Theory and experiments. , 1995, Physical review letters.

[5]  Harold Jeffreys,et al.  On the Formation of Water Waves by Wind , 1925 .

[6]  T. A. Zang,et al.  Spectral methods for fluid dynamics , 1987 .

[7]  T. J. Hanratty,et al.  Weak quadratic interactions of two-dimensional waves , 1971, Journal of Fluid Mechanics.

[8]  Dimitris A. Goussis,et al.  Removal of infinite Eigenvalues in the generalized matrix Eigenvalue problem , 1989 .

[9]  Numerical solution of eigenvalue problems using spectral techniques , 1992 .

[10]  M. McCready,et al.  Origin of roll waves in horizontal gas‐liquid flows , 1988 .

[11]  S. Orszag Accurate solution of the Orr–Sommerfeld stability equation , 1971, Journal of Fluid Mechanics.

[12]  A. P. Hooper,et al.  Nonlinear instability at the interface between two viscous fluids , 1985 .

[13]  P. J. Blennerhassett,et al.  On the generation of waves by wind , 1980, Philosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences.

[14]  S. Deutsch,et al.  Interfacial mode interactions in horizontal gas—liquid flows , 1992, Journal of Fluid Mechanics.

[15]  Thomas J. Hanratty,et al.  Initiation of slugs in horizontal gas‐liquid flows , 1993 .

[16]  Hsueh-Chia Chang,et al.  Spanwise pairing of finite-amplitude longitudinal vortex rolls in inclined free-convection boundary layers , 1991, Journal of Fluid Mechanics.

[17]  Jerry P. Gollub,et al.  Solitary wave dynamics of film flows , 1994 .

[18]  Thomas J. Hanratty,et al.  Interaction between a turbulent air stream and a moving water surface , 1957 .

[19]  Linear stability of stratified channel flow , 1995 .

[20]  Yuriko Renardy,et al.  Instability at the interface between two shearing fluids in a channel , 1985 .

[21]  A. Hooper Long‐wave instability at the interface between two viscous fluids: Thin layer effects , 1985 .

[22]  S. G. Yiantsios,et al.  Linear stability of plane Poiseuille flow of two superposed fluids , 1988 .

[23]  Yuriko Renardy,et al.  Derivation of amplitude equations and analysis of sideband instabilities in two-layer flows , 1993 .

[24]  Hsueh-Chia Chang,et al.  Competition between subharmonic and sideband secondary instabilities on a falling film , 1995 .

[25]  S. G. Bankoff,et al.  Nonlinear long-wave stability of superposed fluids in an inclined channel , 1994, Journal of Fluid Mechanics.

[26]  M. McCready Spectral behavior of capillary waves in gas–liquid flows , 1986 .

[27]  J. Miles On the generation of surface waves by shear flows , 1957, Journal of Fluid Mechanics.

[28]  K. Lindsay,et al.  A practical implementation of spectral methods resistant to the generation of spurious eigenvalues , 1992 .

[29]  E. Powers,et al.  Digital Bispectral Analysis and Its Applications to Nonlinear Wave Interactions , 1979, IEEE Transactions on Plasma Science.

[30]  D. Gottlieb,et al.  Numerical analysis of spectral methods , 1977 .

[31]  G. Sivashinsky,et al.  Irregular wavy flow due to viscous stratification , 1985 .

[32]  T. Brooke Benjamin,et al.  Shearing flow over a wavy boundary , 1959, Journal of Fluid Mechanics.

[33]  Chia-Shun Yih,et al.  Instability due to viscosity stratification , 1967, Journal of Fluid Mechanics.

[34]  R. Miesen,et al.  Hydrodynamic stability of a sheared liquid film , 1995, Journal of Fluid Mechanics.

[35]  A. Craik Wind-generated waves in thin liquid films , 1966, Journal of Fluid Mechanics.

[36]  Hsueh-Chia Chang,et al.  FORMATION OF LARGE DISTURBANCES ON SHEARED AND FALLING LIQUID FILMS , 1996 .

[37]  J. Fabre,et al.  Long waves at the interface between two viscous fluids , 1994 .

[38]  D. Barkley Theory and predictions for finite‐amplitude waves in two‐dimensional plane Poiseuille flow , 1990 .

[39]  Mark J. McCready,et al.  Formation of solitary waves on gas-sheared liquid layers , 1991 .