Wave-Breaking Features of Blocking over Central Siberia and Its Impacts on the Precipitation Trend over Southeastern Lake Baikal

Precipitation over southeastern Lake Baikal features a significant decreasing trend in July and August over 1979–2018 and is closely related to blocking occurrence over central Siberia(45°–70°N,75°–115°E).This study investigates the formation and maintenance of anticyclonic and cyclonic wave-breaking(AWB and CWB)blocking events and their climate impacts on precipitation in the southeastern Lake Baikal area.Both AWB and CWB blocking events are characterized by a cold trough deepening from the sub-Arctic region and a ridge amplifying toward its north over central Siberia,as well as an evident Rossby wave train over midlatitude Eurasia.For AWB blocking events,the ridge and trough pair tilts clockwise and the wave train exhibits a zonal distribution.In contrast,ridge and trough pair associated with CWB blocking events leans anticlockwise with larger-scale,meridional,and more anisotropic signatures.Moreover,the incoming Rossby wave energy associated with CWB blocking events is more evident than for AWB blocking events.Therefore,CWB blocking events are more persistent.AWB blocking events produce more extensive and persistent precipitation over the southeastern Lake Baikal area than CWB blocking events,in which moderate above-normal rainfall is seen in the decaying periods of blockings.A significant decreasing trend is found in terms of AWB blocking occurrence over central Siberia,which may contribute to the downward trend of precipitation over southeastern Lake Baikal.

Energy budget of surface waves in the global ocean

Mechanical energy input from atmosphere and losses from wave-breaking dissipation of sea surface waves are estimated by a direct scheme. This scheme is based on the integration in the wavenumber space of the wind input and breaking dissipation source functions of the MASNUM wave model. The global amount of wind energy input, averaged in 2005, is about 57 TW, and the wave-breaking dissipation summed in deep-water is about 33 TW, over a half of the wind energy input. The residual may be dissipated by beach processes. Global distributions of the energy input and breaking dissipation concentrate in the westerlies of the Southern Hemisphere.

Breaking of a Langmuir wave in cold electron-positron-ion plasmas

The space-time evolution of a given density perturbation in cold homogeneous electron- positron-ion plasma is investigated with an assumption of infinitely massive ions by employing a numerical calculation method. The phase-mixing time and wave-breaking time can be effectively distinguished with this method. It is found that an increase of the ratio of equilibrium ion density to equilibrium electron density can attenuate plasma oscillations, leading to a delay in wave breaking. The dependence of the phase-mixing and wave-breaking times on the amplitude of the initial perturbation is also discussed.

On the Blow-up Phenomena of Cauchy Problem for the Camassa-Holm Equation

We focus on the blow-up phenomena of Cauchy problem for the Camassa-Holm equation. Blow-up can occur only in the form of wave-breaking, i.e. the solution is bounded but its slope becomes unbounded in finite time. We proved that there is such a point that its slope becomes infinite exactly at breaking time. We also gave the precise blow-up rate and the blow-up set.