Measurement of high frequency capillary waves on steep gravity waves

1978 ◽  
Vol 86 (3) ◽  
pp. 401-413 ◽  
Author(s):  
John H. Chang ◽  
Richard N. Wagner ◽  
Henry C. Yuen
Keyword(s):  
Surface Tension ◽  
High Resolution ◽  
Gravity Wave ◽  
Gravity Waves ◽  
Deep Water ◽  
High Frequency ◽  
Qualitative Agreement ◽  
Capillary Wave ◽  
Capillary Waves ◽  
Good Qualitative Agreement

The properties of high frequency capillary waves generated by steep gravity waves on deep water have been measured with a high resolution laser optical slope gauge. The results have been compared with the steady theory of Longuet-Higgins (1963). Good qualitative agreement is obtained. However, the quantitative predictions of the capillary wave slopes cannot be verified by the data because the theory requires knowledge of an idealized quantity - the crest curvature of the gravity wave in the absence of surface tension - which cannot be measured experimentally.

scholarly journals A nonlinear Schrödinger equation for gravity–capillary water waves on arbitrary depth with constant vorticity. Part 1

2018 ◽  
Vol 854 ◽  
pp. 146-163 ◽  
Author(s):  
H. C. Hsu ◽  
C. Kharif ◽  
M. Abid ◽  
Y. Y. Chen
Keyword(s):  
Surface Tension ◽  
Growth Rate ◽  
Gravity Waves ◽  
Capillary Wave ◽  
Modulational Instability ◽  
Capillary Waves ◽  
Rate Of Growth ◽  
Positive Vorticity ◽  
Constant Vorticity ◽  
Wave Trains

A nonlinear Schrödinger equation for the envelope of two-dimensional gravity–capillary waves propagating at the free surface of a vertically sheared current of constant vorticity is derived. In this paper we extend to gravity–capillary wave trains the results of Thomas et al. (Phys. Fluids, 2012, 127102) and complete the stability analysis and stability diagram of Djordjevic & Redekopp (J. Fluid Mech., vol. 79, 1977, pp. 703–714) in the presence of vorticity. The vorticity effect on the modulational instability of weakly nonlinear gravity–capillary wave packets is investigated. It is shown that the vorticity modifies significantly the modulational instability of gravity–capillary wave trains, namely the growth rate and instability bandwidth. It is found that the rate of growth of modulational instability of short gravity waves influenced by surface tension behaves like pure gravity waves: (i) in infinite depth, the growth rate is reduced in the presence of positive vorticity and amplified in the presence of negative vorticity; (ii) in finite depth, it is reduced when the vorticity is positive and amplified and finally reduced when the vorticity is negative. The combined effect of vorticity and surface tension is to increase the rate of growth of modulational instability of short gravity waves influenced by surface tension, namely when the vorticity is negative. The rate of growth of modulational instability of capillary waves is amplified by negative vorticity and attenuated by positive vorticity. Stability diagrams are plotted and it is shown that they are significantly modified by the introduction of the vorticity.

Crest instabilities of gravity waves. Part 1. The almost-highest wave

1994 ◽  
Vol 258 ◽  
pp. 115-129 ◽  
Author(s):  
Michael S. Longuet-Higgins ◽  
R. P. Cleaver
Keyword(s):  
Gravity Wave ◽  
Gravity Waves ◽  
Capillary Waves ◽  
Radius Of Curvature ◽  
Horizontal Distance ◽  
Exponential Rate ◽  
Basic Mode ◽  
Initial Stage ◽  
Small Scales ◽  
Spilling Breaker

It is shown theoretically that the crest of a steep, irrotational gravity wave, considered in isolation, is unstable. There exists just one basic mode of instability, whose exponential rate of growth β equals 0.123(g / R)½, where g denotes gravity and R is the radius of curvature at the undisturbed crest. A volume of water near the crest is shifted towards the forward face of the wave; the ‘toe’ of the instability is at a horizontal distance 0.45R ahead of the crest. The instability may represent the initial stage of a spilling breaker. On small scales, the ‘toe’ may be a source of parasitic capillary waves.

Detection of high frequency gravity waves using high resolution radiosonde observations

2012 ◽  
Vol 77 ◽  
pp. 254-259 ◽  
Author(s):  
P.P. Leena ◽  
M. Venkat Ratnam ◽  
B.V. Krishna Murthy ◽  
S. Vijaya Bhaskara Rao
Keyword(s):  
High Resolution ◽  
Gravity Waves ◽  
High Frequency

Capillary–gravity waves of solitary type and envelope solitons on deep water

1993 ◽  
Vol 252 ◽  
pp. 703-711 ◽  
Author(s):  
Michael S. Longuet-Higgins
Keyword(s):  
Surface Tension ◽  
Dispersion Relation ◽  
Gravity Waves ◽  
Deep Water ◽  
Small Amplitude ◽  
Finite Amplitude ◽  
Surface Slope ◽  
Carrier Wave ◽  
Envelope Solitons ◽  
Special Case

The existence of steady solitary waves on deep water was suggested on physical grounds by Longuet-Higgins (1988) and later confirmed by numerical computation (Longuet-Higgins 1989; Vanden-Broeck & Dias 1992). Their numerical methods are accurate only for waves of finite amplitude. In this paper we show that solitary capillary-gravity waves of small amplitude are in fact a special case of envelope solitons, namely those having a carrier wave of length 2π(T/ρg)1½2 (g = gravity, T = surface tension, ρ = density). The dispersion relation $c^2 = 2(1-\frac{11}{32}\alpha^2_{\max)$ between the speed c and the maximum surface slope αmax is derived from the nonlinear Schrödinger equation for deep-water solitons (Djordjevik & Redekopp 1977) and is found to provide a good asymptote for the numerical calculations.

scholarly journals Intercomparison of AIRS and HIRDLS stratospheric gravity wave observations

2018 ◽  
Vol 11 (1) ◽  
pp. 215-232 ◽  
Author(s):  
Catrin I. Meyer ◽  
Manfred Ern ◽  
Lars Hoffmann ◽  
Quang Thai Trinh ◽  
M. Joan Alexander
Keyword(s):  
High Resolution ◽  
Gravity Wave ◽  
Gravity Waves ◽  
Momentum Flux ◽  
Wave Spectrum ◽  
Horizontal Resolution ◽  
Wave Activity ◽  
Large Variability ◽  
Wave Event ◽  
The Waves

Abstract. We investigate stratospheric gravity wave observations by the Atmospheric InfraRed Sounder (AIRS) aboard NASA's Aqua satellite and the High Resolution Dynamics Limb Sounder (HIRDLS) aboard NASA's Aura satellite. AIRS operational temperature retrievals are typically not used for studies of gravity waves, because their vertical and horizontal resolution is rather limited. This study uses data of a high-resolution retrieval which provides stratospheric temperature profiles for each individual satellite footprint. Therefore the horizontal sampling of the high-resolution retrieval is 9 times better than that of the operational retrieval. HIRDLS provides 2-D spectral information of observed gravity waves in terms of along-track and vertical wavelengths. AIRS as a nadir sounder is more sensitive to short-horizontal-wavelength gravity waves, and HIRDLS as a limb sounder is more sensitive to short-vertical-wavelength gravity waves. Therefore HIRDLS is ideally suited to complement AIRS observations. A calculated momentum flux factor indicates that the waves seen by AIRS contribute significantly to momentum flux, even if the AIRS temperature variance may be small compared to HIRDLS. The stratospheric wave structures observed by AIRS and HIRDLS often agree very well. Case studies of a mountain wave event and a non-orographic wave event demonstrate that the observed phase structures of AIRS and HIRDLS are also similar. AIRS has a coarser vertical resolution, which results in an attenuation of the amplitude and coarser vertical wavelengths than for HIRDLS. However, AIRS has a much higher horizontal resolution, and the propagation direction of the waves can be clearly identified in geographical maps. The horizontal orientation of the phase fronts can be deduced from AIRS 3-D temperature fields. This is a restricting factor for gravity wave analyses of limb measurements. Additionally, temperature variances with respect to stratospheric gravity wave activity are compared on a statistical basis. The complete HIRDLS measurement period from January 2005 to March 2008 is covered. The seasonal and latitudinal distributions of gravity wave activity as observed by AIRS and HIRDLS agree well. A strong annual cycle at mid- and high latitudes is found in time series of gravity wave variances at 42 km, which has its maxima during wintertime and its minima during summertime. The variability is largest during austral wintertime at 60∘ S. Variations in the zonal winds at 2.5 hPa are associated with large variability in gravity wave variances. Altogether, gravity wave variances of AIRS and HIRDLS are complementary to each other. Large parts of the gravity wave spectrum are covered by joint observations. This opens up fascinating vistas for future gravity wave research.

scholarly journals Fourth order nonlinear evolution equations for gravity-capillary waves in the presence of a thin thermocline in deep water

2002 ◽  
Vol 43 (4) ◽  
pp. 513-524 ◽  
Author(s):  
Suma Debsarma ◽  
K.P. Das
Keyword(s):  
Fourth Order ◽  
Deep Water ◽  
Evolution Equations ◽  
Nonlinear Evolution ◽  
Capillary Wave ◽  
Capillary Waves ◽  
Nonlinear Evolution Equations ◽  
Marginal Stability ◽  
Stability And Instability ◽  
The Stability

AbstractFor a three-dimensional gravity capillary wave packet in the presence of a thin thermocline in deep water two coupled nonlinear evolution equations correct to fourth order in wave steepness are obtained. Reducing these two equations to a single equation for oblique plane wave perturbation, the stability of a uniform gravity-capillary wave train is investigated. The stability and instability regions are identified. Expressions for the maximum growth rate of instability and the wavenumber at marginal stability are obtained. The results are shown graphically.

Viscous dissipation in steep capillary–gravity waves

1997 ◽  
Vol 344 ◽  
pp. 271-289 ◽  
Author(s):  
MICHAEL S. LONGUET-HIGGINS
Keyword(s):  
Gravity Waves ◽  
Deep Water ◽  
Steady Motion ◽  
Capillary Waves ◽  
Large Wave ◽  
Order Of Magnitude ◽  
Rate Of Decay ◽  
Rates Of Decay ◽  
Work Done ◽  
Viscous Stresses

Some simple but exact general expressions are derived for the viscous stresses required at the surface of irrotational capillary–gravity waves of periodic or solitary type on deep water in order to maintain them in steady motion. These expressions are applied to nonlinear capillary waves, and to capillary–gravity waves of solitary type on deep water. In the case of pure capillary waves some algebraic expressions are found for the work done by the surface stresses, from which it is possible to infer the viscous rate of decay of free, nonlinear capillary waves.Similar calculations are carried out for capillary–gravity waves of solitary type on deep water. It is shown that the limiting rate of decay of a solitary wave at low amplitudes is just twice that for linear, periodic waves. This is due to the spreading out of the wave envelope at low wave steepnesses. At large wave steepnesses the dissipation increases by an order of magnitude, owing to the sharply increased curvature in the wave troughs. The calculated rates of decay are in agreement with recent observations.

scholarly journals A Comparison between Gravity Wave Momentum Fluxes in Observations and Climate Models

2013 ◽  
Vol 26 (17) ◽  
pp. 6383-6405 ◽  
Author(s):  
Marvin A. Geller ◽  
M. Joan Alexander ◽  
Peter T. Love ◽  
Julio Bacmeister ◽  
Manfred Ern ◽  
...  
Keyword(s):  
High Resolution ◽  
Gravity Wave ◽  
Gravity Waves ◽  
Climate Models ◽  
Radiosonde Data ◽  
Wave Source ◽  
Wide Range ◽  
Momentum Fluxes ◽  
High Resolution Models ◽  
Wave Momentum

Abstract For the first time, a formal comparison is made between gravity wave momentum fluxes in models and those derived from observations. Although gravity waves occur over a wide range of spatial and temporal scales, the focus of this paper is on scales that are being parameterized in present climate models, sub-1000-km scales. Only observational methods that permit derivation of gravity wave momentum fluxes over large geographical areas are discussed, and these are from satellite temperature measurements, constant-density long-duration balloons, and high-vertical-resolution radiosonde data. The models discussed include two high-resolution models in which gravity waves are explicitly modeled, Kanto and the Community Atmosphere Model, version 5 (CAM5), and three climate models containing gravity wave parameterizations, MAECHAM5, Hadley Centre Global Environmental Model 3 (HadGEM3), and the Goddard Institute for Space Studies (GISS) model. Measurements generally show similar flux magnitudes as in models, except that the fluxes derived from satellite measurements fall off more rapidly with height. This is likely due to limitations on the observable range of wavelengths, although other factors may contribute. When one accounts for this more rapid fall off, the geographical distribution of the fluxes from observations and models compare reasonably well, except for certain features that depend on the specification of the nonorographic gravity wave source functions in the climate models. For instance, both the observed fluxes and those in the high-resolution models are very small at summer high latitudes, but this is not the case for some of the climate models. This comparison between gravity wave fluxes from climate models, high-resolution models, and fluxes derived from observations indicates that such efforts offer a promising path toward improving specifications of gravity wave sources in climate models.

Numerical calculations of steady gravity-capillary waves using an integro-differential formulation

1979 ◽  
Vol 94 (4) ◽  
pp. 777-793 ◽  
Author(s):  
James W. Rottman ◽  
D. B. Olfe
Keyword(s):  
Gravity Waves ◽  
Small Amplitude ◽  
Numerical Solutions ◽  
Capillary Wave ◽  
Capillary Waves ◽  
The Other ◽  
Wave Number ◽  
Infinite Depth ◽  
Free Surface Waves ◽  
Differential Formulation

A new integro-differential equation is derived for steady free-surface waves. Numerical solutions of this equation for periodic gravity-capillary waves on a fluid of infinite depth are presented. For the two limiting cases of gravity waves and capillary waves, our results are in excellent agreement with previous calculations. For gravity-capillary waves, detailed calculations are performed near the wave-number at which the classical second-order perturbation solution breaks down. Our calculations yield two solutions in this region, which in the limit of small amplitudes agree with the results obtained by Wilton in 1915; one solution has the small amplitude behaviour of a gravity wave and the other that of a capillary wave, but the numerical results show that at large amplitudes both waves have the characteristics of capillary waves. The calculations also show that the wavenumber range in which two solutions exist increases with increasing wave height.

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