Wave-vortex interaction

We present an experimental study on the effect of a electromagneticaly generated vortex flow on parametrically amplified waves at the surface of a fluid. The underlying vortex flow, generated by a periodic Lorentz force, creates spatio-temporal fluctuations that interact nonlinearly with the standing surface waves. We characterize the bifurcation diagram and measure the power spectrum density (PSD) of the local surface wave amplitude. We show that the parametric instability threshold increases with increasing intensity of the vortex flow.Comment: 8 pages, 10 figures, submitted to Phys. Rev.

Measurement of stimulated Hawking emission in an analogue system

There is a mathematical analogy between the propagation of fields in a general relativistic space-time and long (shallow water) surface waves on moving water. Hawking argued that black holes emit thermal radiation via a quantum spontaneous emission. Similar arguments predict the same effect near wave horizons in fluid flow. By placing a streamlined obstacle into an open channel flow we create a region of high velocity over the obstacle that can include wave horizons. Long waves propagating upstream towards this region are blocked and converted into short (deep water) waves. This is the analogue of the stimulated emission by a white hole (the time inverse of a black hole), and our measurements of the amplitudes of the converted waves demonstrate the thermal nature of the conversion process for this system. Given the close relationship between stimulated and spontaneous emission, our findings attest to the generality of the Hawking process.Comment: 7 pages, 5 figures. This version corrects a processing error in the final graph 5b which multiplied the vertical axis by 2. The graph, and the data used from it, have been corrected. Some minor typos have also been corrected. This version also uses TeX rather than Wor

Self-similarity of wind-driven seas

International audienceThe results of theoretical and numerical study of the Hasselmann kinetic equation for deep water waves in presence of wind input and dissipation are presented. The guideline of the study: nonlinear transfer is the dominating mechanism of wind-wave evolution. In other words, the most important features of wind-driven sea could be understood in a framework of conservative Hasselmann equation while forcing and dissipation determine parameters of a solution of the conservative equation. The conservative Hasselmann equation has a rich family of self-similar solutions for duration-limited and fetch-limited wind-wave growth. These solutions are closely related to classic stationary and homogeneous weak-turbulent Kolmogorov spectra and can be considered as non-stationary and non-homogeneous generalizations of these spectra. It is shown that experimental parameterizations of wind-wave spectra (e.g. JONSWAP spectrum) that imply self-similarity give a solid basis for comparison with theoretical predictions. In particular, the self-similarity analysis predicts correctly the dependence of mean wave energy and mean frequency on wave age Cp / U10. This comparison is detailed in the extensive numerical study of duration-limited growth of wind waves. The study is based on algorithm suggested by Webb (1978) that was first realized as an operating code by Resio and Perrie (1989, 1991). This code is now updated: the new version is up to one order faster than the previous one. The new stable and reliable code makes possible to perform massive numerical simulation of the Hasselmann equation with different models of wind input and dissipation. As a result, a strong tendency of numerical solutions to self-similar behavior is shown for rather wide range of wave generation and dissipation conditions. We found very good quantitative coincidence of these solutions with available results on duration-limited growth, as well as with experimental parametrization of fetch-limited spectra JONSWAP in terms of wind-wave age Cp / U10

Coexistence of Weak and Strong Wave Turbulence in a Swell Propagation

By performing two parallel numerical experiments -- solving the dynamical Hamiltonian equations and solving the Hasselmann kinetic equation -- we examined the applicability of the theory of weak turbulence to the description of the time evolution of an ensemble of free surface waves (a swell) on deep water. We observed qualitative coincidence of the results. To achieve quantitative coincidence, we augmented the kinetic equation by an empirical dissipation term modelling the strongly nonlinear process of white-capping. Fitting the two experiments, we determined the dissipation function due to wave breaking and found that it depends very sharply on the parameter of nonlinearity (the surface steepness). The onset of white-capping can be compared to a second-order phase transition. This result corroborates with experimental observations by Banner, Babanin, Young.Comment: 5 pages, 5 figures, Submitted in Phys. Rev. Letter

Horizon effects with surface waves on moving water

Surface waves on a stationary flow of water are considered, in a linear model that includes the surface tension of the fluid. The resulting gravity-capillary waves experience a rich array of horizon effects when propagating against the flow. In some cases three horizons (points where the group velocity of the wave reverses) exist for waves with a single laboratory frequency. Some of these effects are familiar in fluid mechanics under the name of wave blocking, but other aspects, in particular waves with negative co-moving frequency and the Hawking effect, were overlooked until surface waves were investigated as examples of analogue gravity [Sch\"utzhold R and Unruh W G 2002 Phys. Rev. D 66 044019]. A comprehensive presentation of the various horizon effects for gravity-capillary waves is given, with emphasis on the deep water/short wavelength case kh>>1 where many analytical results can be derived. A similarity of the state space of the waves to that of a thermodynamic system is pointed out.Comment: 30 pages, 15 figures. Minor change

Altimetry for the future: Building on 25 years of progress

In 2018 we celebrated 25 years of development of radar altimetry, and the progress achieved by this methodology in the fields of global and coastal oceanography, hydrology, geodesy and cryospheric sciences. Many symbolic major events have celebrated these developments, e.g., in Venice, Italy, the 15th (2006) and 20th (2012) years of progress and more recently, in 2018, in Ponta Delgada, Portugal, 25 Years of Progress in Radar Altimetry. On this latter occasion it was decided to collect contributions of scientists, engineers and managers involved in the worldwide altimetry community to depict the state of altimetry and propose recommendations for the altimetry of the future. This paper summarizes contributions and recommendations that were collected and provides guidance for future mission design, research activities, and sustainable operational radar altimetry data exploitation. Recommendations provided are fundamental for optimizing further scientific and operational advances of oceanographic observations by altimetry, including requirements for spatial and temporal resolution of altimetric measurements, their accuracy and continuity. There are also new challenges and new openings mentioned in the paper that are particularly crucial for observations at higher latitudes, for coastal oceanography, for cryospheric studies and for hydrology. The paper starts with a general introduction followed by a section on Earth System Science including Ocean Dynamics, Sea Level, the Coastal Ocean, Hydrology, the Cryosphere and Polar Oceans and the “Green” Ocean, extending the frontier from biogeochemistry to marine ecology. Applications are described in a subsequent section, which covers Operational Oceanography, Weather, Hurricane Wave and Wind Forecasting, Climate projection. Instruments’ development and satellite missions’ evolutions are described in a fourth section. A fifth section covers the key observations that altimeters provide and their potential complements, from other Earth observation measurements to in situ data. Section 6 identifies the data and methods and provides some accuracy and resolution requirements for the wet tropospheric correction, the orbit and other geodetic requirements, the Mean Sea Surface, Geoid and Mean Dynamic Topography, Calibration and Validation, data accuracy, data access and handling (including the DUACS system). Section 7 brings a transversal view on scales, integration, artificial intelligence, and capacity building (education and training). Section 8 reviews the programmatic issues followed by a conclusion

Aggregation-fragmentation processes and decaying three-wave turbulence

We use a formal correspondence between the isotropic three-wave kinetic equation and the rate equations for a nonlinear fragmentation-aggregation process to study the wave frequency power spectrum of decaying three-wave turbulence in the infinite capacity regime. We show that the transient spectral exponent is lambda + 1, where lambda is the degree of homogeneity of the wave interaction kernel and derive a formula for the decay amplitude. When lambda = 0 the transient exponent coincides with the thermodynamic equilibrium exponent leading to logarithmic corrections to scaling which we calculate explicitly for the case of constant interaction kernel

Dynamical scaling and the finite-capacity anomaly in three-wave turbulence

We present a systematic study of the dynamical scaling process leading to the establishment of the Kolmogorov-Zakharov (KZ) spectrum in weak three-wave turbulence. In the finite-capacity case, in which the transient spectrum reaches infinite frequency in finite time, the dynamical scaling exponent is anomalous in the sense that it cannot be determined from dimensional considerations. As a consequence, the transient spectrum preceding the establishment of the steady state is steeper than the KZ spectrum. Constant energy flux is actually established from right to left in frequency space after the singularity of the transient solution. From arguments based on entropy production, a steeper transient spectrum is heuristically plausible

Electromagnetic wave scattering from the sea surface in the presence of wind wave patterns

The study is concerned with electromagnetic wave (EM) scattering by a random sea surface in the presence of coherent wave patterns. The coherent patterns are understood in a broad sense as the existence of certain dynamical coupling between linear Fourier components of the water wave field. We show that the presence of weakly nonlinear wave patterns can significantly change the EM scattering compared to the case of a completely random wave field. Generalizing the Random Phase Approximation (RPA) we suggest a new paradigm for EM scattering by a random sea surface. The specific analysis carried out in the paper synthesizes the small perturbation method for EM scattering and a weakly nonlinear approach for wind wave dynamics. By investigating, in detail, two examples of a random sea surface composed of either Stokes waves or horse-shoe ('crescent-shaped') patterns the mechanism of the pattern effect on scattering is revealed. Each Fourier harmonic of the scattered EM field is found to be a sum of contributions due to different combinations of wave field harmonics. Among these 'partial scatterings' there are phase-dependent ones and, therefore, the intensity of the resulting EM harmonic is sensitive to the phase relations between the wind wave harmonics. The effect can be interpreted as interference of partial scatterings due to the co-existence of several phase-related periodic scattering grids. A straightforward generalization of these results enables us to obtain, for a given wind wave field and an incident EM field, an a priori estimate of whether the effects due to the patterns are significant and the commonly used RPA is inapplicable. When the RPA is inapplicable, we suggest its natural generalization by re-defining the statistical ensemble for water surface. First, EM scattering by an 'elementary' constituent pattern should be considered. Each such scattering is affected by the interference because the harmonics comprising the pattern are dynamically linked. Then, ensemble averaging, which takes into account the distribution of the pattern parameters (based on the assumption that the phases between the patterns are random), should be carried out. It is shown that, generally, this interference does not vanish for any statistical ensemble due to dynamical coupling between water wave harmonics. The suggested RPA generalization takes into account weak non-Gaussianity of water wave field in contrast to the traditional RPA which ignores it

On discriminating swell and wind-driven seas in voluntary observing ship data

[1] The global visual wave observations are reanalyzed within the theoretical concept of self-similar wind-driven seas. The core of the analysis is one-parametric dependencies of wave height on wave period. Theoretically, wind-driven seas are governed by power-like laws with exponents close to Toba's one 3/2 while the corresponding swell exponent (À1/2) has an opposite signature. This simple criterion was used and appeared to be adequate to the problem of swell and wind-driven waves discrimination. This theoretically based discrimination does not follow exactly the Voluntary Observing Ship (VOS) data. This important issue is considered both in the context of methodology of obtaining VOS data and within the physics of wind waves. The results are detailed for global estimates and for analysis of particular areas of the Pacific Ocean. Prospects of further studies are discussed. In particular, satellite data are seen to be promising for tracking ocean swell and for studies of physical mechanisms of its evolution. Citation: Badulin, S. I., and V. G. Grigorieva (2012), On discriminating swell and wind-driven seas in Voluntary Observing Ship data