Flow in heated straight rotating pipe

Fully developed laminar flow in a straight heated rotating pipe which includes the influence of both, coriolis force and buoyancy force, has been considered analytically. The solution has been obtained in terms of series expansions; the solution is therefore restricted to small values of the parameters involved.     

Derivation of microscopic unified Bohr–Mottelson rotational model

In a previous article, we derived a microscopic version of the phenomenological Bohr–Mottelson unified rotational model for rotation about a single axis. In this article, we generalize the derivation to that for rotation about all the three axes. As in the previous derivation, we apply the nuclear Hamiltonian directly to the rotational-model wavefunction instead of using the usual canonical transformation. In this way, we avoid using redundant coordinates or imposing any constraints on the rotationally-invariant rotational-model intrinsic wavefunction. We show that, in the transformed nuclear Schrödinger equation, the Coriolis coupling term vanishes exactly only for a choice of the rotational-model Euler angles that is consistent with angle-angular momentum commutation relation and rotational invariance of the intrinsic wavefunction. For this choice of the Euler angles, the kinematic moment-of-inertia tensor, collective-rotation velocity field, and flow vorticity have the rigid-flow characteristics. This quantum rigid flow reduces to irrotational free-vortex flow in the limit of a single particle. We derive a microscopic effective rotation-intrinsic unified Schrödinger equation for the states of a rotational band that reduces to the phenomenological, unified, tri-axial quantum rigid-rotor model in the limit that the off-diagonal elements of the kinematic inertia tensor operator can be neglected. The model derivation shows that a multi-fermion system with unpaired or paired (quasi) particles rotates rigidly and a single-particle system rotates irrotationally if the intrinsic system is rotationally invariant.     

Effects of spanwise system rotation on turbulent stripes in a plane Poiseuille flow

In the transitional channel flow, the large-scale intermittent structure of localised turbulence, which is called the turbulent stripe pattern, can be found in the form of stripe arrangement. The structure of the turbulent stripe pattern is an oblique laminar–turbulent banded pattern and is inclined with respect to the streamwise direction. We performed direct numerical simulation at a transitional Reynolds number and very low-rotation numbers, and focused on the turbulent stripe pattern in the plane Poiseuille flow subjected to spanwise system rotation. We captured the turbulent stripe pattern in a rotating channel flow and found the augmentation and diminution of the turbulent stripe pattern were affected by the spanwise rotation. The contents of the discussion are the spatial size of the turbulent stripe pattern on the basis of the instantaneous flow fields, the energy spectra, and various statistics relating to the spanwise velocity component that characterise the turbulent stripe pattern. The turbulent stripe pattern was found to contain kinetic energy that was larger in very weakly rotating flows than in the static system. It was also found that the magnitude of the spanwise secondary flow increases, while the quasi-laminar region is wider at a very lowrotation number.     

The Degenerate Vibrations of BCl3, BBr3 and BI3 with Application of Keating Coordinates

The experimental works of vibrational spectroscopy and normal coordinate analyses for BCl₃, BBr₃ and BI₃ are reviewed extensively. Harmonic force fields of the E' species are produced using isotopic frequencies and Coriolis constants as additional data, respectively. The usefulness of Keating coordinates versus valence coordinates as basis of force field approximations is discussed. The conclusions are not unequivocal, but they go in favour of the Keating coordinates when the reliability of the different computations is taken into account. Boron trichloride is treated specifically in some detail. Final force fields are proposed for the title molecules with the aid of the mass influence on Coriolis constants.     

Computational study of a supersonic free jet rotating perpendicular to the streamwise direction

We study the flow structure of supersonic jets rotating perpendicular to the streamwise direction using RANS simulations, and we assess the performance of different turbulence model rotation corrections. The Coriolis and centrifugal terms were added to the equations of motion to perform calculations in this non-inertial (rotating) frame of reference. An explicit, cell-centred, finite-volume numerical method, coupled to a k?ε turbulence model, was used for the computations. The turbulence model rotation corrections of Howard et al. (1980), Park and Chung (1999), and Cazalbou et al. (2005) were attempted. In the absence of experimental data for jets rotating perpendicular to the streamwise direction, the rotation corrections were examined against the available measurements of a swirling jet; the comparison of the numerical and experimental data indicates that the Cazalbou et al. (2005 Cazalbou, J.B. 2005. Two-equation modeling of turbulent rotating flows. Physics of Fluids, 17(5): 1–14. [Crossref], [Web of Science ®] , [Google Scholar]) and Park and Chung (1999 Park, J.Y. and Chung, M.K. 1999. A model for the decay of rotating homogeneous turbulence. Physics of Fluids, 11(6): 1544–1549. [Crossref], [Web of Science ®] , [Google Scholar]) corrections improve the performace of the turbulence model. Simulations were then run of a supersonic jet rotating perpendicular to the stream direction at 0, 50, 100 and 150 rad/s, using no turbulence model rotation correction, and using the three rotation corrections. The results indicate that the Cazalbou et al. (2005 Cazalbou, J.B. 2005. Two-equation modeling of turbulent rotating flows. Physics of Fluids, 17(5): 1–14. [Crossref], [Web of Science ®] , [Google Scholar]) correction is more physical than the other two, as it yields results that are qualitatively consistent with the known effects of rotation: that turbulence is enhanced and suppressed on the concave and convex sides of a rotating jet centreline, respectively, and that the effect of rotation saturates as the rotation rate increases. The findings are in qualitative agreement with the available literature.     

Quasi-hydrostatic Primitive Equations for Ocean Global Circulation Models

Global existence of weak and strong solutions to the quasi-hydrostatic primitive equations is studied in this paper. This model, that derives from the full non-hydrostatic model for geophysical fluid dynamics in the zero-limit of the aspect ratio, is more realistic than the classical hydrostatic model, since the traditional approximation that consists in neglecting a part of the Coriolis force is relaxed. After justifying the derivation of the model, the authors provide a rigorous proof of global existence of weak solutions, and well-posedness for strong solutions in dimension three.     

Study of vibration-rotation levels in formamide with high resolution FTIR spectroscopy: The ν12, 2ν12, ν11, and ν9 bands

The far infrared and infrared spectra of formamide (HCONH₂) have been recorded at high resolution (0.00125 cm⁻¹) in the region of 90-1060 cm⁻¹. Over 20,000 transitions from the out-of-plane NH₂ wagging motion (n₁₂ = 1 ← 0 fundamental, n₁₂ = 2 ← 0 overtone, n₁₂ = 2 ← 1 difference bands), torsion (n₁₁ = 1 ← 0 bands), and out-of-phase NCO/NH₂ bend (n₉ = 1 ← 0 bands) have been assigned. Molecular parameters have been obtained for the ground state and the unperturbed n₁₂ = 1 state. The least-squares fit calculations were completed with the microwave data available in the literature. The complicated resonance system between the n₁₂ = 2, n₁₁ = 1, and n₉ = 1 states has been investigated carefully. Thus, we have been able to verify almost all resonances (avoided crossing) existing in the region J, K investigated. In the coupled Hamiltonian used for the fit, all Watson’s reduced parameters, including the octic ones and 16 Coriolis coupling parameters were taken into account. The rms deviation obtained from the fit was 0.000247 cm⁻¹.     

The ν7, ν8, and ν11 bands of propynal, C2HCHO, in the 650 cm region

The infrared spectrum of propynal, C₂HCHO, is studied at high resolution (0.003 cm⁻¹) in the range 570-640 cm⁻¹. The relatively intense ν₁₁ (CC-H out-of-plane bend, 693 cm⁻¹) and ν₇ (CC-H in-plane bend, 651 cm⁻¹) fundamental bands are linked by a strong a-type Coriolis interaction. The somewhat weaker ν₈ (CCO in-plane bend, 614 cm⁻¹) fundamental has a significant Fermi-type interaction with the “dark” background state 3ν₉ (∼618 cm⁻¹). About 1400 lines are assigned and analyzed in terms of a four-state fit in order to obtain accurate band origins, rotational and centrifugal distortion parameters, and Fermi and Coriolis interaction parameters. This represents the first systematic high-resolution infrared study of propynal.