论简化Navier-Stokes方程组(SNSE)

本文论述简化 Navier-Stokes 方程组(SNSE),利用十种 SNSE分析Jeffery-Hamel流动并简要分析已知完全 Navier-Stokes 方程组(CNSE)精确解的八类流动。表明:不同SNSE结果之间的实际差异能够大大超出O(Re~(-1/2))量级的理论误差范围,甚至给出不同的流动图案。因此,SNSE 的粘性项如何取舍值得重视。内外层匹配SNSE和薄层二阶SNSE的解在八类流动情况下均与CNSE的精确解完全一致;而所有其它SNSE 的解则与CNSE的精确解不完全一致,它们的解在不少情况下实际就是经典边界层理论的解。内外层匹配SNSE包含了法向轴相对流向轴剪切的剪应力项和法向轴伸缩的法应力项以及与该法应力项同量级的粘性项,且对惯性项和粘性-惯性项相互关系的处理较合理,故在力学上和数学上都比较可取。

Simplified Navier-Stokes equations (SNSE)

Ten kinds of the simplified Navier-Stokes equations (SNSE) are reviewed and also used to calculate the Jeffery-Hamel flow as well as to analyze briefly the seven kinds of flows to which the exact solutions of the complete Navier-Stokes equations (CNSE) have been found. Analysis shows that the actual differences among the solutions of the different SNSE can go beyond the range of the order of magnitude of Re-1/2 and result even in different flow patterns, therefore, how to choose the viscous terms included in the SNSE is worthy of notice where Re=S∞u∞ L/μ∞ is the Reynolds numbers. For the aforesaid eight kinds of flows, the solutions to the inner-outer-layer-matched SNSE and to the thin-layer-2-order SNSE agree completely with the exact solutions to CNSE. But the solutions to all the other SNSE are not completely consistent with the exact solutions to CNSE and not a few of them are actually the solutions of the classical boundary layer theory. The innerouter-layer-matched SNSE contains the shear stress causing angular displacement of the inormal axis with respect to the streamwise axis and the normal stress causing expansion-contraction in the direction of the normal axis and the viscous terms being of the order of magnitude of the normal stress; and it can also reasonably treat the inertial terms as well as the relation between the viscous and inertial terms. Therefore, it seems promising in respects of both mechanics and mathematics.

Molecular phylogeography and population structure of a mid-elevation montane frog Leptobrachium ailaonicum in a fragmented habitat of southwest China

Leptobrachium ailaonicum is a vulnerable anuran restricted to a patchy distribution associated with small mountain streams surrounded by forested slopes at mid-elevations (approximately 2000-2600 m) in the subtropical Mount Wuliang and Mount Ailao ranges in southwest China (Yunnan Province) and northern Vietnam. Given high habitat specificity and lack of suitable habitat in lower elevations between these ranges, we hypothesized limited gene flow between populations throughout its range. We used two mitochondrial genes to construct a phylogeographic pattern within this species in order to test our hypothesis. We also examined whether this phylogeographic pattern is a response to past geological events and/or climatic oscillations. A total of 1989 base pairs were obtained from 81 individuals of nine populations yielding 51 unique haplotypes. Both Bayesian and maximum parsimony phylogenetic analyses revealed four deeply divergent and reciprocally monophyletic mtDNA lineages that approximately correspond to four geographical regions separated by deep river valleys. These results suggest a long history of allopatric separation by vicariance. The distinct geographic distributions of four major clades and the estimated divergence time suggest spatial and temporal separations that coincide with climatic and paleogeographic changes following the orogeny and uplift of Mount Ailao during the late Miocene to mid Pliocene in southwest China. At the southern distribution, the presence of two sympatric yet differentiated clades in two areas are interpreted as a result of secondary contact between previously allopatric populations during cooler Pleistocene glacial cycles. Analysis of molecular variance indicates that most of the observed genetic variation occurs among the four regions implying long-term interruption of maternal gene flow, suggesting that L ailaonicum may represent more than one distinct species and should at least be separated into four management units corresponding to these four geographic lineages for conservation. (C) 2009 Elsevier Inc. All rights reserved.