Growth of surface wind-waves in water of finite depth: A laboratory experiment

Branger, Hubert; Manna, M. A.; Luneau, Christopher; Abid, Malek; Kharif, Christian

doi:10.1016/j.coastaleng.2022.104174

Cited by 7 publications

(6 citation statements)

References 77 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…To validate these studies, laboratory experiments have been conducted by Branger et al. (2022), showing a good match with the predictions of Montalvo et al. (2013 a ).…”

Section: Introductionmentioning

confidence: 60%

Wind-generated waves on a water layer of finite depth

2023

View full text Add to dashboard Cite

In this paper, we study the linear stability of a two-dimensional shear flow of an air layer overriding a water layer of finite depth. The air layer is considered to be of an infinite extent with an exponential velocity profile. Three different background conditions are considered in the finite-depth water layer: a quiescent background, a linear velocity profile and a quadratic velocity profile. It is known that the cases of the quiescent water layer and the linear velocity profile allow for analytical treatment. We further provide an analytical solution for the case of the quadratic velocity field: we specifically consider a flow-reversal profile, although the result could be generalized to other quadratic profiles as well. The role of water layer depth on the growth rate of the Miles and rippling instabilities is studied in each of the three cases. Using asymptotic analysis, with the air–water density ratio being a small parameter, we obtain an analytical expression for the growth rate of the Miles mode and discuss the condition for the existence of a long-wave cutoff for these profiles. We provide analytical expressions for the stability boundary in the parameter space of inverse squared Froude number and wavenumber. In scenarios where a long-wave cutoff does not exist, we have carried out a long-wave asymptotic study to obtain the growth rate behaviour in that regime.

show abstract

“…To validate these studies, laboratory experiments have been conducted by Branger et al. (2022), showing a good match with the predictions of Montalvo et al. (2013 a ).…”

Section: Introductionmentioning

confidence: 60%

Wind-generated waves on a water layer of finite depth

2023

View full text Add to dashboard Cite

show abstract

“…where c d is evaluated at a representative value c d = 0.0028 (see Tang et al 1996). We note here that Branger et al (2022) showed from several laboratory experiments that c d had a dependence on the depth for very shallow water, kh < 1.8. We attribute this to the higher and steeper waves that form in shallow water and take account of this through the dependence of W a = u a on the wave amplitude that we have developed here in (2.43).…”

Section: Wind Forcingmentioning

confidence: 81%

“…In the literature there are several other approximations that have been used, many based on moving the lower air-flow boundary from y = 0 to y = y * , the roughness length scale, and then analysing the near-surface turbulent air flow. A series of papers (Montalvo et al 2013a,b;Latifi et al 2017;Branger et al 2022) used a two-term critical-level Bessel function approximation to represent the modal function, sometimes combined with the lower boundary modification. These and other approximations give similar O(1) estimates for β.…”

Section: Formulation and Long-wave Approximationmentioning

confidence: 99%

See 1 more Smart Citation

Evolution of wind-induced wave groups in water of finite depth

Maleewong,

Grimshaw

2024

J. Fluid Mech.

View full text Add to dashboard Cite

The generation of water waves by wind is a fundamental and much-studied problem of scientific and operational concern. One mechanism that has obtained a wide degree of acceptance and use is the Miles air shear flow instability theory in which water waves grow due to energy transfer from the air at a critical level where the wave phase speed matches the wind speed. In this paper we revisit and extend this theory by examining how the predicted wave growth rate depends on the water depth and the wind shear parameters. At the same time we include frictional effects due to water bottom stress and at the water surface, and add an additional driving term due to wave stress in the air near the sea surface, using a turbulent parametrisation. The theory is developed using a frictional modification of the usual potential flow theory for water waves, the modified Euler equations, coupled to linearised air-flow equations. To assist our analysis we develop a long-wave approximation for the key Miles growth parameter, which explicitly shows how this depends on the water depth and the wind shear parameters. Since our focus is on the development of wave groups, we present a forced nonlinear Schrödinger equation in which the forcing term describes wave growth or decay. For very shallow water the modified Euler equations are reduced to their shallow-water counterpart, which are briefly discussed using Riemann invariants.

show abstract

“…The models proposed in these studies are in fair agreement with the data and empirical relationships obtained from the Lake George experiment as well as with the data from the Australian Shallow Water Experiment (Donelan et al [11,12], Young [13,14]). Recently, in experimental facilities, Branger et al [15] studied the effect of finite depth on wave growth. The results obtained from these studies were in agreement with the theoretical curves predicted by Montalvo et al [8].…”

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

View full text Add to dashboard Cite

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.

show abstract

Growth of surface wind-waves in water of finite depth: A laboratory experiment

Cited by 7 publications

References 77 publications

Wind-generated waves on a water layer of finite depth

Wind-generated waves on a water layer of finite depth

Evolution of wind-induced wave groups in water of finite depth

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

Contact Info

Product

Resources

About