The form of the asymptotic depth-limited wind-wave spectrum: Part III — Directional spreading

The directional spreading of both the wavenumber and frequency spectra of finite-depth wind generated waves at the asymptotic depth limit are examined. The analysis uses the Wavelet Directional Method, removing the need to assume a form for the dispersion relationship. The paper shows that both the wavenumber and frequency forms are narrowest at the spectral peak and broaden at wavenumbers (frequencies) both above and below the peak. The directional spreading of the wavenumber spectrum is bi-modal above the spectral peak. In contrast, the frequency spectrum is uni-modal. This difference is shown to be the result of energy in the wind direction being displaced from the linear dispersion shell. A full parametric relationship for the directional spreading of the wavenumber spectrum is developed. The analysis clearly shows that typical dispersion relationships are questionable at high frequencies and that such effects can be significant. This result supports greater attention being focussed on the routine recording of wavenumber spectra, rather than frequency spectra.     

Some statistical characteristics of large deepwater waves around the Korean Peninsula

The relationship between significant wave height and period, the variability of significant wave period, the spectral peak enhancement factor, and the directional spreading parameter of large deepwater waves around the Korean Peninsula have been investigated using various sources of wave measurement and hindcasting data. For very large waves comparable to design waves, it is recommended to use the average value of the empirical formulas proposed by Shore Protection Manual in 1977 and by Goda in 2003 for the relationship between significant wave height and period. The standard deviation of significant wave periods non-dimensionalized with respect to the mean value for a certain significant wave height varies between 0.04 and 0.21 with a typical value of 0.1 depending upon different regions and different ranges of significant wave heights. The probability density function of the peak enhancement factor is expressed as a lognormal distribution, with its mean value of 2.14, which is somewhat smaller than the value in the North Sea. For relatively large waves, the probability density function of the directional spreading parameter at peak frequency is also expressed as a lognormal distribution.     

Second-Oorder Analytic Solutions of Nonlinear Interactions of Edge Waves on A Plane Sloping Bottom

Based on the full water-wave equation, a second-order analytic solution for nonlinear interaction of short edge waves on a constant plane sloping bottom is presented in this paper. For special case of slope angle b=p/2, this solution can be reduced to the same order solution of deep water gravity surface waves traveling along parallel coastline. Interactions between two edge waves including progressive, standing and partially reflected standing waves were also discussed. The unified analytic expressions with transfer functions for kinematic-dynamic elements of edge waves were also discussed. The random model of the unified wave motion processes for linear and nonlinear irregular edge waves is formulated, and the corresponding theoretical autocorrelation and spectral density functions of the first and second orders are derived. The boundary conditions for the determining determination of the parameters of short edge wave are suggested, that may be seen as one special simple edge wave excitation mechanism and an extension to the sea wave refraction theory. Finally some computation results are demonstrated.     

短脉冲激光在实验室天体物理方面的研究进展

随着啁啾脉冲放大技术(Chirped Pulse Amplification,CPA)的飞速发展,激光功率密度实现了飞跃式的提升,利用短脉冲激光开展实验室天体物理研究的条件日趋成熟.短脉冲激光与靶相互作用可以产生相对论粒子(正负电子、质子、中子等)和高能电磁辐射(X射线、γ射线),这些粒子和辐射的产生过程与天体中的某些...     

On the stability of stratified plane couette flow

Abstract

Unbounded stratified plane Couette flow is shown to be stable against small amplitude disturbances. The Brunt-Väisälä frequency is assumed to be constant. Both viscosity and thermal diffusion are included, and shown to be stabilizing.     

Non linear waves in two dimensional keplerian flows

Abstract

Accretion discs in astrophysics are fundamental for converting gravitational binding energy into observed electromagnetic radiation. We study the behavior of waves in a two dimensional supersonic Keplerian flow inside a given gravitational potential. We present the effects of shearing and rotation on short waves, and the numerical study of the dynamical stability of such flows with respect to various perturbations. We show that a large class of dynamical effects, due to pressure and associated to short time scales, may be excited.     

Finite-amplitude mountain waves in a compressible atmosphere including the effects of dissipation

Abstract

Adiabatic, two-dimensional, steady-state finite-amplitude, hydrostatic gravity waves produced by flow over a ridge are considered. Nonlinear self advection steepens the wave until the streamlines attain a vertical slope at a critical height z_c. The height z_c , where this occurs, depends on the ridge crest height and adiabatic expansion of the atmosphere. Dissipation is introduced in order to balance nonlinear self advection, and to maintain a marginal state above z_c. The approach is to assume that the wave is inviscid except in a thin layer, small compared to a vertical wavelength, where dissipation cannot be neglected. The solutions in each region are matched to obtain a continuous solution for the streamline displacement δ. Solutions are presented for different values of the nondimensional dissipation parameter β. Eddy viscosity coefficients and the thickness of the dissipative layer are expressed as functions of β, and their magnitudes are compared to other theoretical evaluations and to values inferred from radar measurements of the stratosphere.

The Fourier spectrum of the solution for z ≫ z_c is shown to decay exponentially at large vertical wave numbers n. In comparison, a spectral decay law n ^?-8/3 characterizes the marginal state of the wave at z = z_c .     

Planetons: An example of large amplitude solitary waves

Abstract

The term ‘‘solitary wave'’ is usually used to denote a steadily propagating permanent form solution of a nonlinear wave equation, with the permanency arising from a balance between steepening and dispersive tendencies. It is known that large-scale thermal anomalies in the ocean are subject to a steepening mechanism driven by the beta effect, while at the smaller deformation scale, such phenomena are highly dispersive. It is shown here that the evolution of a physical system subject to both effects is governed by the ‘‘frontal semi-geostrophic equation'’ (FSGE), which is valid for large amplitude thermocline disturbances. Solitary wave solutions of the FSGE (here named planetons) are calculated and their properties are described with a view towards examining the behavior of finite amplitude solitary waves. In contrast, most known solitary wave solutions belong to weakly nonlinear wave equations (e.g., the Korteweg—deVries (KdV) equation).

The FSGE is shown to reduce to the KdV equation at small amplitudes. Classical sech² solitons thus represent a limiting class of solutions to the FSGE. The primary new effect on planetons at finite amplitudes is nonlinear dispersion. It is argued that due to this effect the propagation rates of finite amplitude planetons differ significantly from the ‘‘weak planeton'', or KdV, dispersion relation. Planeton structure is found to be simple and reminiscent of KdV solitons. Numerical evidence is presented which suggests that collisions between finite amplitude solitary waves are weakly inelastic, indicating the loss of true soliton behavior of the FSGE at moderate amplitudes. Lastly, the sensitivity of solitary waves to the existence of a nontrivial far field is demonstrated and the role of this analysis in the interpretation of lab experiments and the evolution of the thermocline is discussed.     

Topographic instability and multiple equilibria on an f-plane

Abstract

The flow of a two-layer flow in a rotating channel on an f-plane over topography with sinusoidal variation of height in a direction parallel to the flow is investigated. When the two layers flow in opposite directions a resonance is found when the topographic scale matches the free mode of the system. We examine the stability of the forced mode in the vicinity of this resonance by means of a perturbation expansion of the topographic height. Both subresonant and super-resonant instabilities are found and their equilibration is examined. For small values of the dissipation multiple equilibria are found. The topographic drag releases potential energy even when the flow is baroclinically stable.