Effect of viscosity on wind-driven gravitation waves

IF 4.1 2区 工程技术 Q1 MECHANICS Physics of Fluids Pub Date : 2024-09-11 DOI:10.1063/5.0221941
C. Chaubet, N. Kern, M. A. Manna
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Abstract

We address the question of how viscosity impacts the growth of gravitation waves, such as those on the ocean, when they are driven by wind. There is so far no general rigorous theory for this energy transfer. We extend Miles' approach [J. W. Miles, “On the generation of surface waves by shear flows,” J. Fluid Mech. 3, 185–204 (1957)], using the same logarithmic wind profile, to incorporate bulk viscosity and derive modified growth rates. Exploiting the fact that water waves fall into the “weak viscosity” regime, we produce analytical expressions for the growth rate, which we solve using the numerical method proposed by Beji and Nadaoka [“Solution of Rayleigh's instability equation for arbitrary wind profiles,” J. Fluid Mech. 500, 65–73 (2004)]. Our results confirm that corrections to the growth rates are significant for wavelengths below a meter, and for weak to modest wind strengths. We show that all wave growth is suppressed, due to viscous effects, below a critical wind strength. We also show that the wave age corresponding to a developed sea is reduced by viscosity. We quantitatively characterize the zones, in terms of wind strength and wavelength, for which the wave growth is suppressed by viscosity.
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粘度对风引力波的影响
我们要解决的问题是,当风力驱动引力波(如海洋上的引力波)时,粘度如何影响引力波的增长。迄今为止,还没有关于这种能量传递的通用严格理论。我们扩展了迈尔斯的方法[J.W. Miles, "On the generation of surface waves by shear flows," J. Fluid Mech.3, 185-204 (1957)],使用相同的对数风廓线,加入了体积粘度并推导出修正的增长率。利用水波属于 "弱粘性 "机制这一事实,我们得出了增长率的解析表达式,并使用 Beji 和 Nadaoka 提出的数值方法进行了求解("任意风廓线的瑞利不稳定方程求解",《流体机械》,500, 65-73 (2004))。500, 65-73 (2004)].我们的结果证实,对于波长低于一米、风力从弱到强的情况,对波速增长的修正是显著的。我们表明,在临界风力以下,由于粘性效应,所有波浪的增长都受到抑制。我们还表明,粘滞效应会降低发育海相应的波龄。我们从风力和波长的角度定量地描述了波浪增长受粘性抑制的区域。
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来源期刊
Physics of Fluids
Physics of Fluids 物理-力学
CiteScore
6.50
自引率
41.30%
发文量
2063
审稿时长
2.6 months
期刊介绍: Physics of Fluids (PoF) is a preeminent journal devoted to publishing original theoretical, computational, and experimental contributions to the understanding of the dynamics of gases, liquids, and complex or multiphase fluids. Topics published in PoF are diverse and reflect the most important subjects in fluid dynamics, including, but not limited to: -Acoustics -Aerospace and aeronautical flow -Astrophysical flow -Biofluid mechanics -Cavitation and cavitating flows -Combustion flows -Complex fluids -Compressible flow -Computational fluid dynamics -Contact lines -Continuum mechanics -Convection -Cryogenic flow -Droplets -Electrical and magnetic effects in fluid flow -Foam, bubble, and film mechanics -Flow control -Flow instability and transition -Flow orientation and anisotropy -Flows with other transport phenomena -Flows with complex boundary conditions -Flow visualization -Fluid mechanics -Fluid physical properties -Fluid–structure interactions -Free surface flows -Geophysical flow -Interfacial flow -Knudsen flow -Laminar flow -Liquid crystals -Mathematics of fluids -Micro- and nanofluid mechanics -Mixing -Molecular theory -Nanofluidics -Particulate, multiphase, and granular flow -Processing flows -Relativistic fluid mechanics -Rotating flows -Shock wave phenomena -Soft matter -Stratified flows -Supercritical fluids -Superfluidity -Thermodynamics of flow systems -Transonic flow -Turbulent flow -Viscous and non-Newtonian flow -Viscoelasticity -Vortex dynamics -Waves
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