scholarly journals Numerical investigation of turbulence of surface gravity waves

2022 ◽  
Vol 933 ◽  
Author(s):  
Zhou Zhang ◽  
Yulin Pan
Keyword(s):  
Size Effect ◽  
Energy Flux ◽  
Gravity Waves ◽  
Narrow Band ◽  
Finite Size ◽  
Surface Gravity ◽  
Finite Size Effect ◽  
Wave Turbulence ◽  
Surface Gravity Waves ◽  
Free Decay

In this paper, we numerically study the wave turbulence of surface gravity waves in the framework of Euler equations of the free surface. The purpose is to understand the variation of the scaling of the spectra with wavenumber $k$ and energy flux $P$ at different nonlinearity levels under different forcing/free-decay conditions. For all conditions (free decay and narrow-band and broad-band forcing) that we consider, we find that the spectral forms approach the wave turbulence theory (WTT) solution $S_\eta \sim k^{-5/2}$ and $S_\eta \sim P^{1/3}$ at high nonlinearity levels. With a decrease of nonlinearity level, the spectra for all cases become steeper, with the narrow-band forcing case exhibiting the most rapid deviation from WTT. We investigate bound waves and the finite-size effect as possible mechanisms causing the spectral variations. Through a tri-coherence analysis, we find that the finite-size effect is present in all cases, which is responsible for the overall steepening of the spectra and the reduced capacity of energy flux at lower nonlinearity levels. The fraction of bound waves in the domain generally decreases with the decrease of nonlinearity level, except for the narrow-band case, which exhibits a transition at a critical nonlinearity level below which a rapid increase is observed. This increase serves as the main reason for the fastest deviation from WTT with the decrease of nonlinearity in the narrow-band forcing case.

Radiation of internal waves from groups of surface gravity waves

2017 ◽  
Vol 829 ◽  
pp. 280-303 ◽  
Author(s):  
S. Haney ◽  
W. R. Young
Keyword(s):  
Internal Waves ◽  
Energy Flux ◽  
Gravity Waves ◽  
Three Dimensions ◽  
Stokes Drift ◽  
Surface Gravity ◽  
Fourth Power ◽  
Buoyancy Frequency ◽  
Surface Gravity Waves ◽  
Short Period

Groups of surface gravity waves induce horizontally varying Stokes drift that drives convergence of water ahead of the group and divergence behind. The mass flux divergence associated with spatially variable Stokes drift pumps water downwards in front of the group and upwards in the rear. This ‘Stokes pumping’ creates a deep Eulerian return flow that sets the isopycnals below the wave group in motion and generates a trailing wake of internal gravity waves. We compute the energy flux from surface to internal waves by finding solutions of the wave-averaged Boussinesq equations in two and three dimensions forced by Stokes pumping at the surface. The two-dimensional (2-D) case is distinct from the 3-D case in that the stratification must be very strong, or the surface waves very slow for any internal wave (IW) radiation at all. On the other hand, in three dimensions, IW radiation always occurs, but with a larger energy flux as the stratification and surface wave (SW) amplitude increase or as the SW period is shorter. Specifically, the energy flux from SWs to IWs varies as the fourth power of the SW amplitude and of the buoyancy frequency, and is inversely proportional to the fifth power of the SW period. Using parameters typical of short period swell (e.g. 8 s SW period with 1 m amplitude) we find that the energy flux is small compared to both the total energy in a typical SW group and compared to the total IW energy. Therefore this coupling between SWs and IWs is not a significant sink of energy for the SWs nor a source for IWs. In an extreme case (e.g. 4 m amplitude 20 s period SWs) this coupling is a significant source of energy for IWs with frequency close to the buoyancy frequency.

Turbulent structure beneath surface gravity waves sheared by the wind

1996 ◽  
Vol 328 ◽  
pp. 313-344 ◽  
Author(s):  
L. Thais ◽  
J. Magnaudet
Keyword(s):  
Gravity Waves ◽  
Wind Waves ◽  
Vertical Direction ◽  
Direct Interaction ◽  
Water Layer ◽  
Surface Gravity ◽  
Wave Turbulence ◽  
Orbital Contribution ◽  
Surface Gravity Waves ◽  
Turbulent Statistics

New experiments have been carried out in a large laboratory channel to explore the structure of turbulent motion in the water layer beneath surface gravity waves. These experiments involve pure wind waves as well as wind-ruffled mechanically generated waves. A submersible two-component LDV system has been used to obtain the three components of the instantaneous velocity field along the vertical direction at a single fetch of 26 m. The displacement of the free surface has been determined simultaneously at the same downstream location by means of wave gauges. For both types of waves, suitable separation techniques have been used to split the total fluctuating motion into an orbital contribution (i.e. a motion induced by the displacement of the surface) and a turbulent contribution. Based on these experimental results, the present paper focuses on the structure of the water turbulence. The most prominent feature revealed by the two sets of experiments is the enhancement of both the turbulent kinetic energy and its dissipation rate with respect to values found near solid walls. Spectral analysis provides clear indications that wave–turbulence interactions greatly affect energy transfers over a significant frequency range by imposing a constant timescale related to the wave-induced strain. For mechanical waves we discuss several turbulent statistics and their modulation with respect to the wave phase, showing that the turbulence we observed was deeply affected at both large and small scales by the wave motion. An analysis of the phase variability of the bursting suggests that there is a direct interaction between the waves and the underlying turbulence, mainly at the wave crests. Turbulence budgets show that production essentially takes place in the wavy region of the flow, i.e. above the wave troughs. These results are finally used to address the nature of the basic mechanisms governing wave–turbulence interactions.

scholarly journals Modeling and control of surface gravity waves in a model of a copper converter

2008 ◽  
Vol 32 (9) ◽  
pp. 1696-1710 ◽  
Author(s):  
Eduardo Godoy ◽  
Axel Osses ◽  
Jaime H. Ortega ◽  
Alvaro Valencia
Keyword(s):  
Gravity Waves ◽  
Surface Gravity ◽  
Modeling And Control ◽  
Copper Converter ◽  
Surface Gravity Waves ◽  
And Control

Irrotational, progressive surface gravity waves near the limiting height

1973 ◽  
Vol 29 (3) ◽  
pp. 94-105 ◽  
Author(s):  
Ken Sasaki ◽  
Takashi Murakami
Keyword(s):  
Gravity Waves ◽  
Surface Gravity ◽  
Surface Gravity Waves

scholarly journals Theoretical Investigation of the Size Effect on the Oxygen Adsorption Energy of Coinage Metal Nanoparticles

2021 ◽  
Author(s):  
Amir H. Hakimioun ◽  
Elisabeth M. Dietze ◽  
Bart D. Vandegehuchte ◽  
Daniel Curulla-Ferre ◽  
Lennart Joos ◽  
...  
Keyword(s):  
Particle Size ◽  
Size Effect ◽  
Adsorption Energy ◽  
Single Point ◽  
Finite Size ◽  
Geometry Optimization ◽  
Oxygen Adsorption ◽  
Finite Size Effect ◽  
Full Geometry Optimization ◽  
Coinage Metal

AbstractThis study evaluates the finite size effect on the oxygen adsorption energy of coinage metal (Cu, Ag and Au) cuboctahedral nanoparticles in the size range of 13 to 1415 atoms (0.7–3.5 nm in diameter). Trends in particle size effects are well described with single point calculations, in which the metal atoms are frozen in their bulk position and the oxygen atom is added in a location determined from periodic surface calculations. This is shown explicitly for Cu nanoparticles, for which full geometry optimization only leads to a constant offset between relaxed and unrelaxed adsorption energies that is independent of particle size. With increasing cluster size, the adsorption energy converges systematically to the limit of the (211) extended surface. The 55-atomic cluster is an outlier for all of the coinage metals and all three materials show similar behavior with respect to particle size. Graphic Abstract

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