Three-layer fluid flow over a small obstruction on the bottom of a channel

Panda, Srikumar; Martha, S. C.; Chakrabarti, A.

doi:10.21914/anziamj.v56i0.7753

Cited by 3 publications

(3 citation statements)

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“…These unknowns can be determined once the mixed coupled boundary value problem described in relations (1)- (9) is solved. In the following section, the above boundary value problem is solved using a similar kind of mathematical procedure, i.e., perturbation analysis along with Fourier transform technique, as described in Panda et al (2015) .…”

Section: Description and Mathemati-cal Formulationmentioning

confidence: 99%

A Study on Inviscid Flow with a Free Surface over an Undulating Bottom

Panda

2016

JAFM

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In this paper, the problem involving inviscid flow with a free surface over an undulating bottom is studied within the framework of linear theory. Applying perturbation analysis in conjunction with the Fourier transform technique, the boundary value problem arising from the flow problem is solved analytically. Behaviour of both interface and free-surface profiles, which are unknown at the outset, are analyzed. It is found that each profile (interface and free-surface) possesses a wave free region at the far upstream, followed by a modulated downstream wave. It also observed, for the first time, that the amplitude of the downstream wave is varying. Further, the effects of various system parameters are analyzed and demonstrated in graphical forms.

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Section: Description and Mathemati-cal Formulationmentioning

confidence: 99%

A Study on Inviscid Flow with a Free Surface over an Undulating Bottom

Panda

2016

JAFM

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“…There also exists an analytical study for a bounded three-layer flow. Panda et al [50] calculated the stable linear interfacial motion in a channel with bottom topography using the Fourier transform technique. There also exist some numerical studies for the motion of interfaces in a multi-layer fluid flow.…”

Section: Introductionmentioning

confidence: 99%

Motion of unstable two interfaces in a three-layer fluid with a non-zero uniform current

Matsuoka¹

2021

Fluid Dyn. Res.

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The nonlinear motion of two interfaces in a three-layer fluid with density stratification is investigated theoretically and numerically. We consider the situation such that a uniform current is present in one of the three layers. The linear dispersion relation is calculated by the Newton's method, from which the initial conditions for numerical computations are determined. When the uniform current is present in the upper (lower) layer, strong vorticity is induced on the upper (lower) interface, and it rolls up involving the other interface at the late stage of computations. When the current is present in the middle layer, a varicose wave appears at the initial stage, and it evolves into an asymmetric heart-shaped vortex sheet at the last computed stage. These phenomena are presented using the vortex sheet model (VSM) with and without regularizations.

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“…Free-surface problems occur in many aspects of science and engineering. They can be defined as problems whose mathematical formulation involves surfaces that have to be found as part of the solution; for some recent development on the topic (see [1][2][3][4][5][6]) and the references therein. In this literature, we show some contributions of researchers to the finding of a mathematical solution for free-surface problems.…”

Section: Introductionmentioning

confidence: 99%