Modulational instability, wave breaking and formation of large scale dipoles in the atmosphere

In the present Letter we use the Direct Numerical Simulation (DNS) of the Navier-Stokes equation for a two-phase flow (water and air) to study the dynamics of the modulational instability of free surface waves and its contribution to the interaction between ocean and atmosphere. If the steepness of the initial wave is large enough, we observe a wave breaking and the formation of large scale dipole structures in the air. Because of the multiple steepening and breaking of the waves under unstable wave packets, a train of dipoles is released and propagate in the atmosphere at a height comparable with the wave length. The amount of energy dissipated by the breaker in water and air is considered and, contrary to expectations, we observe that the energy dissipation in air is larger than the one in the water. Possible consequences on the wave modelling and on the exchange of aerosols and gases between air and water are discussed

Factors influencing beef cattle marketing behavior in pastoral areas of Kenya: the role of livestock market information

Marketing transactions take place in an environment where information is shared and exchanged among and between sellers, buyers and middlemen. It is argued that traders and middlemen have a competitive advantage over producers in negotiating for prices, because the former have access to prices in both primary and terminal markets, while the latter only have limited access to prices in the primary markets. This Research Brief highlights the situation regarding access to livestock marketing information by producers in pastoral markets of Kenya. Results show that livestock marketing information was not accessible to producers from September 2004 to September 2005, and hence did not play a significant role in influencing market prices. Subsequent analyses also show that producers consider a number of attributes when pegging prices to their animals, and that these tally with the categorization system developed by the Livestock Information Network and Knowledge System (LINKS) project. Further findings suggest that past efforts to develop livestock marketing information systems have been dogged by limited capacity to provide information that is accurate, timely, reliable, and spatially coherent. This has been exacerbated by failure to effectively use existing media and complement these with emerging information communication technologies to disseminate the information. LINKS has since responded to these factors through improvements in geographical coverage, accuracy, reliability and timeliness in the overall livestock market information system, as well as through improved information dissemination systems; improvements that have strengthened LINKS, allowing it to function as the foundation for the National Livestock Marketing Information System in Kenya

On the existence of a fully developed wind-sea spectrum

We consider the energy transfer equation for well-developed ocean waves under the influence of wind, and study the conditions for the existence of an equilibrium solution in which wind input, wave-wave interaction and dissipation balance each other. For the wind input we take the parameterization proposed by Snyder and others, which was based on their measurements in the Bight of Abaco and which agrees with Miles's theory. The wave-wave interaction is computed with an algorithm given recently by S. Hasselmann and others. The dissipation is less well-known, but we will make the general assumption that it is quasi-linear in the wave spectrum with a factor coefficient depending only on frequency and integral spectral parameters. In the first part of this paper we investigate whether the assumption that the equilibrium spectrum exits and is given by the Pierson-Moskowitz spectrum with a standard type of angular distribution leads to a reasonable dissipation function. We find that this is not the case. Even if one balances the total rate of change for each frequency (which is possible), a strong angular imbalance remains. Thus the assumed source terms are not consistent with this type of asymptotic spectrum. In the second part of the paper we choose a different approach. We assume that the dissipation is given and perform numerical experiments simulating fetch-limited growth, to see under which conditions a stationary solution can be reached. For the dissipation we take K. Haseelmann's form with two unknown parameters. From our analysis it follows that for a certain range of values of these parameters, a quasi-equilibrium solution results. We estimate the relation between dissipation parameters and asymptotic growth rates. For equilibrium spectra, the input, dissipation and nonlinear-transfer source functions are all significant in the energy-containing range of the spectrum. The energy balance proposed by Zakharov and Filonenko in 1966 and Kitaigorodskii in 1983, in which dissipation is assumed to be significant only at high frequencies, yields a spectrum that grows too rapidly and does not approach equilibrium. One of our equilibrium solutions has a one-dimensional spectrum that lies close to the Pierson-Moskowitz spectrum. However, the angular distribution differs in some important features from standard spreading functions. The energy balance of this equilibrium spectrum is analysed in detail

Weak Turbulent Kolmogorov Spectrum for Surface Gravity Waves

We study the long-time evolution of gravity waves on deep water exited by the stochastic external force concentrated in moderately small wave numbers. We numerically implement the primitive Euler equations for the potential flow of an ideal fluid with free surface written in canonical variables, using expansion of the Hamiltonian in powers of nonlinearity of up to fourth order terms. We show that due to nonlinear interaction processes a stationary energy spectrum close to $|k| \sim k^{-7/2}$ is formed. The observed spectrum can be interpreted as a weak-turbulent Kolmogorov spectrum for a direct cascade of energy.Comment: 4 pages, 5 figure

Freak Waves in Random Oceanic Sea States

Freak waves are very large, rare events in a random ocean wave train. Here we study the numerical generation of freak waves in a random sea state characterized by the JONSWAP power spectrum. We assume, to cubic order in nonlinearity, that the wave dynamics are governed by the nonlinear Schroedinger (NLS) equation. We identify two parameters in the power spectrum that control the nonlinear dynamics: the Phillips parameter $\alpha$ and the enhancement coefficient $\gamma$. We discuss how freak waves in a random sea state are more likely to occur for large values of $\alpha$ and $\gamma$. Our results are supported by extensive numerical simulations of the NLS equation with random initial conditions. Comparison with linear simulations are also reported.Comment: 7 pages, 6 figures, to be published in Phys. Rev. Let

Freely decaying weak turbulence for sea surface gravity waves

We study numerically the generation of power laws in the framework of weak turbulence theory for surface gravity waves in deep water. Starting from a random wave field, we let the system evolve numerically according to the nonlinear Euler equations for gravity waves in infinitely deep water. In agreement with the theory of Zakharov and Filonenko, we find the formation of a power spectrum characterized by a power law of the form of $|{\bf k}|^{-2.5}$.Comment: 4 pages, 3 figure

Changes in wave climate over the northwest European shelf seas during the last 12,000 years

Because of the depth attenuation of wave orbital velocity, wave-induced bed shear stress is much more sensitive to changes in total water depth than tidal-induced bed shear stress. The ratio between wave- and tidal-induced bed shear stress in many shelf sea regions has varied considerably over the recent geological past because of combined eustatic changes in sea level and isostatic adjustment. In order to capture the high-frequency nature of wind events, a two-dimensional spectral wave model is here applied at high temporal resolution to time slices from 12 ka BP to present using paleobathymetries of the NW European shelf seas. By contrasting paleowave climates and bed shear stress distributions with present-day conditions, the model results demonstrate that, in regions of the shelf seas that remained wet continuously over the last 12,000 years, annual root-mean-square (rms) and peak wave heights increased from 12 ka BP to present. This increase in wave height was accompanied by a large reduction in the annual rms wave- induced bed shear stress, primarily caused by a reduction in the magnitude of wave orbital velocity penetrating to the bed for increasing relative sea level. In regions of the shelf seas which remained wet over the last 12,000 years, the annual mean ratio of wave- to (M-2) tidal-induced bed shear stress decreased from 1 (at 12 ka BP) to its present-day value of 0.5. Therefore compared to present- day conditions, waves had a more important contribution to large-scale sediment transport processes in the Celtic Sea and the northwestern North Sea at 12 ka BP