Kozai–Lidov oscillations triggered by a tilt instability of detached circumplanetary discs

ABSTRACT Circumplanetary discs can be linearly unstable to the growth of disc tilt in the tidal potential of the star–planet system. We use 3D hydrodynamical simulations to characterize the disc conditions needed for instability, together with its long-term evolution. Tilt growth occurs for disc aspect ratios, evaluated near the disc outer edge, of H/r ≳ 0.05, with a weak dependence on viscosity in the wave-like regime of warp propagation. Lower mass giant planets are more likely to have circumplanetary discs that satisfy the conditions for instability. We show that the tilt instability can excite the inclination to above the threshold where the circumplanetary disc becomes unstable to Kozai–Lidov (KL) oscillations. Dissipation in the KL unstable regime caps further tilt growth, but the disc experiences large oscillations in both inclination and eccentricity. Planetary accretion occurs in episodic accretion events. We discuss implications of the joint tilt–KL instability for the detectability of circumplanetary discs, for the obliquity evolution of forming giant planets, and for the formation of satellite systems.

Boundary Layer Stability Regime at DACCIWA Site Using Gradient Richardson Number

Meteorological data including air temperature and wind speed which were collected from DACCIWA measurement site at a tropical agricultural field site in Ile-Ife (7.55oE, 4.56oE), south-western Nigeria have been used to classify boundary layer stability regimes using gradient Richardson number. Three categories were considered to deduce the pattern of stability conditions namely stable, unstable and neutral conditions for 3-hourly intervals at 0.00, 03.00, 06.00, 09.00, 12.00, 15.00, 18.00 and 21.00 hours from 15th June to 31st July 2016. The data were sampled every 1sec and stored subsequently as 10 minutes averages for all the measured parameters. The data was further reduced to 30 minutes averages for easy analysis and manipulation in the calculation of gradient Richardson number used for boundary layer stability regime characterization. The results showed that the month of June 2016 had prevalence of stable regime from 0:00 – 6:00 am and 6:00 pm; 9:00 am was predominantly neutral and shared similar pattern with 9:00 pm. Unstable regime was slightly observed at 12:00 pm and majorly observed at 3:00 pm. The month of July had a little shift from what was observed in the month of June. Predominance of neutral conditions was observed from 9:00 pm to 9:00 am; Hours of 12:00 – 3:00 pm were dominated by unstable regime while 6:00 pm was dominated by stable regime.

Instabilities and transient growth of the stratified Taylor–Couette flow in a Rayleigh-unstable regime

The stability of the Taylor–Couette flow is analysed when there is a stable density stratification along the axial direction and when the flow is centrifugally unstable, i.e. in the Rayleigh-unstable regime. It is shown that not only the centrifugal instability but also the strato-rotational instability can occur. These two instabilities can be explained and well described by means of a Wentzel–Kramers–Brillouin–Jeffreys asymptotic analysis for large axial wavenumbers in inviscid and non-diffusive limits. In the presence of viscosity and diffusion, numerical results reveal that the strato-rotational instability becomes dominant over the centrifugal instability at the onset of instability when the axial density stratification is sufficiently strong. Linear transient energy growth is next investigated for counter-rotating cylinders in the stable regime of the Froude number–Reynolds number parameter space. We show that there exist two types of transient growth mechanism analogous to the lift up and the Orr mechanisms in homogeneous fluids but with the additional effect of density perturbations. The dominant mechanism depends on the stratification: when the stratification is strong, non-axisymmetric three-dimensional perturbations achieve the optimal energy growth through the Orr mechanism while for moderate stratification, axisymmetric perturbations lead to the optimal transient growth by a lift-up mechanism involving internal waves.

Numerical studies on the dynamics of an open triangle in a vertically oscillatory flow

A direct-forcing fictitious domain method is employed to study the dynamics of an open triangle in a vertically oscillatory flow. The flow structures, the vertical force and the torque on the fixed body are analysed for the stable flow regime in which the flow structures form and evolve exactly in the same way in each period and the unstable regime, respectively. Our results indicate that in the stable flow regime for the body with upright orientation, the steady streaming structure mainly comprises two vortex pairs located respectively above and below the body. Due to up–down asymmetry of the body, the pair below the body produces a larger vertical force on the body than the upper pair, which is mainly responsible for the non-zero average force at relatively high Reynolds numbers. The average force increases with increasing Reynolds number or increasing dimensionless period for the parameter range studied, due to the vortex effects. In the unstable regime, a vortex pair is ejected downward from each body edge. The irregular motion of the emitted vortices below the body leads to the irregular fluctuation of the vertical force. Regarding the torque on a tilted body, in the stable regime, the body experiences a restoring torque when its vertex angle is larger than a critical value being close to (and smaller than) 60°, and otherwise a destructive torque, irrespective of the value of tilt angle. For a fixed vertex angle, the torque magnitude is largest when the tilt angle is around 45°. In the unstable regime, the persistent ejection of the vortex pair during upward flow and corresponding restoring torque are observed for a large tilt angle with one edge aligned close to the horizontal direction, as in the experiment of Liu et al. (Phys. Rev. Lett., vol. 108, 2012, 068103). For a relatively small tilt angle, the emission direction of the vortex pair has intermittency, leading to the intermittency in the direction of torque. The reasons for the above observations are discussed. The predictions on the stable orientation for a hovering body in the stable flow regime and the irregular orientation in the unstable regime are confirmed in the dynamic simulation of a freely moving body. The body with the stable horizontal orientation in case of small vertex angle migrates along the body-shape-diverging direction.

Influence of combustion instabilities on the heater appliance with atmospheric gas burner and their elimination by cross flow of air

This paper presents results of experimental investigation on elimination of combustion oscillations caused by new low pollution burner which was integrated in a gas heater. The method is known as a passive method, based on introducing the air in the combustion chamber. Because the efficacy of the method is highly dependent of the way the air is injected some methods were investigated and compared. The paper also presents effects on pollution characteristics during its operation in the unstable regime.