Static and Dynamic Optical Analysis of Micro Wrinkle Formation on a Liquid Surface

A spatially periodic voltage was used to create a dielectrophoresis induced periodic micro wrinkle deformation on the surface of a liquid film. Optical Coherence Tomography provided the equilibrium wrinkle profile at submicron accuracy. The dynamic wrinkle amplitude was derived from optical diffraction analysis during sub-millisecond wrinkle formation and decay, after abruptly increasing or reducing the voltage, respectively. The decay time constant closely followed the film thickness dependence expected for surface tension driven viscous levelling. Modelling of the system using numerical solution of the Stokes flow equations with electrostatic forcing predicted that wrinkle formation was faster than decay, in accord with observations.

Absolute instability in shock-containing jets

We present an analysis of the linear stability characteristics of shock-containing jets. The flow is linearised around a spatially periodic mean, which acts as a surrogate for a mean flow with a shock-cell structure, leading to a set of partial differential equations with periodic coefficients in space. Disturbances are written using the Floquet ansatz and Fourier modes in the streamwise direction, leading to an eigenvalue problem for the Floquet exponent. The characteristics of the solution are directly compared with the locally parallel case, and some of the features are similar. The inclusion of periodicity induces minor changes in the growth rate and phase velocity of the relevant modes for small shock amplitudes. On the other hand, the eigenfunctions are now subject to modulation related to the periodicity of the flow. Analysis of the spatio-temporal growth rates led to the identification of a saddle point between the Kelvin–Helmholtz mode and the guided jet mode, characterising an absolute instability mechanism. Frequencies and mode shapes related to the saddle points for two conditions (associated with axisymmetric and helical modes) are compared with screech frequencies and the most energetic coherent structures of screeching jets, resulting in a good agreement for both. The analysis shows that a periodic shock-cell structure has an impulse response that grows upstream, leading to oscillator behaviour. The results suggest that screech can occur in the absence of a nozzle, and that the upstream reflection condition is not essential for screech frequency selection. Connections to previous models are also discussed.

S-, P- and R-striations as attractors for electron phase trajectories in spatially periodic resonance fields

A new point of view on the appearance of S-, P- and R-striations in a positive column of inert gases is proposed, based on a dynamic analysis of the resonance properties of electron phase trajectories in spatially periodic fields. The positive column may be considered as a resonator containing a set of resonant modes. Like a tuning fork, being disturbed, it responds with one of the modes, in particular with of S-, P-, or R-modes or striations, depending on the discharge conditions. The dynamic approach eliminates the difficulties of the kinetic theory associated with the long length of the solution of Boltzmann equation, which is much greater than the length of the positive column.

Triglobal infinite-wing shock-buffet study

This article uses triglobal stability analysis to address the question of shock-buffet unsteadiness, and associated modal dominance, on infinite wings at high Reynolds number, expanding upon recent biglobal work, aspiring to elucidate the flow phenomenon's origin and characteristics. Infinite wings are modelled by extruding an aerofoil to finite aspect ratios and imposing a periodic boundary condition without assumptions on spanwise homogeneity. Two distinct steady base flows, spanwise uniform and non-uniform, are analysed herein on straight and swept wings. Stability analysis of straight-wing uniform flow identifies both the oscillatory aerofoil mode, linked to the chordwise shock motion synchronised with a pulsation of its downstream shear layer, and several monotone (non-oscillatory), spatially periodic shock-distortion modes. Those monotone modes become outboard travelling on the swept wing with their respective frequencies and phase speeds correlated with the sweep angle. In the limiting case of very small wavenumbers approaching zero, the effect of sweep creates branches of outboard and inboard travelling modes. Overall, triglobal results for such quasi-three-dimensional base flows agree with previous biglobal studies. On the contrary, cellular patterns form in proper three-dimensional base flow on straight wings, and we present the first triglobal study of such an equilibrium solution to the governing equations. Spanwise-irregular modes are found to be sensitive to the chosen aspect ratio. Nonlinear time-marching simulations reveal the flow evolution and distinct events to confirm the insights gained through dominant modes from routine triglobal stability analysis.

DIFFUSION IN MOMENTUM OF RELATIVISTIC ELECTRONS WITH A THERMAL SPREAD PASSING THROUGH AN UNDULATOR

The longitudinal momentum diffusion of electrons moving in a spatially periodic magnetic field of an undulator is investigated, taking into account their initial energy spread. Expressions for the coefficient are obtained and the dependences of the diffusion coefficient are determined both on the distance traveled by the electrons in the undulator and on the value of the initial energy spread of the electrons. The possibility of decreasing the wavelength in X-ray free electron lasers is discussed.

Spatially Developing Modes: The Darcy–Bénard Problem Revisited

In this paper, the instability resulting from small perturbations of the Darcy–Bénard system is explored. An analysis based on time–periodic and spatially developing Fourier modes is adopted. The system under examination is a horizontal porous layer saturated by a fluid. The two impermeable and isothermal plane boundaries are considered to have different temperatures, so that the porous layer is heated from below. The spatial instability for the system is defined by taking into account both the spatial growth rate of the perturbation modes and their propagation direction. A comparison with the neutral stability condition determined by using the classical spatially periodic and time–evolving Fourier modes is performed. Finally, the physical meaning of the concept of spatial instability is discussed. In contrast to the classical analysis, based on spatially periodic modes, the spatial instability analysis, involving time–periodic Fourier modes, is found to lead to the conclusion that instability occurs whenever the Rayleigh number is positive.