Mode coupling analysis and differential rotation in a flow driven by a precessing cylindrical container

We present a theoretical weakly nonlinear analysis of the dynamics of an inviscid flow submitted to both rotation and precession of an unbounded cylindrical container, by considering the coupling of two Kelvin (inertial) waves. The parametric centrifugal instability known for this system is shown to saturate when one expands the Navier–Stokes equation to higher order in the assumed small precession parameter (ratio of precession to rotation frequencies) with the derivation of two coupled Landau equations suitable to describe the dynamics of the modes. It is shown that an azimuthal mean flow with differential rotation is generated by this modes coupling. The time evolution of the associated dynamical system is studied. These theoretical results can be compared with water experiments and also to some numerical simulations where viscosity and finite length effects cannot be neglected.     

A Note on Standing Internal Inertial Gravity Waves of Finite Amplitude

The effects of finite amplitude are examined in two-dimensional, standing, internal gravity waves in a rectangular container which rotates about a vertical axis at frequency f/ 2. Expressions are given for the velocity components, density fluctuations and isopycnal displacements to second order in the wave steepness in fluids with buoyancy frequency, N , of general form, and the effect of finite amplitude on wave frequency is given in an expansion to third order. The first order solutions, and the solutions to second order in the absence of rotation, are shown to conserve energy during a wave cycle. Analytical solutions are found to second order for the first two modes in a deep fluid with N proportional to sech( az ), where z is the upward vertical coordinate and a is scaling factor. In the absence of rotation, results for the first mode in the latter stratification are found to be consistent with those for interfacial waves. An analytical solution to fourth order in a fluid with constant N is given and used to examine the effects of rotation on the development of static instability or of conditions in which shear instability may occur. As in progressive internal waves, an effect of rotation is to enhance the possibility of shear instability for waves with frequencies close to f . The analysis points to a significant difference between the dynamics of standing waves in containers of limited size and progressive internal waves in an unlimited fluid; the effect of boundaries on standing waves may inhibit the onset of instability. A possible application of the analysis is to transverse oscillations in long, narrow, steep-sided lakes such as Loch Ness, Scotland.     

Convection in rotating annular channels heated from below. Part 2. Transitions from steady flow to turbulence

We report the results of fully three-dimensional numerical simulations of nonlinear convection in a Boussinesq fluid in an annular channel rotating about a vertical axis with lateral no-slip or stress-free sidewalls, stress-free top and bottom, uniformly heated from below, a problem first studied by Davies-Jones and Gilman (1971 Davies-Jones, RP and Gilman, PA. 1971. Convection in a rotating annulus uniformly heated from below.. J. Fluid Mech., 46: 65–81.  [Google Scholar]) and Gilman (1973 Gilman, PA. 1973. Convection in a rotating annulus uniformly heated from below. Part 2. Nonlinear results. J. Fluid Mech., 57: 381–400.  [Google Scholar]). A substantial range of the Rayleigh number R (R_c≤R≤O(100 R_c)), where R_c denotes the critical value at the onset of convection) is considered. It is found that the wall-localized convection mode, unaffected by the velocity boundary condition imposed on the sidewalls, is nonlinearly robust. Both directions of travelling waves, one propagating against the sense of rotation near the outer sidewall and the other propagating in the same sense as the rotation in the vicinity of the inner sidewall, are always present in the nonlinear solutions. In contrast to nonlinear convection in a rotating Bénard layer, neither convection rolls nor the Küpper–Lortz instability can exist in a rotating annular channel because of the effect of the sidewalls. It is the nonlinear interaction between the wall-localized modes and the internal mode that plays an essential role in determining the nonlinear properties of convection in a rotating annular channel. Our studies reveal systematically the various nonlinear phenomena, from steady travelling waves trapped in the vicinities of the sidewalls to convective turbulence exhibiting columnar structure.     

Instability of flows near the onset of convection in a rotating layer with stress-free horizontal boundaries

We investigate instability of convective flows of simple structure (rolls, standing and travelling waves) in a rotating layer with stress-free horizontal boundaries near the onset of convection. We show that the flows are always unstable to perturbations, which are linear combinations of large-scale modes and short-scale modes, whose wave numbers are close to those of the perturbed flows. Depending on asymptotic relations of small parameters α (the difference between the wave number of perturbed flows and the critical wave number for the onset of convection) and ε (ε² being the overcriticality and the perturbed flow amplitude being O(ε)), either small-angle or Eckhaus instability is prevailing. In the case of small-angle instability for rolls the largest growth rate scales as ε^8/5, in agreement with results of Cox and Matthews (Cox, S.M. and Matthews, P.C., Instability of rotating convection. J. Fluid. Mech., 2000, 403, 153–172) obtained for rolls with k = k _c . For waves, the largest growth rate is of the order ε^4/3. In the case of Eckhaus instability the growth rate is of the order of α².     

Temporal variation of large scale flows in the solar interior

We attempt to detect short-term temporal variations in the rotation rate and other large scale velocity fields in the outer part of the solar convection zone using the ring diagram technique applied to Michelson Doppler Imager (MDI) data. The measured velocity field shows variations by about 10 m/s on the scale of few days.     

The excited spin state of Comet 2P/Encke

Ways to rationalize the different periods (e.g., 15.08 h, Luu and Jewitt, 1990, Icarus 86, 69-81; 11.01 h, Fernández et al., 2004, Icarus, in this issue; Lowry et al., 2003, Lunar Planet. Sci. XXXIV, Abstract 2056) seen in near aphelion R-band light curves of Comet 2P/Encke are explored. We show that the comet is usually active at aphelion and it's observed light curves contain signal from both the nucleus and an unresolved coma. The coma contribution to the observed brightness is generally found to dominate with the nucleus providing from 28 to 87% of the total brightness. The amplitude of the observed variations cannot be explained by the nucleus alone and are due to coma activity. We show that some seven periodicities exist in the observed light curves at various times and that this is likely the result of an active nucleus spinning in an excited spin state. The changing periodicities are probably due to changes in the relative strengths of the active areas. We work out possible excited states based on experience with model light curves and by using an analogy to light curve observations of Comet 1P/Halley for which the spin state has been separately determined from spacecraft observations. There is a possibility of a fully relaxed principal axis spin state (0.538 d⁻¹; P=44.6 h) but, because it provides a poorer fit to the observed periodicities than the best fit excited state together with the absence of a peak near 1.08 d⁻¹ (2fφ) in the frequency spectrum of the Fernández et al. (2000, Icarus 147, 145-160) thermal IR lightcurve, we consider it unlikely. Both SAM and LAM excited states are allowed by the underlying periodicities and additional information is needed to choose between these. Our choice of a low excitation SAM state, i.e., one in which the instantaneous spin axis nutates around the total angular momentum vector in a motion that is characterized by limited angular oscillations around the long axis, is based on Sekanina's (1988, Astron J. 95, 911-924, 1988, Astron. J. 96, 1455-1475) interpretation of the fan coma that this comet often displays. We argue that possible LAM states are excluded either because they are too difficult to excite or because they would be inconsistent with the formation of the observed fan morphology. Two possible SAM states emerge that provide good fits to the observed periodicities, one with a precessional frequency for the long axis about the total angular momentum vector of 1.614 d⁻¹ (P?=14.9 h) and an oscillation frequency around the long axis of 0.539 d⁻¹ (Pψ=44.5 h) and a second with a precessional frequency of 2.162 d⁻¹ (P?=11.1 h) combined with an oscillation around the long axis of 0.502 d⁻¹ (Pψ=47.8 h). While either solution is possible, the latter is, in a least squares sense, more likely to be the actual spin state. In both cases the direction of the total angular momentum vector (αM,δM[J2000]=198.6, −0.3 deg) is assumed to be defined by the evolving geometry and morphology of the coma (Sekanina, 1988, Astron J. 95, 911-924, 1988, Astron. J. 96, 1455-1475; Festou and Barale, 2000, Astron J. 119, 3119-3132). We discuss the possible locations of the primary active areas found by Sekanina (1988, Astron J. 95, 911-924, 1988, Astron. J. 96, 1455-1475) and, while they are at high cometographic latitudes, they do not have to be physically located close the region were the axis of maximum moment of inertia pierces the surface (i.e., at high cometocentric latitude). We offer a new interpretation of the 10.7 μm data by Fernández et al. (2000, Icarus 147, 145-160) which yields an axial ratio a/b=2.04. This, with the two SAM states that we have found, requires that b/c>1.18 or >1.09 implying a significant asymmetry in the shape of the elongated nucleus. For the observed fan morphology to be maintained, the true axial ratio b/c cannot be much larger than these limiting values otherwise the amplitude of the oscillation about the long axis becomes too large and the fan morphology would be destroyed. The precise phasing of the spin modes, i.e., the value of the Euler angles at a particular time, is not determinable from the current data set, but a set of well sampled thermal infrared observations of the nucleus covering many periods and a wide range of observing geometries could provide this information in the future as well as clearly distinguishing between the two excited spin states.     

Rotation velocity and neutral hydrogen distribution dependency on magnetic field strength in spiral galaxies

The rotation velocity of a simulated plasma galaxy is compared to the rotation curves of Sc type spiral galaxies. Both show flat rotation curves with velocities of the order of several hundred kilometers per second, modified by E × B instabilities. Maps of the strength and distribution of galactic magnetic fields and neutral hydrogen regions, as-well-as as predictions by particle-in-cell simulations run in the late 1970s, are compared to Effelsberg observations.Agreement between simulation and observation is best when the simulation galaxy masses are identical to the observational masses of spiral galaxies. No dark matter is needed.     

1m红外太阳望远镜光电导行系统中像场旋转的分析

云南天文台1m红外太阳望远镜(YNST)光电导行系统是基于检测太阳像在面阵CMOS图像传感器上的偏移量作为反馈控制信号的高精度闭环跟踪系统[1]。由于YNST是一个地平式装置,在太阳像偏移检测量中存在着像场旋转量,为了获取稳定清晰的太阳像,必须对检测量进行消旋[2]才能达到光电导行系统的跟踪要求。根据球面天文学及天体测量学的知识并结合导行镜的光学系统,推导了光电导行系统中像场旋转的变化规律并对其进行模拟分析。     

Centrifuge modeling of load-deformation behavior of rocking shallow foundations

Shallow foundations supporting building structures might be loaded well into their nonlinear range during intense earthquake loading. The nonlinearity of the soil may act as an energy dissipation mechanism, potentially reducing shaking demands exerted on the building. This nonlinearity, however, may result in permanent deformations that also cause damage to the building. Five series of tests on a large centrifuge, including 40 models of shear wall footings, were performed to study the nonlinear load-deformation characteristics during cyclic and earthquake loading. Footing dimensions, depth of embedment, wall weight, initial static vertical factor of safety, soil density, and soil type (dry sand and saturated clay) were systematically varied. The moment capacity was not observed to degrade with cycling, but due to the deformed shape of the footing–soil interface and uplift associated with large rotations, stiffness degradation was observed. Permanent deformations beneath the footing continue to accumulate with the number of cycles of loading, though the rate of accumulation of settlement decreases as the footing embeds itself.     

Analogue modelling of the influence of shape and particle/matrix interface lubrication on the rotational behaviour of rigid particles in simple shear

The rotational behaviour of a rigid particle embedded in a linear viscous matrix undergoing cylindrical simple shear (Couette) flow was studied in 2D rock-analogue experiments. The influence of particle shape (elliptical vs. monoclinic), aspect ratio and the nature of the matrix/particle interface (lubricated vs. unlubricated) was investigated. Both matrix (PDMS) and lubricant (liquid soap) were linear viscous, with a viscosity ratio of ca. 10⁴. Without lubricant, the rotational behaviour of all particles closely approximates the Jeffery theory. Lubricated monoclinic particles with the long diagonal initially parallel to the shear direction show back rotation and approach a stable position. Lubricated elliptical particles initially parallel to the shear direction also show back rotation but only transiently stabilize. Weak planar zones in the matrix adjacent to unlubricated elliptical particles do not induce backward rotation. In general for elliptical particles, rotation rate as a function of orientation depends on axial ratio and thickness of the lubricant mantle. For thick mantles (initially >10% of the volume of the particle), rotation rates are faster than Jeffery theory. For very thin mantles they are markedly slower compared with thick mantles, particularly when the long axis is nearly parallel to the shear direction. Rotation rates are never strictly zero, so true stabilization does not occur. However, for more elongate particles (axial RATIO=6) rotation rates are so slow that a very strong shape preferred orientation would develop in a lubricated elliptical particle population. In experiments, the volume of lubricant is constant and the thickness adjacent to the long side of the particle progressively decreases with increasing strain. In natural examples of porphyroclast systems, the weak mantle continually develops by recrystallization and/or cataclasis of the rigid clast core and a steady state between production and thinning could be attained, potentially leading to true stabilization for particles with a high axial ratio.