Instabilities of natural convection in a periodically heated layer

Natural convection in an infinite horizontal layer subject to periodic heating along the lower wall has been investigated using a combination of numerical and asymptotic techniques. The heating maintains the same mean temperatures at both walls while producing sinusoidal temperature variations along one horizontal direction, with its spatial distribution characterized by the wavenumber $\alpha $ and the amplitude expressed in terms of a Rayleigh number $R{a}_{p} $. The primary response of the system takes the form of stationary convection consisting of rolls with the axis orthogonal to the heating wave vector and structure determined by the particular values of $R{a}_{p} $ and $\alpha $. It is shown that for sufficiently large $\alpha $ convection is limited to a thin layer adjacent to the lower wall with a uniform conduction zone emerging above it; the temperature in this zone becomes independent of the heating pattern and varies in the vertical direction only. Linear stability of the above system has been considered and conditions leading to the emergence of secondary convection have been identified. Secondary convection gives rise to either longitudinal rolls, transverse rolls or oblique rolls at the onset, depending on $\alpha $. The longitudinal rolls are parallel to the primary rolls and the transverse rolls are orthogonal to the primary rolls, and both result in striped patterns. The oblique rolls lead to the formation of convection cells with aspect ratio dictated by their inclination angle and formation of rhombic patterns. Two mechanisms of instability have been identified. In the case of $\alpha = O(1)$, parametric resonance dominates and leads to a pattern of instability that is locked in with the pattern of heating according to the relation ${\delta }_{cr} = \alpha / 2$, where ${\delta }_{cr} $ denotes the component of the critical disturbance wave vector parallel to the heating wave vector. The second mechanism, the Rayleigh–Bénard (RB) mechanism, dominates for large $\alpha $, where the instability is driven by the uniform mean vertical temperature gradient created by the primary convection, with the critical disturbance wave vector ${\delta }_{cr} \rightarrow 1. 56$ for $\alpha \rightarrow \infty $ and the fluid response becoming similar to that found in the case of a uniformly heated wall. Competition between these mechanisms gives rise to non-commensurable states in the case of longitudinal rolls and the appearance of soliton lattices, to the formation of distorted transverse rolls, and to the appearance of the wave vector component in the direction perpendicular to the forcing direction. A rapid stabilization is observed when the heating wavenumber is reduced below $\alpha \approx 2. 2$ and no instability is found when $\alpha \lt 1. 6$ in the range of $R{a}_{p} $ considered. It is shown that $\alpha $ plays the role of an effective pattern control parameter and its judicious selection provides a means for the creation of a wide range of flow responses.

On parametric instabilities in HF heating of the ionosphere

The initial processes excited directly by high-frequency (HF) heating waves include parametric decay instabilities, which decay the HF heating wave to a frequency-downshifted Langmuir/upper hybrid sideband together with an ion acoustic/lower hybrid wave as the decay mode, and oscillating two stream instabilities, which decay the HF heating wave to two oppositely propagating Langmuir/upper hybrid sidebands and purely growing mode/field-aligned density irregularities. These instabilities provide effective channels to convert heating waves to electrostatic plasma waves in the F region of the ionosphere. The following-up parametric instabilities include the cascades of Langmuir pump waves into Langmuir sidebands and ion acoustic waves/lower hybrid waves, and the decay of upper hybrid waves to Langmuir sidebands and ion decay modes, as well as the filamentation of those HF electrostatic waves to generate field-aligned density irregularities. The instability thresholds, growth rates, angular distribution and regions of excitation are determined.

Generation of extra and very low-frequency (ELF/VLF) radiation by ionospheric electrojet modulation using high-frequency (HF) heating waves

Extra and very low-frequency (ELF/VLF) wave generation by modulated polar electrojet currents is studied numerically. Through Ohmic heating by the amplitude-modulated high-frequency heating wave, the conductivity and thus the current of the electrojet are modulated accordingly to set up the ionospheric antenna current. Stimulated thermal instability, which can further enhance the electrojet current modulation, is studied. It is first analysed analytically to determine the threshold heating power for its excitation. The nonlinear evolutions of the generated ELF/VLF waves enhanced by the instability are then studied numerically. Their spectra are also evaluated. The field intensity of the emission at the fundamental modulation frequency is found to increase with the modulation frequency in agreement with the Tromso observations. The efficiency enhancement by the stimulated thermal instability is hampered by inelastic collisions of electrons with neutral particles (mainly due to vibration excitation of N2), which cause this instability to saturate at low levels. However, the electron inelastic collision loss rate drops rapidly to a low value in the energy regime from 3.5 to 6 eV. As the heating power exceeds a threshold level, significant electron heating enhanced by the instability is shown, which indeed causes a steep drop in the electron inelastic collision loss rate. Consequently, this instability saturates at a much higher level, resulting to a near step increase (of about 10–13 dB depending on the modulation wave form) in the spectral intensity of ELF radiation. The dependence of the threshold power of the HF heating wave on the modulation frequency is determined.

Disk-Instability Model for Outbursts of Dwarf Novae: Fine Mesh Calculations

We have executed fine mesh calculations which can almost fully resolve the transition front in the accretion disk of dwarf novae. Results show that the effects of thermal diffusion become very important only when the heating wave passes by. But it is unlikely that they cause drastic changes’ in the situation of wave propagation. The validity of the localized front approximation is examined. It is found that this approximation is relatively good for heating waves but it is marginal for cooling waves.

Axial heating of magnetically confined plasma with CO2 lasers

The coupled electron–ion heating equations, neglecting losses, in a CO2 laser heated solenoid are solved for a laser intensity varying with time as I = I0t2/3. An analytical solution, without restriction on the ratio of electron-to-ion temperatures Te/Ti is found, showing Te,i ~ t2/3.The heating wave which propagates along the solenoid is found to be supersonic having a velocity independent of time and varying as I03/5. Low intensity heating is found to maximize Ti/Te and minimize plasma length and laser energy requirements. The heating wave propagation is found to be consistent with an optical thickness of order unity in the heated plasma column. Considerations of electron–ion energy transfer, supersonic heating wave propagation, and laser beam trapping lead to an optimum laser intensity parameter [Formula: see text].