Interlayer sodium ions of montmorillonite were exchanged with hydroxy-bismuth polycations which were prepared from bismuth perchlorate solutions by the addition of NaOH. Assuming the charge density of the silicate layer to be unchanged, the compositions of the polycations involved in the exchange can be estimated from the amount of bismuth taken up by the montmorillonite and from the ignition loss between 110° and 800°C. The derived compositions are near [Bi6(OH)16]2+ irrespective of the ratio of OH:Bi in the perchlorate solution. The basal spacing of the hydroxy-bismuth montmorillonites is about 16 Å at 110°C, which corresponds to that of hydroxy-chromium montmorillonite having a high surface area of about 250 m2/g. The surface areas of the hydroxy-bismuth montmorillonites, however, are less than 80 m2/g.

The linear stability of the Stuart vortices, which is a model of arrays of vortices often observed in the atmosphere and the oceans, in rotating stratified fluids is investigated by local and modal stability analysis. As in the case of the two-dimensional (2-D) Taylor–Green vortices, five types of instability appear in general: the pure-hyperbolic instability, the strato-hyperbolic instability, the rotational-hyperbolic instability, the centrifugal instability and the elliptic instability. The condition for each instability and the estimate of the growth rate derived by Hattori & Hirota (J. Fluid Mech., vol. 967, 2023, A32) are shown to also be useful for the Stuart vortices, which supports their applicability to general flows. The properties of each instability depend on stratification and rotation in a way similar to the case of the 2-D Taylor–Green vortices. For the Stuart vortices, however, the centrifugal instability and the elliptic instability become more dominant than the three hyperbolic instabilities in comparison to the 2-D Taylor–Green vortices; this is explained by the larger ratios of the maximum vorticity and the strain rate at the elliptic stagnation points to the strain rate at the hyperbolic stagnation points. Direct correspondence between the modal and local stability results is further established by comparing unstable modes to solutions to the local stability equations; this is useful for identifying the types of modes since the mechanism of instability is readily known in the local stability analysis. This helps us to discover the modes of the ring-type elliptic instability, which have been predicted only theoretically.

The linear stability of the two-dimensional Taylor–Green vortices, which is a spatially periodic array of vortices, in rotating stratified fluids is investigated by local and modal stability analysis. Five types of instability appear in general: the pure hyperbolic instability, the strato-hyperbolic instability, the rotational-hyperbolic instability, the centrifugal instability and the elliptic instability. The condition for each instability and the estimate of the growth rate, which are useful in interpreting numerical results, are obtained in the framework of local stability analysis. Realizability of an instability is introduced to predict whether an unstable mode corresponding to an unstable region found in the local stability analysis exists at finite Reynolds numbers. In the absence of stratification, the pure hyperbolic instability is dominant for weak rotation; it is stabilized for strong rotation. For strong anti-cyclonic rotation, the elliptic instability or the centrifugal instability becomes dominant depending on the parameter values; further stronger rotation stabilizes both instabilities. For strong cyclonic rotation, the rotational-hyperbolic instability or the elliptic instability becomes dominant, although the growth rate is smaller than the anti-cyclonic cases. Strong stratification changes the stability properties. The strato-hyperbolic instability occurs for weak rotation. The rotational-hyperbolic instability and the elliptic instability are weakened under cyclonic rotation, while the latter survives and extends the unstable range under anti-cyclonic rotation. The pure hyperbolic instability and the centrifugal instability are less affected by stratification. The mode structures of each instability are in good agreement with the corresponding solution to local stability equations, confirming the physical mechanism of the instability.

The linear stability of a periodic array of vortices in stratified fluid is studied by modal stability analysis. Two base flows are considered: the two-dimensional Taylor–Green vortices and the Stuart vortices. In the case of the two-dimensional Taylor–Green vortices, four types of instability are identified: the elliptic instability, the pure hyperbolic instability, the strato-hyperbolic instability and the mixed hyperbolic instability, which is a mixture of the pure hyperbolic and the strato-hyperbolic instabilities. Although the pure hyperbolic instability is most unstable for the non-stratified case, it is surpassed by the strato-hyperbolic instability and the mixed hyperbolic instability for the stratified case. The strato-hyperbolic instability is dominant at large wavenumbers. Its growth rate tends to a constant along each branch in the large-wavenumber and inviscid limit, implying that the strato-hyperbolic instability is not stabilized by strong stratification. Good agreement between the structure of the strato-hyperbolic instability mode and the corresponding local solution is observed. In the case of the Stuart vortices, the unstable modes are classified into three types: the pure hyperbolic instability, the elliptic instability and the mixed-type instability, which is a mixture of the pure hyperbolic and the elliptic instabilities. Stratification decreases the growth rate of the elliptic instability, which is expected to be stabilized by stronger stratification, although it is not completely stabilized within the range of Froude numbers considered. The present results imply that both the pure hyperbolic instability and the strato-hyperbolic instability are important in stably stratified flows of geophysical or planetary scale.

The stability of stably stratified vortices is studied by local stability analysis. Three base flows that possess hyperbolic stagnation points are considered: the two-dimensional (2-D) Taylor–Green vortices, the Stuart vortices and the Lamb–Chaplygin dipole. It is shown that the elliptic instability is stabilized by stratification; it is completely stabilized for the 2-D Taylor–Green vortices, while it remains and merges into hyperbolic instability near the boundary or the heteroclinic streamlines connecting the hyperbolic stagnation points for the Stuart vortices and the Lamb–Chaplygin dipole. More importantly, a new instability caused by hyperbolic instability near the hyperbolic stagnation points and phase shift by the internal gravity waves is found; it is named the strato-hyperbolic instability; the underlying mechanism is parametric resonance as unstable band structures appear in contours of the growth rate. A simplified model explains the mechanism and the resonance curves. The growth rate of the strato-hyperbolic instability is comparable to that of the elliptic instability for the 2-D Taylor–Green vortices, while it is smaller for the Stuart vortices and the Lamb–Chaplygin dipole. For the Lamb–Chaplygin dipole, the tripolar instability is found to merge with the strato-hyperbolic instability as stratification becomes strong. The modal stability analysis is also performed for the 2-D Taylor–Green vortices. It is shown that global modes of the strato-hyperbolic instability exist; the structure of an unstable eigenmode is in good agreement with the results obtained by local stability analysis. The strato-hyperbolic mode becomes dominant depending on the parameter values.

The infrared astronomical satellite AKARI performed an all sky survey at six infrared bands. We report here on the calibration of the all-sky image data, observed in the four long wavelength bands with the FIS instrument (AKARI Far-infrared All Sky Survey : AFASS). The preliminary image attains a calibration uncertainty and sensitivity of better than ~ 30% and ~ 10 MJy str−1, respectively, for all four bands. The point spread function (PSF) is obtained via a stacking technique. The data are shown to be useful for exploring the internal structure and dust spectral energy distributions (SEDs) of nearby galaxies.

We perform the numerical hydrodynamical calculation of cluster cooling flow including the mass deposition process and examine evolution of cooling flow. We take two mass deposition models. In one model, mass deposition occurs in large extent. In other model, mass deposition occurs only in central region. In any model, diagnostics of X-ray surface brightness do not agree with observation in any evolutional phases.