A novel method is created to detect the process of the abrupt change, which has not been mentioned yet in traditional research. By building an ideal time series with a transition process, the results show that the process could be detected clearly. When applied to a climate index, this method detects five processes, and all of them have reappeared via the “start-end states” phase diagram. Additionally, it is detectable that the persist time of the process is related to global warming.

Our conceptual model describes global temperature and vegetation extent. We use elements from Daisyworld and classical energy balance models and add an ocean with sea ice. The model exhibits oscillatory behavior within a plausible range of parameter values. Its periodic solutions have sawtooth behavior that is characteristic of relaxation oscillations, as well as suggestive of Quaternary glaciation cycles. The model is one of the simplest of its kind to produce such oscillatory behavior.

Two-dimensional numerical simulations of the shoaling of an internal solitary wave (ISW) in the South China Sea have been undertaken. Peak amplitudes are attained at depths of 250 and 600m. Horizontal resolutions of 50m are required to simulate the formation of a pedestal in shallow water behind the shoaling wave. At a depth of 200m, waves can exceed maximum ISW amplitudes by 50%. Sensitivity to the bathymetry and stratification and the effects of rotation are considered.

An analytical weakly nonlinear model of Benjamin–Feir instability of a Stokes wave on nonuniform unidirectional current is presented. In contrast to the models based on versions of the cubic Schrodinger equation the current variations could be strong, which allows us to examine the blockage of waves. Waves may overpass the blocking barrier produced by strong adverse current. We find reasonable correspondence between the results of model simulations and available experimental results.

The work aims to check one of the assumptions under which the kinetic equation for water waves was derived in order to understand whether it can be applied to situations described by the Phillips spectrum, which includes rough sea. We evaluated a spectral line width of the spectrum from the simulations in the framework of primordial dynamical equations at different levels of nonlinearity in the system, and showed that it remains narrow even for the situations described by the Phillips spectrum.

The objective of this paper is to study the dynamics of turbulence near a pycnocline, both in the free regime and under the action of an internal wave (IW) propagating along a pycnocline by direct numerical simulation (DNS). Turbulence is initially induced in a horizontal layer above the pycnocline. The DNS results show that turbulence kinetic energy (TKE) is significantly enhanced as compared to the TKE in the absence of IW, and most of the TKE is localized in the vicinity of the pycnocline.

The paper presents new analytical solutions for both the coseismic slip and the interseismic evolution of a fault with two asperities of different strengths. It enlightens the relationship between the state of the fault before a seismic event and the number and sequence of slipping modes in the event. It shows that the knowledge of the source function of a seismic event constrains the subsequent evolution of the system. The model is applied to the fault that generated the 1964 Alaska earthquake.