Tian Ji-wei

Study of long-wave breaking

This paper reports study on the mechanism of long-wave breaking in a one-dimensional open channel, without bottom friction, or with linear bottom friction. In general, the wave breaking phenomenon is related to the notion of “blow-up of solution” and can be studied by using the blow-up theory of partial differential equations (PDE). A pair of Riemann invariants are introduced to transform the governing equations into ordinary differential equations (ODE) along the characteristic directions of the governing equations. From the properties of the solutions of the ODE, the time and location of wave breaking are estimated and the criterion of long-wave breaking for the case with linear bottom friction is obtained.

New method to obtain the power spectra of hidden variables and its application to ocean data

A novel method is proposed to obtain the power spectra of hidden variables in a chaotic time series. By embedding the data in phase space, and recording the conditional probability density of points that the trajectory encounters as it evolves in the reconstructed phase space, it is possible to recover the power spectra of hidden variables in chaotic time series through a spectral analysis over the conditional probability density time series. The method is robust in the application to Lorenz system, 4-dimension Rössler system and rigid body motion by linear feedback system (LFRBM). Applying the method to the time series of sea surface temperature (SST) of the South China Sea, we obtained the power spectra of the wind speed (WS) from SST data. Furthermore, the results showed that there exists an important nonlinear interaction between the SST and the WS.

Quadratic correction to the linear wave spectrum of two-dimensional random waves

A perturbation expansion methods first three order solutions of two-dimensional random gravity waves in finite uniform depth were used as bases to derive the quadratic correction to the linear wave spectrum (i.e., the quadratic spectrum). For infinite water depth, the expression of the quadratic spectrum given in this paper is much simpler than that of Sclavounos (1992) and Olemz and Milgram (1995).

Calculations of wave breaking probability and distribution of breaking wave heights in deep water

This practical method for calculating the probability of a wave breaking and the distribution of breaking wave heights is based on the joint probability distribution of wave heights and periods derived by Sun Fu and the breaking criterion obtained by Ochi and Tsai from measurements of irregular waves generated in a tank. Computations for different sea states using the P-M spectrum and the JONSWAP spectrum showed that the probability of wave breaking (or the distribution of breaking wave heights) in the deep ocean can be determined, at least approximated, from the zero, the first and the second moments of the wave spectrum.

On long-wave breaking IV. Numerical results

This paper is a sequel to Tians (1994) preceding paper in which the blow-up theory was suggested for finding an analytical (as opposed to a numerical) description of long-wave breaking. The present long-wave breaking numerical results agree quite well with the authors previous analytical and theoretical results.

NLS equation of internal waves in weakly stratified ocean

The NLS (Non-Linear Schrödinger) equation of internal waves in a weakly stratified ocean is derived in phase coordinates in terms of the RPM (Reductive Perturbation Method). It was shown that whenAB>0 there exist modulation forms of envelope soliton anddn, and that whenAB<0 there are three modulation forms: dark soliton,sn andcn Only if {ie121-1} the side-band perturbation, is stable, otherwise unstable. For the stable side-band perturbation there exists a modulation form ofKdV soliton.

ON LONG-WAVES BREAKING II.IN A HALF INFINITE CHANNEL WITH BOTTOM SLOPE

The propagation of long-waves, such as tidal waves from the coastal ocean into shallow estuarine waters, often produces asymmetries of velocity and water level in time series resulting in long-wave breaking. Tian (1994) studied the mechanism of long-wave breaking in an infinite channel with constant depth, consideringnth power bottom friction. This study is for the case of a half infinite channel with bottom slope, taking linear bottom friction into account. The wave breaking time and wave breaking location are estimated and the criteria for long-wave breaking in this particular case are obtained. The results obtained can also be easily applied to the case considering wind stress.

On long-wave breaking I. Consideringnth power bottom friction

Longwave breaking is the agent for many important upper ocean layer processes including the transfer of horizontal momentum. In a previous study on the process of longwave breaking, only linear bottom friction was considered. In this paper, we discuss the longwave breaking phenomena in the more general case ofnth power bottom friction. Using the theory of blowup of solution, the criterion for the time and location of the longwave breaking can be obtained.

CHARACTER OF SIMPLIFIED NAVIER-STOKES EQUATIONS FOR NEAR THE LEADING EDGE PART OF TWO-DIMENSIONAL LAMINAR FLOW PAST A FLAT PLATE*

Starting from the Simplified Navier-Stokes(SNS) equations presented at first by Godovachev-Kuzmin-Tsopov, and Gao Zhi, Davis, the authors analyze the character of the SNS equations for the laminar flow near the leading edge of a flat plate and far away from the plate by using the Weiner-Hopf method and Fourier transform. It is proved that the solution of the SNS equations agree with the solution of the Navier-Stokes equations for flow near the leading edge of the plate and far away from the plate. How to match the solution of the SNS equations to the Blasius solution of the boundary layer equations is also discussed.