On the Evolution of Finite-amplitude Disturbance to the Barotropic and Baroclinic Quasigeostrophic Flows

Some new results on the evolution of finite-amplitude disturbances to the nonlinearly stable and unstable quasigeostrophic flows are presented. Both barotropic and multilayer baroclinic problems are investigated. The upper (lower) bounds on the energy and potential enstrophy of disturbances to the nonlinearly stable(unstable) basic flows are established.

Finite-amplitude vibration of a bubble in water

The numerical results obtained by Rayleigh-Plesset （R-P） equation failed to agree with the experimental Mie scattering data of a bubble in water without inappropriately increasing the shear viscosity and decreasing the surface tension coefficient. In this paper, a new equation proposed by the present authors （Qian and Xiao） is solved. Numerical solutions obtained by using the symbolic computation program from both the R-P equation and the Qian-Xiao （Q-X） equation clearly demonstrate that Q-X equation yields best results matching the experimental data （in expansion phase）. The numerical solutions of R-P equation also demonstrate the oscillation of a bubble in water depends strongly upon the surface tension and the shear viscosity coefficients as well as the amplitude of driving pressure, so that the uniqueness of the numerical solutions may be suspected if they are varied arbitrarily in order to fit the experimental data. If the bubble＇s vibration accompanies an energy loss such as the light radiation during the contract phase, the mechanism of the energy loss has to be taken into account. We suggest that by use of the bubble＇s vibration to investigate the state equations of aqueous solutions seem to be possible. We also believe that if one uses this equation instead of R-P equation to deal with the relevant problems such as the ＇phase diagrams for sonoluminescing bubbles＇, etc., some different results may be expected.

Experimental investigation on finite-amplitude standingwaves:Ⅰ. The properties of second harmonic

Experimental investigations on one dimensional finite-amplitude standing wave field were carried out comprehensively. The measurement system of experiment is presented. In this instalment, the properties of the second harmonics are discussed in particular. Experimental results show that: the harmonics produced in the standing wave at finite-amplituds will be resonance when their frequency happens to agree to one of the resonance frequcecies of the tube whether the driving frequency is in resonance or not. This is shown by the curve of the sound pressure level of the second harmonic (SPL2) as a function of driving frequency when the sound pressure level of the fundamental (SPL1) is kept at a constant. This curve can be approximated by a harmonic function. This phenomenon is accounted for MAA's extended theory and numerical values are compared at the frequencies where the second harmonic is at minima.

Theory of finite-amplitude standing waves

A new approach to the theory of finite-amplitude standing waves in proposed, and foumulas of steady wave forms are derived from the fundamental equations of hydrodynamios, as an endeavor to settle the long-time disputable situation.

A generic approach to the dynamical interpretation of ocean-atmosphere processes

This paper summarizes the recent development of a portable self-contained system to unravel the intricate multiscale dynamical processes from real oceanic flows, which are in nature highly nonlinear and intermittent in space and time. Of particular focus are the interactions among largescale, mesoscale, and submesoscale processes.We firsu introduce the concept of scale window, and an orthogonal subspace decomposition technigue called multiscale window transform (MWT). Established on MWT is a rigorous formalism of multiscale transport, perfect transfer, and multiscale conversion, which makes a new methodology, multiscale energy and vorticity analysis (MS-EVA). A direct application of the MS-EVA is the development of a novel localized instability analysis, generalizing the classical notion of hydrodynamic instability to finite amplitude processes on irregularly variable domains. The theory is consistent with the analytical solutions of Eady's model and Kuo's model, the benchmark models of baroclinic instability and barotropic instability; it is further validated with a vortex shedding control problem. We have put it to application with a variety of complicated real ocean problems, which would be otherwise very difficult, if not impossible, to tackle. Briefly shown in this paper include the dynamical studies of a highly variable open ocean front, and a complex coastal ocean circulation. In the former, it is found that underlying the frontal meandering is a convective instability followed by an absolute instability, and correspondingly a rapid spatially amplifying mode locked into a temporally growing mode; in the latter, we see a real ocean example of how upwelling can be driven by winds through nonlinear instability, and how winds may excite the ocean via an avenue which is distinctly different from the classical paradigms. This system is mathematically rigorous, physically robust, and practically straightforward.

AGEOSTROPHIC THEORY OF ZONAL FLOW ACCELERATION AND WAVE-ACTIVITY CONSERVATION LAW

Motivated by ageostrophic interactions of wave and basic flow,the generalized relationships between 3-dimensional Eliassen-Palm flux and basic flows,which are suitable for small-amplitude and finite-amplitude disturbances,are derived.The local area-averaged and density-weighted mean flows are chosen as the basic flows.Under the assumption that the steady basic flows vary slowly in time and space,a quasi-conservative law of small amplitude wave activity is derived from Ertel's potential vorticity equation in isentropic coordinates. The expressions of the new 3-D Eliassen-Palm flux and wave activity are presented in terms of Eulerian quantities so that they can be readily calculated by using observation data or model output data.