Stability of a Shear Layer between Parallel Streams

Betchov, R.; Szewczyk, Albin A.

doi:10.1063/1.1710959

Cited by 168 publications

(94 citation statements)

References 6 publications

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“…The decrease of l/W E with increasing horizontal shear observed in the weak horizontal shear range in Fig. 21, where Re is below 40, appears to be consistent with the results of Betchov and Szewczyk (1963). However, the remarkable increase of l/W E with increasing horizontal shear above that range appears to be quite curious.…”

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confidence: 74%

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Numerical Study of Horizontal Shear Instability Waves along Narrow Cold Frontal Rainbands

Kawashima

2011

Journal of the Atmospheric Sciences

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The effects of variations in low-level ambient vertical shear and horizontal shear on the alongfront variability of narrow cold frontal rainbands (NCFRs) that propagate into neutral and slightly unstable environments are investigated through a series of idealized cloud-resolving simulations.In cases initialized with slightly unstable sounding and weak ambient cross-frontal vertical shears, core-gap structures of precipitation along NCFRs occur that are associated with wavelike disturbances that derive their kinetic energy mainly from the mean local vertical shear and buoyancy. However, over a wide range of environmental conditions, core-gap structures of precipitation occur because of the development of a horizontal shear instability (HSI) wave along the NCFRs.The growth rate and amplitude of the HSI wave decrease significantly as the vertical shear of the ambient cross-front wind is reduced. These decreases are a consequence of the enhancement of the low-level local vertical shear immediately behind the leading edge. The strong local vertical shear acts to damp the vorticity edge wave on the cold air side of the shear zone, thereby suppressing the growth of the HSI wave through the interaction of the two vorticity edge waves. It is also noted that the initial wavelength of the HSI wave increases markedly with increasing horizontal shear. The local vertical shear around the leading edge is shown to damp long HSI waves more strongly than short waves, and the horizontal shear dependency of the wavelength is explained by the decrease in the magnitude of the vertical shear relative to that of the horizontal shear.

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supporting

confidence: 74%

“…Numerical analyses of shear instabilities for viscid parallel flows by Betchov and Szewczyk (1963) indicate that the most unstable wavelength decreases with increasing Re if the Re is smaller than approximately 40-50.…”

mentioning

confidence: 99%

Numerical Study of Horizontal Shear Instability Waves along Narrow Cold Frontal Rainbands

Kawashima

2011

Journal of the Atmospheric Sciences

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“…We begin by exploring the effects of finite eddy viscosity in the simple case of an unstratified shear layer. We extend the results of Betchov and Szewczyk (1963), who examined the special case of uniform viscosity (our model 1). At large Re h , the four eddy viscosity models give nearly the same growth rate, phase velocity, and wavelength (Figs.…”

Section: B Results For a Set Of Idealized Modelsmentioning

confidence: 71%

Diurnal Shear Instability, the Descent of the Surface Shear Layer, and the Deep Cycle of Equatorial Turbulence

Smyth

Thorpe

2013

Journal of Physical Oceanography

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A new theory of shear instability in a turbulent environment is applied to eight days of velocity and density profiles from the upper-equatorial Pacific. This period featured a regular diurnal cycle of surface forcing, together with a clear response in upper-ocean mixing. During the day, a layer of stable stratification and shear forms at the surface. During late afternoon and evening, this stratified shear layer descends, leaving the nocturnal mixing layer above it. Using high-resolution current measurements, the detailed structure of the descending shear layer is seen for the first time. Linear stability analysis is conducted using a new method that accounts for the effects of preexisting turbulence on instability growth. Shear instability follows a diurnal cycle linked to the afternoon descent of the surface shear layer. This cycle is revealed only when the effect of turbulence is accounted for in the stability analysis. The cycle of instability leads the diurnal mixing cycle, typically by 2-3 h, consistent with the time needed for instabilities to grow and break. Late at night, the resulting turbulence suppresses further instabilities, lending an asymmetry to the mixing cycle that has not been noticed in previous measurements. Deep cycle mixing is triggered by instabilities formed as the descending shear layer merges with the marginally unstable shear of the Equatorial Undercurrent. In the morning, turbulence decays and the upper ocean restratifies. Wind accelerates the near-surface flow to form a new unstable shear layer, and the cycle begins again.

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“…Its numerical solution is not straightforward due to stiffness caused by extreme (too large or too small) values of the governing nondimensional parameters (large Reynolds and Peclet numbers, and small capillary number). We used two numerical methods to solve the problem, the shooting method supplemented with the Gram-Schmidt orthogonalization [48][49][50][51] and the compound matrix method [52][53][54]. The fourth-order adaptive Runge-Kutta technique was used for numerical integration and the Muller's method was employed for root finding.…”

Section: B Basic State Linear Stability Analysismentioning

confidence: 99%

Linear stability analysis of a horizontal phase boundary separating two miscible liquids

Kheniene

Vorobev

2013

Phys. Rev. E

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The evolution of small disturbances to a horizontal interface separating two miscible liquids is examined. The aim is to investigate how the interfacial mass transfer affects development of the Rayleigh-Taylor instability and propagation and damping of the gravity-capillary waves. The phase-field approach is employed to model the evolution of a miscible multiphase system. Within this approach, the interface is represented as a transitional layer of small but nonzero thickness. The thermodynamics is defined by the Landau free energy function. Initially, the liquid-liquid binary system is assumed to be out of its thermodynamic equilibrium, and hence, the system undergoes a slow transition to its thermodynamic equilibrium. The linear stability of such a slowly diffusing interface with respect to normal hydro-and thermodynamic perturbations is numerically studied. As a result, we show that the eigenvalue spectra for a sharp immiscible interface can be successfully reproduced for long-wave disturbances, with wavelengths exceeding the interface thickness. We also find that thin interfaces are thermodynamically stable, while thicker interfaces, with the thicknesses exceeding an equilibrium value, are thermodynamically unstable. The thermodynamic instability can make the configuration with a heavier liquid lying underneath unstable. We also find that the interfacial mass transfer introduces additional dissipation, reducing the growth rate of the Rayleigh-Taylor instability and increasing the dissipation of the gravity waves. Moreover, mutual action of diffusive and viscous effects completely suppresses development of the modes with shorter wavelengths.

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Stability of a Shear Layer between Parallel Streams

Cited by 168 publications

References 6 publications

Numerical Study of Horizontal Shear Instability Waves along Narrow Cold Frontal Rainbands

Numerical Study of Horizontal Shear Instability Waves along Narrow Cold Frontal Rainbands

Diurnal Shear Instability, the Descent of the Surface Shear Layer, and the Deep Cycle of Equatorial Turbulence

Linear stability analysis of a horizontal phase boundary separating two miscible liquids

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