Effect of variation in density on the stability of bilinear shear currents with a free surface

Barros, Ricardo; Voloch, José Felipe

doi:10.1063/1.5133454

Cited by 4 publications

(3 citation statements)

References 41 publications

(85 reference statements)

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“…It is known that the plane interfacial waves on a constant vorticity current are stable (e.g. Chesnokov et al 2017;Barros & Voloch 2020), and there is no long-wave instability unlike the case of the piecewise-constant current discussed earlier. We think that this explains the difference in the behaviour of the wavefronts of interfacial ring waves in these two examples.…”

Section: Singular Solution For the Interfacial Ring Waves: Rigid-lid Approximationmentioning

confidence: 99%

Wavefronts and modal structure of long surface and internal ring waves on a parallel shear current

2021

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We study long surface and internal ring waves propagating in a stratified fluid over a parallel shear current. The far-field modal and amplitude equations for the ring waves are presented in dimensional form. We re-derive the modal equations from the formulation for plane waves tangent to the ring wave, which opens a way to obtaining important characteristics of the ring waves (group speed, wave action conservation law) and to constructing more general ‘hybrid solutions’ consisting of a part of a ring wave and two tangent plane waves. The modal equations constitute a new spectral problem, and are analysed for a number of examples of surface ring waves in a homogeneous fluid and internal ring waves in a stratified fluid. Detailed analysis is developed for the case of a two-layered fluid with a linear shear current where we study their wavefronts and two-dimensional modal structure. Comparisons are made between the modal functions (i.e. eigenfunctions of the relevant spectral problems) for the surface waves in homogeneous and two-layered fluids, as well as the interfacial waves described exactly and in the rigid-lid approximation. We also analyse the wavefronts of surface and interfacial waves for a large family of power-law upper-layer currents, which can be used to model wind generated currents, river inflows and exchange flows in straits. Global and local measures of the deformation of wavefronts are introduced and evaluated.

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Section: Singular Solution For the Interfacial Ring Waves: Rigid-lid Approximationmentioning

confidence: 99%

Wavefronts and modal structure of long surface and internal ring waves on a parallel shear current

2021

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“…The stability of the flow under disturbances of arbitrary wavenumber is assumed. For a detailed study of the stability (which is beyond the scope of our study) we refer to [1] and the references therein.…”

Section: Hamiltonian Formulationmentioning

confidence: 99%

On the intermediate long wave propagation for internal waves in the presence of currents

Cullen

Ivanov

2020

European Journal of Mechanics - B/Fluids

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A model for the wave motion of an internal wave in the presence of current in the case of intermediate long wave approximation is studied. The lower layer is considerably deeper, with a higher density than the upper layer. The flat surface approximation is assumed. The fluids are incompressible and inviscid. The model equations are obtained from the Hamiltonian formulation of the dynamics in the presence of a depth-varying current. It is shown that an appropriate scaling leads to the integrable Intermediate Long Wave Equation (ILWE). Two limits of the ILWE leading to the integrable Benjamin-Ono and KdV equations are presented as well.

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“…Furthermore, the existence of stagnation points can generate flows where the pressure at the bottom boundary is out of phase with the free surface [11,12]. Many other authors have investigated waves with constant vorticity [11,13,14,15,16,17,18,19,20,21,22]. The readers are referred to the work by Nachbin and Ribeiro-Jr [23] for a review on numerical strategies adopted for capturing the flow beneath waves with constant vorticity.…”

Section: Introductionmentioning

confidence: 99%

An investigation of the flow structure beneath solitary waves with constant vorticity on a conducting fluid under normal electric fields

2023

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The motion of an interface separating two fluids under the effect of electric fields is a subject that has picked the attention of researchers from different areas. While there is an abundance of studies investigating the free surface wave properties, very few works have examined the associated velocity field within the bulk of the fluid. Therefore, in this paper, we investigate numerically the flow structure beneath solitary waves with constant vorticity on an inviscid conducting fluid bounded above by a dielectric gas under normal electric fields in the framework of a weakly nonlinear theory. Elevation and depression solitary waves with constant vorticity are computed by a pseudo-spectral method and a parameter sweep on the intensity of the electric field is carried out in order to study its role in the appearance of stagnation points. We find that for elevation solitary waves the location of stagnation points does not change significantly with variations of the electric field. For depression solitary waves, on the other hand, the electric field acts as a catalyser that makes possible the appearance of stagnation points - in the sense that in its absence there is no stagnation point.

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Effect of variation in density on the stability of bilinear shear currents with a free surface

Cited by 4 publications

References 41 publications

Wavefronts and modal structure of long surface and internal ring waves on a parallel shear current

Wavefronts and modal structure of long surface and internal ring waves on a parallel shear current

On the intermediate long wave propagation for internal waves in the presence of currents

An investigation of the flow structure beneath solitary waves with constant vorticity on a conducting fluid under normal electric fields

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