Grundlagen der Grenzschicht-Meteorologie: Einführung in die by Helmut Kraus

By Helmut Kraus

Den untersten Teil der Erdatmosphäre, der von der Erdoberfläche direkt beeinflusst wird, nennt guy die atmosphärische Grenzschicht. Sie gehört zur unmittelbaren Umwelt der meisten Lebewesen (Mensch, Tier, Pflanzenwelt) und erhält dadurch und durch viele ihrer eigenen Prozesse und Eigenschaften eine besondere Bedeutung. Deshalb hat sich auch ein eigenes Teilgebiet der Meteorologie, die Grenzschicht-Meteorologie, entwickelt. Dieses Buch stellt die wesentlichen Grundlagen dieser Disziplin zusammen und erläutert sie. Dabei stehen einerseits physikalische Gesetze der Hydrodynamik (z. B. der Turbulenz) und der Thermodynamik, andererseits die stark interdisziplinär ausgerichtete Mikrometeorologie bzw. Mikroklimatologie im Vordergrund des Interesses. Dieses Buch möchte Leser ansprechen, die an der Meteorologie und vor allem an der bodennahen Atmosphäre interessiert sind. Darüber hinaus wendet es sich an alle, die sich mit der Wechselwirkung zwischen Erdoberfläche und Atmosphäre auseinandersetzen, z. B. an Geographen, Bodenkundler und Pflanzenökologen.

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At a physical level, this instability can be explained by the fact that magnetic flux lines repel one another and so the gauge field Bµ acts to disrupt the vortex, whereas the effect of the Higgs field φ is to confine the vortex so as to minimize the volume in which |φ| = λ. The strengths of the two competing fields are proportional to the ranges 1/m V and 1/m H of their carrier particles, and so the gauge field wins out if m V < m H . 1 See, for example, Weinberg [Wei72, pp 362–3], where it is shown that any stress–energy tensor T µν generated as a functional derivative of an action integral is conserved, provided that the lagrangian Ä µ is invariant under general coordinate transformations.

Variation of P and Q as functions of ρ in the case b = 1 and n = 1. 64) for large ρ, where p0 , q0 , p∞ and q∞ are positive constants to be determined. Thus (recalling that ρ = m Hr ) the Higgs field falls off exponentially with a characteristic √ length scale 1/m H , while the vector field has a characteristic decay scale 1/( bm H ) ≡ 1/m V . The larger of these two length scales defines the radius of the Nielsen–Olesen vortex. 65) respectively, where X = ρ −1 s P − 12 (Q 2 − 1) and Y = ρ Q − s P Q.

In view of the cylindrical symmetry of the problem, much of the analysis that follows is simplified by converting from Minkowski coordinates x µ = [t, x, y, z] to cylindrical coordinates x µ = [t, r, θ, z]. 58) where a prime denotes d/dρ and b = 12 e2 /β 2 ≡ m 2V /m 2H is the so-called Bogomol’nyi parameter. 59) where η ≡ − det(ηµν ) is the norm of the determinant of the metric tensor. 60) where X denotes any of the field variables in the lagrangian. 61) and Q + ρ −1 Q − ρ −2 P 2 Q = 12 (Q 2 − 1)Q.

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