Wind-generated waves on a water layer of finite depth

Kadam, Yashodhan; Patibandla, Ramana; Roy, Anubhab

doi:10.1017/jfm.2023.483

Cited by 3 publications

(2 citation statements)

References 53 publications

(183 reference statements)

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“…Analytical progress on the rippling instability in deep water has only been made for piece-wise linear or exponential currents; see Young & Wolfe (2014) for a review. Finally, Kadam, Patibandla & Roy (2023) gave an exact analytical treatment of the stability of an exponential wind profile over a finite-depth water layer that is either quiescent or has linear or quadratic current profiles. For the quadratic current, they introduced spheroidal wave functions to assess the stability of a shear flow.…”

Section: Introductionmentioning

confidence: 99%

Flow-driven interfacial waves: an inviscid asymptotic study

Bonfils,

Mitra,

Moon

et al. 2023

J. Fluid Mech.

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Motivated by wind blowing over water, we use asymptotic methods to study the evolution of short wavelength interfacial waves driven by the combined action of these flows. We solve the Rayleigh equation for the stability of the shear flow, and construct a uniformly valid approximation for the perturbed streamfunction, or eigenfunction. We then expand the real part of the eigenvalue, the phase speed, in a power series of the inverse wavenumber and show that the imaginary part is exponentially small. We give expressions for the growth rates of the Miles (J. Fluid Mech., vol. 3, 1957, pp. 185–204) and rippling (e.g. Young & Wolfe, J. Fluid Mech., vol. 739, 2014, pp. 276–307) instabilities that are valid for an arbitrary shear flow. The accuracy of the results is demonstrated by a comparison with the exact solution of the eigenvalue problem in the case when both the wind and the current have an exponential profile.

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Section: Introductionmentioning

confidence: 99%

Flow-driven interfacial waves: an inviscid asymptotic study

Bonfils,

Mitra,

Moon

et al. 2023

J. Fluid Mech.

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“…Thomas et al [7] and Montalvo et al [8,9] have extended the Miles theory to finite depth. More recent studies on finite depth were conducted by Kadam et al [10].…”

Section: Introductionmentioning

confidence: 99%

Korteweg–De Vries–Burger Equation with Jeffreys’ Wind–Wave Interaction: Blow-Up and Breaking of Soliton-like Solutions in Finite Time

Manna,

Latifi

2023

Fluids

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In this study, the evolution of surface water solitary waves under the action of Jeffreys’ wind–wave amplification mechanism in shallow water is analytically investigated. The analytic approach is essential for numerical investigations due to the scale of energy dissipation near coasts. Although many works have been conducted based on the Jeffreys’ approach, only some studies have been carried out on finite depth. We show that nonlinearity, dispersion, and anti-dissipation are the dominating phenomena, obeying an anti-diffusive and fully nonlinear Serre–Green–Naghdi (SGN) equation. Applying an appropriate perturbation method, the current research yields a Korteweg–de Vries–Burger-type equation (KdV-B), combining weak nonlinearity, dispersion, and anti-dissipation. This derivation is novel. We show that the continuous transfer of energy from wind to water results in the growth over time of the KdV-B soliton’s amplitude, velocity, acceleration, and energy, while its effective wavelength decreases. This phenomenon differs from the classical results of Jeffreys’ approach and is due to finite depth. In this study, it is shown that expansion and breaking occur in finite time. These times are calculated and expressed with respect to soliton- and wind-appropriateparameters and values. The obtained values are measurable in experimental facilities. A detailed analysis of the breaking time is conducted with regard to various criteria. By comparing these times to the experimental results, the validity of these criteria are examined.

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Free surface water waves generated by instability of an exponential shear flow in arbitrary depth

Abid,

Kharif

2024

Physics of Fluids

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The stability of an exponential current in water to infinitesimal perturbations in the presence of gravity and capillarity is revisited and reformulated using the Weber and Froude numbers. Some new results on the generation of gravity-capillary waves are presented, which supplement the previous works of Morland et al. [“Waves generated by shear layer instabilities,” Proc. Math. Phys. Sci. 433, 441–450 (1991)] and Young and Wolfe [“Generation of surface waves by shear-flow instability,” J. Fluid Mech. 739, 276–307 (2014)] on finite depth. To consider perturbations at much larger scales, special attention is given to the stability of exponential currents only in the presence of gravity. More precisely, the present investigation reveals significant insights into the stability of exponential shear currents under different environmental conditions. Notably, we have identified that the dimensionless growth rate increases with the Froude number, providing a deeper understanding of the interplay between shear layer thickness and surface velocity. Furthermore, our analysis elucidates the dimensional wavelength of the most unstable mode, emphasizing its relevance to the characteristic shear layer thickness. Additionally, within the realm of gravity-capillary instabilities, we have established a sufficient condition for the stability of exponential currents based on the Weber number. Our findings are supported by stability diagrams at finite depth, showing how the size of stable domains correlates with the characteristic thickness of the shear layer. Moreover, we have explored the stability of a thin film of liquid in an exponential shearing flow, further enriching our understanding of the complex dynamics involved in such systems.

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Wind-generated waves on a water layer of finite depth

Cited by 3 publications

References 53 publications

Flow-driven interfacial waves: an inviscid asymptotic study

Flow-driven interfacial waves: an inviscid asymptotic study

Korteweg–De Vries–Burger Equation with Jeffreys’ Wind–Wave Interaction: Blow-Up and Breaking of Soliton-like Solutions in Finite Time

Free surface water waves generated by instability of an exponential shear flow in arbitrary depth

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