Self-similar adiabatic flow headed by a magnetogasdynamic cylindrical shock wave in a rotating non-ideal gas

Similarity solutions are obtained for one-dimensional adiabatic flow behind a magnetogasdynamic cylindrical shock wave propagating in a rotating non-ideal gas in presence of an azimuthal magnetic field. The density of the medium ahead of the shock is assumed to be constant. In order to obtain the similarity solutions the angular velocity of the ambient medium is assumed to be obeying a power law and to be decreasing as the distance from the axis increases. It is found that the similarity solutions exist, in both the cases, when the initial magnetic field is constant or obeying a power law. The effects of an increase in the value of the index for variation of angular velocity of the ambient medium, in the value of the parameter of the non-idealness of the gas and in the strength of the initial magnetic field are obtained.     

On a dynamo driven topographically by longitudinal libration

Variation in the angular velocity Ω of a planetary body is called libration or longitudinal libration when the Ω-axis is fixed in direction. This motion of the body's solid mantle drives motions in its fluid core, either by viscous coupling across the core-mantle interface S, or topographically when S is asymmetric with respect to the Ω-axis, the only case considered in this article. A significant topographically-driven flow is identified having uniform vorticity within S and no component parallel to the Ω-axis. Its dynamic stability depends on the amplitude, Ω ₁, of the sinusoidally varying part of Ω and on the ratio, b/a, of the lengths of the principal axes of S, assumed spheroidal. In (Ω ₁/Ω ₀, b/a) parameter space where Ω ₀ is the average Ω, islands are shown to exist where the constant vorticity states are dynamically unstable. These are surrounded by a sea in which they are stable. When the fluid is slightly viscous, a state in the stable sea retains its uniform vorticity structure except in a viscous boundary layer on S in which the flow acquires a component parallel to the Ω-axis. For (Ω ₁/Ω ₀, b/a) on an island where the uniform vorticity state is unstable, an “alternative flow” exists, which is three-dimensional and is examined here. Assuming that the core is electrically conducting, kinematic dynamos are sought. Uniform vorticity flow appears to be non-regenerative but, when it is stable and viscosity acts to create a sufficiently strong boundary layer flow, dynamo action may occur. It is shown that the alternative flow that exists on an instability island in (Ω ₁/Ω ₀,?b/a) space can be vigorously regenerative.     

Motion on two-dimensional manifolds in rotating coordinates

The two degree-of-freedom system in rotating coordinates: \.u – 2nv = V _x, \.v + 2nu = V _y, \.x = u, \.y = v and its Jacobi integral define a time-dependent velocity field on a differentiable, two-dimensional manifold of integral curves. Explicit time dependence is determined by the dynamical system, coordinate frame, and initial conditions. In the autonomous cases, orbits are level curves of an autonomous function satisfying a second-order, quasi-linear, partial differential equation of parabolic type. Important aspects of the theory are illustrated for the two-body problem in rotating coordinates.     

Response of the Baltic Sea to climate change—theory and observations

The dynamics controlling the response of the Baltic Sea to changed atmospheric and hydrologic forcing are reviewed and demonstrated using simple models. The response time for salt is 30 times longer than for heat in the Baltic Sea. In the course of a year, the Baltic Sea renews most of its heat but only about 3% of its salt. On the seasonal scale, surface temperature and ice-coverage are controlled by the atmospheric conditions over the Baltic Sea as demonstrated by e.g. the strong inter-annual variations in winter temperature and ice-coverage due to variations in dominating wind directions causing alternating mild and cold winters. The response of surface temperature and ice-coverage in the Baltic Sea to modest climate change may therefore be predicted using existing statistics. Due to the long response time in combination with complicated dynamics, the response of the salinity of the Baltic Sea cannot be predicted using existing statistics but has to be computed from mechanistic models. Salinity changes primarily through changes in the two major forcing factors: the supply of freshwater and the low-frequency sea level fluctuations in the Kattegat. The sensitivity of Baltic Sea salinity to changed freshwater supply is investigated using a simple mechanistic steady-state model that includes baroclinic geostrophic outflow from the Kattegat, the major dynamical factor controlling the freshwater content in the Kattegat and thereby the salinity of water flowing into the Baltic Sea. The computed sensitivity of Baltic Sea surface salinity to changes of freshwater supply is similar to earlier published estimates from time-dependent dynamical models with higher resolution. According to the model, the Baltic Sea would become fresh at a mean freshwater supply of about 60 000 m³ s⁻¹, i.e. a 300% increase of the contemporary supply. If the freshwater supply in the different basins increased in proportion to the present-day supply, the Bothnian Bay would become fresh already at a freshwater supply of about 37 000 m³ s⁻¹ and the Bothnian Sea at a supply of about 45 000 m³ s⁻¹. The assumption of baroclinic geostrophic outflow from the Kattegat, crucial for the salinity response of the Baltic Sea to changed freshwater supply, is validated using daily salinity profiles for the period 1931–1977 from lightship Läsö Nord.     

Flow of a double-diffusive stratified fluid in a differentially-rotating cylinder

Abstract

A study has been made of a basic state of axisymmetric flow, at large rotational Reynolds numbers, in a double-diffusive stratified fluid contained in a vertically-mounted, differentially-rotating cylindrical cavity. The aim is to describe the qualitative characteristics of the flow of a fluid, the density of which is stratified by two diffusive effects, i.e., temperature and salinity gradients. Attention is confined to situations in which the temperature and salinity gradients make opposing contributions to the overall density profile, the undisturbed stratification being gravitationally stable. Finite difference numerical solutions of the governing Navier-Stokes equations have been obtained using the Boussinesq approximation. The results are presented in a way that illustrates the explicit effects of double-diffusivity when the cavity aspect ratio, height/radius, is O(1). The principal non-dimensional parameters characterizing the flow field are identified. In the interior core, the primary dynamic balance is between the horizontal density gradient and the vertical shear of the prevailing azimuthal velocity. The effective stratification is seen to decrease as the double-diffusivity increases, even if the overall stratification parameter, St, is held constant. The solute field contains a very thin boundary layer structure at large Lewis numbers. The effective stratification increases with the Prandtl number. Results have been derived for extreme values of the cavity aspect ratio. For small cavity aspect ratios, the dominant dynamic ingredients are viscous diffusion and rotation. For large aspect ratios, the bulk of the flow field is determined by the rotating sidewall. In this case, the direct influence of the double-diffusivity is minor.     

基于1.2m望远镜自适应光学系统激光信标转盘式机械快门的研究

基于激光信标发射和接收共光路系统中探测器受杂散光影响的关键问题,设计了一种新型转盘式机械快门装置,对光信号进行高频率开关控制,从而对自适应光学系统的波前探测器起到彻底保护作用.设计时,分析了瑞利信标的采样厚度以及快门开关与脉冲激光器的发射、探测器探测时间的时序控制.     

Invariant shape solutions of the spinning three craft Coulomb tether problem

In this paper we study shape-preserving formations of three spacecraft, where the formation keeping forces arise from the electric charges deposed on each craft. Inspired by Lagrange’s 3-body problem, the general conditions that guarantee preservation of the geometric shape of the electrically charged formation are derived. While the classical collinear configuration is a solution to the problem, the equilateral triangle configuration is found to only occur with unbounded relative motion. The three collinear spacecraft problem is analyzed and the possible solutions are categorized based on the spacecraft mass–charge ratio. Precise statements on the number of solutions associated with each category are provided. Finally, a methodology is proposed to study boundedness of the collinear solution that is inspired by past understanding and results for the 3-body problem. Given the initial position and the velocity vectors of each craft along with the charges, analytical solutions are provided describing the resulting relative motion.     

Laboratory studies of the effects of interrupted, sloping topography on intermediate depth boundary currents in linearly stratified fluids

Laboratory experiments are described which provide insight into the interaction of intermediate depth boundary currents (IDBCs) with interrupted sloping topography. Specifically, they contribute to the debate over meddy formation on the Iberian continental slope. The experiments were performed in a rectilinear rotating tank filled initially with a linearly-stratified fluid. A false bottom sloped away from the side-wall along which the current flowed, and was interrupted by a gap of variable length. The effects of varying gap length and rotation rate on the boundary current were observed.In the first of two sets of experiments, the current flowed above the slope, along the vertical sidewall. In the second, the current flowed along the sloping bottom. In the former, current nose speed was consistent with geostrophic predictions, but decreased in the presence of a gap in the topography. Kelvin wave radiation is postulated as a reason for this. The IDBCs exhibited vortical lateral intrusions at values of the Burger number Bu=(N₀/Ω)² at which counterpart flat-bottom studies had been stable, implying that the sloping topography had a de-stabilising effect. Energy measurements and qualitative observations suggest the intrusions were due to mixed barotropic/baroclinic instabilities, the latter dominating at higher rotation rates.In the second configuration, four distinct flows were observed, distinguished by the deformation radius:gap width ratio R_D/G^*. For a range of values of R_D/G^*, attached eddies formed at the upstream end of the gap. They remained at this position, unlike those in similar studies of surface boundary currents (Klinger, 1993). Their persistence and ability to move downstream – salient factors for meddy – formation were greater for a finite gap size than a permanent change from sloping to flat bottom.     

Nonlinear Convection in a Rotating Annulus with a Finite Gap

Thermal convection in a fluid-filled gap between the two corotating, concentric cylindrical sidewalls with sloping curved ends driven by radial buoyancy was first studied by Busse (Busse, F.H., "Thermal instabilities in rapidly rotating systems", J. Fluid Mech . 44 , 441-460 (1970)). The annulus model captures the key features of rotating convection in full spherical geometry and has been widely employed to study convection, magnetoconvection and dynamos in planetary systems, usually in connection with the small-gap approximation neglecting the effect of azimuthal curvature of the annulus. This article investigates nonlinear thermal convection in a rotating annulus with a finite gap through numerical simulations of the full set of nonlinear convection equations. Three representative cases are investigated in detail: a large-gap annulus with the ratio of the radii ( s i and s o ) of the sidewalls ξ = s i / o s = 0.1, a medium-gap annulus with ξ = 0.35 and a small-gap annulus with ξ = 0.8. Near the onset of convection, the effect of rapid rotation through the sloping ends forces the first (Hopf) bifurcation in the form of small-scale, steadily drifting rolls (thermal Rossby waves). At moderately large Rayleigh numbers, a variety of different convection patterns are found, including mixed-mode steadily drifting, quasi-periodic (vacillating) and temporally chaotic convection in association with various temporal and spatial symmetry-breaking bifurcations. Our extensive simulations suggest that competition between nonlinear and rotational effects with increasing Rayleigh number leads to an unusual sequence of bifurcation characterized by enlarging the spatial scale of convection.