Smooth Bore in a Two-Layer Fluid

Makarenko, N. G.

doi:10.1007/978-3-0348-8627-7_22

Cited by 17 publications

(16 citation statements)

References 4 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The Froude numbers (1.2) and (1.5) are precisely equal when β = √ ρ. Makarenko (1992) used bifurcation theory to prove the existence of fronts. In addition to these local results, global results have been obtained by Amick & Turner (1986).…”

Section: Introductionmentioning

confidence: 99%

On internal fronts

Dias

Vanden‐Broeck

2003

J. Fluid Mech.

View full text Add to dashboard Cite

The propagation of nonlinear fronts in a channel flow of two contiguous homogeneous fluids of different densities is considered. Each fluid layer is of finite depth. The study is restricted to steady flows in a frame of reference moving with the front. The full governing equations are integrated numerically. The numerical method is based on boundary integral equation techniques. Although the propagation of waves in two-layer fluids is a classical problem, this is the first time that fronts have been directly computed. The limiting configuration of fronts as their amplitude increases is discussed and shown to depend on whether the front is of elevation or of depression.

show abstract

Section: Introductionmentioning

confidence: 99%

On internal fronts

Dias

Vanden‐Broeck

2003

J. Fluid Mech.

View full text Add to dashboard Cite

show abstract

“…This fact follows immediately from the exact mass, momentum and energy relations. Existence of bore-like solution of Euler equations near a modified (cubic) KdV limit was proved rigorously in the paper by Makarenko (1992) for the Froude numbers Eq. (22) with sufficiently small a.…”

Section: Interfacial Waves In a Two-fluid Systemmentioning

confidence: 96%

Conjugate flows and amplitude bounds for internal solitary waves

Makarenko

Maltseva

Kazakov

2009

Nonlin. Processes Geophys.

Self Cite

View full text Add to dashboard Cite

Abstract. Amplitude bounds imposed by the conservation of mass, momentum and energy for strongly nonlinear waves in stratified fluid are considered. We discuss the theoretical scheme which allows to determine broadening limits for solitary waves in the terms of a given upstream density profile. Attention is focused on the continuously stratified flows having multiple broadening limits. The role of the mean density profile and the influence of fine-scale stratification are analyzed.

show abstract

“…2a) is located in the first quadrant of the plane F ; this is a bifurcation point for internal waves of the smooth bore type and plateau-shaped solitary waves in a two-layer fluid [7,8]. Let us consider the level lines γ 0 (F, σ, λ(F 2 )) = M σ 2 in the vicinity of this point.…”

Section: Long-wave Approximationmentioning

confidence: 99%

“…The presence of such a layer substantially affects the asymptotic behavior of solitary waves of the leading mode. In particular, a region of parameters is found, where the branching of solutions at the points of the spectrum boundary differs from the bifurcation of solitary waves to plateau-and bore-type waves for the model of a two-layer fluid [7,8].…”

Section: Introductionmentioning

confidence: 99%

Asymptotic models of internal stationary waves

Makarenko

Mal’tseva

2008

J Appl Mech Tech Phy

Self Cite

View full text Add to dashboard Cite

Equations of stationary long waves on the interface between a homogeneous fluid and an exponentially stratified fluid are considered. An equation of the second-order approximation of the shallow water theory inheriting the dispersion properties of the full Euler equations is used as the basic model. A family of asymptotic submodels is constructed, which describe three different types of bifurcation of solitary waves at the boundary points of the continuous spectrum of the linearized problem. Introduction.Equations of an inviscid two-layer fluid with a piecewise-constant density experiencing a jump at the interface between the layers are used (see [1,2]) as a mathematical model of internal waves in a pynocline. In this model, solitary waves and smooth bores are described by the equation of the second-order approximation of the shallow water theory, which was derived by Ovsyannikov [3]. Such an equation was obtained in [4] for the case with no slipping of the layers in the main flow. A similar approximation for long waves in a fluid with a piecewise-constant Brunt-Väisälä frequency was considered in [5]. It was noted [6] that asymptotic series for solitary waves are highly sensitive to small perturbations of the density field. The main objective of the present work is to estimate the influence of weak continuous stratification on the parameters of nonlinear waves on the interface. The behavior of the critical parameters of wave motion with stratification vanishing in one of the layers is studied. The density of the fluid in the second layer is assumed to be constant. The basic feature of this limit transition is the concentration of the spectra of higher modes in a narrow band of the boundary-layer type in the plane of bifurcation parameters. The presence of such a layer substantially affects the asymptotic behavior of solitary waves of the leading mode. In particular, a region of parameters is found, where the branching of solutions at the points of the spectrum boundary differs from the bifurcation of solitary waves to plateau-and bore-type waves for the model of a two-layer fluid [7,8].

show abstract

Smooth Bore in a Two-Layer Fluid

Cited by 17 publications

References 4 publications

On internal fronts

On internal fronts

Conjugate flows and amplitude bounds for internal solitary waves

Asymptotic models of internal stationary waves

Contact Info

Product

Resources

About