大地形背风波的转槽实验研究

文中利用转槽在相似定律及动力无量纲数的控制下,对旋转层结流越过大地形产生的背风波做了一系列的实验.实验及分析结果表明,无量纲数中Froude数是最重要的参数,发现在层结适当时背风波同旋涡结构在山的下风方同时出现.在无旋转情况下,在Froude数适当时仍然存在着明显的背风波,但旋转的作用能增加背风波的波动幅度,特别是起着引发下坡流的作用.文中最后还讨论了背风波在季风区内对低层涡旋发展的驱动作用及有待进一步研究的问题.     

A nonlinear dynamo driven by rapidly rotating convection

In Kim et al. (Kim, E., Hughes, D.W. and Soward, A.M., “An investigation into high conductivity dynamo action driven by rotating convection”, Geophys. Astrophys. Fluid Dynam. 91, 303–332 ().) we investigated kinematic dynamo action driven by rapidly rotating convection in a cylindrical annulus. Here we extend this work to consider self-consistent nonlinear dynamo action in which the back-reaction of the Lorentz force on the flow is taken into account. In particular, we investigate, as a function of magnetic Prandtl number, the evolution of an initially weak magnetic field in two different types of convective flow – one chaotic and the other integrable. On saturation, the latter shows a systematic dependence on the magnetic Prandtl number whereas the former appears not to. In addition, we show how, in keeping with the findings of Cattaneo et al. (Cattaneo, F., Hughes, D.W. and Kim, E., “Suppression of chaos in a simplified nonlinear dynamo model”, Phys. Rev. Lett. 76, 2057–2060 ().), saturation of the growth of the magnetic field is brought about, for the originally chaotic flow, by a strong suppression of chaos.     

Rotating channel flow: Control and upstream currents

Abstract

Theory and experiments are presented for critically controlled flow of a layer of inviscid rotating fluid. Flow is controlled by a level passage. For a wide upstream channel of fixed depth (i.e. constant potential vorticity) the volume flux on the right-hand wall is unaffected by passage flow. This suggests that specifying Bernoulli potential on the right-hand passage wall produces a physically well-posed condition. The specification results in one less dimensionless number than was required by previous formulations to specify flow in the controlled passage. The upstream flow needs the same number as before, so that a range of upstream conditions produce exactly the same passage flow. A laboratory study is conducted using a thin layer of water under air. This is pumped in steadily at various locations in a deep rotating upstream basin, with fluid leaving through a level passage. All currents in the upstream basin cross to the left-hand wall as the current approaches the passage over a sloping bottom. The current crosses back to the right-hand wall within the passage. Velocity profiles of currents agree reasonably well with constant potential vorticity theory. To the right of the detached upstream current is a closed gyre that connects the upstream flows (that have different patterns depending on source location) with the unique passage flows. The results suggest that gyres upstream of critically controlling passages in the ocean might serve as adjustment regions between the relatively unconstrained upstream flows and the tightly controlled passage flows.     

Vortical and wave modes in 3D rotating stratified flows: random large-scale forcing

Utilizing an eigenfunction decomposition, we study the growth and spectra of energy in the vortical (geostrophic) and wave (ageostrophic) modes of a three-dimensional (3D) rotating stratified fluid as a function of ε = f/N, where f is the Coriolis parameter and N is the Brunt–Vaisala frequency. Throughout, we employ a random large-scale forcing in a unit aspect ratio domain and set these parameters such that the Froude and Rossby numbers are roughly comparable and much less than unity. Working in regimes characterized by moderate Burger numbers, i.e. Bu = 1/ε² < 1 or Bu ≥ 1, our results indicate profound change in the character of vortical and wave mode interactions with respect to Bu = 1. Indeed, previous analytical work concerning the qualitatively different nature of these interactions has been in limiting conditions of rotation or stratification domination (i.e. when Bu ? 1 or Bu ? 1, respectively). As with the reference state of ε = 1, for ε < 1 the wave mode energy saturates quite quickly and the ensuing forward cascade continues to act as an efficient means of dissipating ageostrophic energy. Further, these saturated spectra steepen as ε decreases: we see a shift from k ^?1 to k ^?5/3 scaling for k _f < k < k _d (where k _f and k _d are the forcing and dissipation scales, respectively). On the other hand, when ε > 1 the wave mode energy never saturates and comes to dominate the total energy in the system. In fact, in a sense the wave modes behave in an asymmetric manner about ε = 1. With regard to the vortical modes, for ε ≤ 1, the signatures of 3D quasigeostrophy are clearly evident. Specifically, we see a k ^?3 scaling for k _f < k < k _d and, in accord with an inverse transfer of energy, the vortical mode energy never saturates but rather increases for all k < k _f . In contrast, for ε > 1 and increasing, the vortical modes contain a progressively smaller fraction of the total energy indicating that the 3D quasigeostrophic subsystem, though always present, plays an energetically smaller role in the overall dynamics. Combining the vortical and wave modes, the total energy for k > k _f and ε ≤ 1 shows a transition as k increases wherein the vortical modes contain a large portion of the energy at large scales, while the wave modes dominate at smaller scales. There is no such transition when ε > 1 and the wave modes dominate the total energy for all k > k _f .     

Interactions of isolated vortices I: Modons colliding with modons

Abstract

Collisions between isolated(i.e. localized) dipolar vortex states, called modons, are examined in various numerical solutions of the quasigeostrophic, equivalent barotropic equation. For a range of parameters, the collision interactions are soliton-like in that the vorticity maxima are displaced (phase-shifted) with only small speed changes and little excitation of internal degrees of freedom. For other parameters, new “inelastic” effects are observed, including speed changes due to vorticity rearrangement, vorticity filamentation, modon “capture” or “fusion” in an overtaking collision, and the “fission” of a modon into its component vorticity monopoles in a head-on collision.     

The role of the helicity spectrum function in turbulent dynamo theory

Abstract

It is shown that, for general homogeneous turbulence, the anti-symmetric part of the spectrum tensor can be expressed in terms of a single scalar function H(k,ω) (the helicity spectrum function). Under the first-order smoothing approximation, the coefficients α _ij β _ijk in the expansion of the mean electromotive force in terms of the mean magnetic field are determined; α _ij is a weighted integral of H(k,ω), and β _ijk contains a part β(a)ijk which is likewise a weighted integral of H(k, ω). When the turbulence is axisymmetric, β(a)ijk contains Rädler's (1969a) “Ω ∧ J-effect”. It is shown that when the turbulence is statistically symmetric about a plane perpendicular to the axis of symmetry, then βij = O but the Rädler effect is non-zero. Explicit expressions for αij and βijk are given when the velocity field is generated by random forcing in a rotating medium. Finally, it is shown by means of a local analysis that the Rädler effect, in conjunction with uniform mean shear, can give rise to non-oscillatory dynamo action, and it is argued that this effect may be significant in the well-mixed interior of a stellar convection zone, where by symmetry the α-effect may be weak.     

The structure of separated flow past a circular cylinder in a rotating frame

Abstract

This paper examines the detailed E ^1/4-layer structure of separated flow past a circular cylinder in a low-Rossby-number rotating fluid as the Ekman number E tends to zero. This structure is based on an initial proposal by Page (1987) but with some modifications in response to further evidence, outlined both in this paper and elsewhere, on the behaviour of E ^1/4-layer flows in this context. Numerical calculations for flow in an E ^1/4 shear layer along the separated free streamline are described and the mass flux from this layer is then used to calculate the higher-order flow within the separation bubble. The flow structure is found to have two forms, depending on the value of the O(1) parameter λ, and these are compared with results from published “Navier-Stokes” type calculations for the flow at small but finite values of E.     

Quasi-free-decay magnetic modes in planetary cores

A new category of hydromagnetic waves in a rotating conducting fluid within a spherical shell geometry is investigated. These quasi-free-decay magnetic modes are based on particular solutions of the induction equation where the magnetic diffusion plays the central role. These solutions, normally only decaying with time, become propagative owing to the combined action of the background magnetic field and the rotation. The amplitude and sign of their azimuthal phase drift strongly depend on morphology and magnitude of the background magnetic field. The validity domain of these quasi-free-decay (QFD)-modes is related to the Elsasser number and is written as Λ???1. It follows that these modes dissipate quickly before propagating out. This restriction falls when the above criterion is no longer fulfilled (Λ?～?1), the corresponding modes evolving towards distorted QFD-modes. A systematic study of these QFD-modes is made in the limit of small Elsasser number (Λ???1), for the different symmetries allowed. Application to the Earth's and other planetary cores is then examined for an Elsasser number up to Λ?≈?O(1), in relation to the geomagnetic secular variation and the frozen-flux approximation.     

北半球东半部对流层夏季平均环流形成物理机制的流体模拟实验

在旋转流体盘中做物理实验 ,模拟研究北半球东半部对流层夏季平均大气环流的形成物理机制。用镍铬电阻丝通电加热实验盘底作为热源 ,用冷水循环的铜管对实验盘底制冷作为冷源。将热源及冷源分布在绘有北半球极赤射面投影地图的底面上。人工地制造出中高纬西风带及越赤道气流模型。用流体物理模拟实验方法研究北半球东半部对流层夏季平均大气环流物理机制。逐个地试验了海陆温差、青藏高原地形及其高空热源、中高纬西风带 ,及来自南半球的越赤道气流的作用