Ocean swell within the kinetic equation for water waves

Effects of wave-wave interactions on ocean swell are studied. Results of extensive simulations of swell evolution within the duration-limited setup for the kinetic Hasselmann equation at long times up to $10^6$ seconds are presented. Basic solutions of the theory of weak turbulence, the so-called Kolmogorov-Zakharov solutions, are shown to be relevant to the results of the simulations. Features of self-similarity of wave spectra are detailed and their impact on methods of ocean swell monitoring are discussed. Essential drop of wave energy (wave height) due to wave-wave interactions is found to be pronounced at initial stages of swell evolution (of order of 1000 km for typical parameters of the ocean swell). At longer times wave-wave interactions are responsible for a universal angular distribution of wave spectra in a wide range of initial conditions.Comment: Submitted to Journal of Geophysical Research 18 July 201

Universality of Sea Wave Growth and Its Physical Roots

Modern day studies of wind-driven sea waves are usually focused on wind forcing rather than on the effect of resonant nonlinear wave interactions. The authors assume that these effects are dominating and propose a simple relationship between instant wave steepness and time or fetch of wave development expressed in wave periods or lengths. This law does not contain wind speed explicitly and relies upon this asymptotic theory. The validity of this law is illustrated by results of numerical simulations, in situ measurements of growing wind seas and wind wave tank experiments. The impact of the new vision of sea wave physics is discussed in the context of conventional approaches to wave modeling and forecasting.Comment: submitted to Journal of Fluid Mechanics 24-Sep-2014, 34 pages, 10 figure

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

Radiological impact of surface water and sediment near uranium mining sites

The aim of this study is to assess the radiological impact of surface water and sediment around uranium mining sites 20 years after their closing. The areas under observations are 31 former classical underground uranium mining and exploratory sites in Bulgaria, named as objects. The extraction and processing of uranium ores in the Republic of Bulgaria were ended in 1992. To assess the radiological impact of radionuclides field expeditions were performed to sample water and bottom sediment. The migration of uranium through surface water was examined as one of the major pathways for contamination spread. The range of uranium concentration in water flowing from the mining sites was from 0.012 to 6.8 mgU l −1 with a geometric mean of 0.192 mgU l . The uranium concentrations in water downstream the mining sites were approximately 3 times higher than the background value (upstream). The concentrations of U nat , 226 Ra, 210 Pb, and 232 Th in the sediment of downstream river were higher than those upstream by 3.4, 2.6, 2, and 1.7 times, respectively. The distribution coefficient of uranium reflects its high mobility in most of the sites. In order to evaluate the impact on people as well as site prioritization for more detailed assessment and water management, screening dose assessments were done

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