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.     

中国近海海面地形的计算与研究

介绍了海面地形的研究现状,并根据几何水准求得了中国近海的海平面倾斜及其精度.给出应用水文资料计算中国近海海面地形的公式及其计算结果.探讨了由球函数模型计算中国近海海面地形的理论和方法,并对不同方法进行了比较,得出了一些有益的结论.     

Simulation of flow over pool-riffle topography: A consideration of the velocity reversal hypothesis

Computer flow simulations using the HEC-2 step-backwater routine are used to demonstrate the effect of systematically varying river channel width, riffle spacing and channel roughness on the shear velocity, section-mean velocity and energy slope in fixed-bed pool-riffle sequences. Initial scaling is obtained by utilizing published information on hydraulic parameters within reaches of the River Severn. Subsequently this restriction is relaxed and the effect of varying parameter combinations within realistic limits is explored. The purpose of this exercise is to isolate those scenarios which may preclude or promote the occurrence of a competence ‘reversal’, such that pools scour at high flow whilst deposition occurs on riffles. It is concluded that rivers in which pools are hydraulically rougher than riffles are likely to demonstrate a competence reversal. For prescribed conditions, the critical discharge at which a reversal occurs is a negative function of riffle spacing and riffle width relative to pool width. Downstream variation in hydraulic roughness also has implications for the phase relationship of shear velocity maxima and minima in relation to the extremes in pool-riffle topography.     

Late Quaternary kinematics of the Pallatanga strike-slip fault (Central Ecuador) from topographic measurements of displaced morphological features

The northeast-trending Pallatanga right-lateral strike-slip fault runs across the Western Cordillera connecting N50E-N70E trending normal faults in the Gulf of Guayaquil with N-S reverse faults in the Interandean Depression. Over most of its length, the fault trace has been partly obscured by erosional processes and can be inferred in the topography only at the large scale. Only the northern fault segment, which follows the upper Rio Pangor valley at elevations above 3600 m, is prominent in the morphology. Valleys and ridges cut and offset by the fault provide an outstanding record of right-lateral cumulative fault displacement. The fault geometry and kinematics of this particular fault segment can be determined from detailed topographic levellings. The fault strikes N30E and dips 75 to the NW. Depending on their size and nature, transverse morphological features such as tributaries of the Rio Pangor and intervening ridges, reveal right-lateral offsets which cluster around 27 ± 11m, 41.5 ± 4 m, 590 ± 65 m and 960 ± 70 m. The slip vector deduced from the short-term offsets shows a slight reverse component with a pitch of about 11.5 SW. The 41.5 ± 4 m displacements are assumed to be coeval with the last glacial termination, yielding a mean Holocene slip-rate of 2.9- 4.6 mm yr⁻¹. Assuming a uniform slip rate on the fault in the long term, the 27 m offset appears to correlate with an identified middle Holocene morphoclimatic event, and the long term offsets of 590 m and 960 m coincide with the glacial terminations at the beginning of the last two interglacial periods.     

EFFECTS OF THE ENVELOPE DEGREE OF OROGRAPHY ON THE SIMULATED CLIMATE PROPERTIES

A primitive equation model with a zonal domain and a p-σ incorporated vertical coordinate systemis used to study the effects of the envelope degree of orography on the simulated properties of bothwinter and summer climates.Results show that the orography with a larger envelope degree can im-prove the simulations to certain extent,especially in winter.It is found that the simulated propertiesof climate are mainly determined by the co-effects of the land-sea and the orographic distributions,and the envelope degree of orography has a secondary effect.However it should be taken properly inorder to improve simulations:otherwise,it would be harmful.Different envelope degrees of orogra-phy can be adopted in different areas.     

EFFECTS OF TOPOGRAPHY ON PROPAGATION AND DEVELOPMENT OF INERTIA GRAVITY WAVE

Effects of topography on the propagation and development of inertia gravity waves areinvestigated by means of WKBJ method.The equation of wave action conservation is obtained.It isfound that the inertia gravity wave tends to propagate to the higher elevation area,meanwhile theamplitudes of the waves increase.While the inertia gravity waves propagate to a lower elevation area,their amplitudes decrease.     

考虑β随纬度变化下的Rossby孤立波与偶极子阻塞

利用文献[4]得到的推广的β平面近似式为f=f0+β0 y—（δ0/2）y2,研究由δ0项所引起的一类Rossby孤立波，而不考虑基流切变和地形等因子的作用。经过计算可以发现，当经向波数为1时，这种孤立波具有显著的南低北高的偶极子阻塞结构，它主要存在于弱西风气流中，并且偶极子的能量随着纬度的增高更容易集中(即高纬偶极子结构趋于局地化)，因而，β随纬度的变化可能是中高纬度地区偶极子阻塞产生的原因之一。