Linear instability of Vlasov-Maxwell systems revisited-A Hamiltonian approach

<p style='text-indent:20px;'>We consider linear stability of steady states of 1<inline-formula><tex-math id="M1">\begin{document}$ \frac{1}{2} $\end{document}</tex-math></inline-formula> and 3DVlasov-Maxwell systems for collisionless plasmas. The linearized systems canbe written as separable Hamiltonian systems with constraints. By using ageneral theory for separable Hamiltonian systems, we recover the sharp linearstability criteria obtained previously by different approaches. Moreover, weobtain the exponential trichotomy estimates for the linearized Vlasov-Maxwellsystems in both relativistic and nonrelativistic cases.</p>

Instability of the attachment line boundary layer in a supersonic swept flow

Theoretical analysis of attachment-line instabilities is performed for supersonic swept flows using the compressible Hiemenz approximation for the mean flow and the successive approximation procedures for disturbances. The theoretical model captures the dominant attachment-line modes in wide ranges of the sweep Mach number ${M_e}$ and the wall temperature ratio. It is shown that these modes behave similar to the first and second Mack modes in the boundary layer flow. This similarity allows us to extrapolate the knowledge gained for Mack modes to the attachment-line instabilities. In particular, we find that at sufficiently large ${M_e}$ , the dominant attachment-line instability is associated with the synchronisation of slow and fast modes of acoustic nature. Point-by-point comparisons of the theoretical predictions with the experiments of Gaillard et al. (Exp. Fluids, vol. 26, 1999, pp. 169–176) demonstrate that at ${M_e} > 4$ , the theory captures a significant drop of the transition onset Reynolds number, which is below the contamination criterion of Poll $({R_\mathrm{\ast }} = 250)$ at ${M_e} > 6$ . This contradicts the generally accepted assumption that the attachment-line flow is stable for ${R_\mathrm{\ast }} \le 250$ . The theoretical critical Reynolds numbers lie well below the experimental transition-onset Reynolds numbers. Stability computations using the Navier–Stokes mean flow and accounting for the leading-edge curvature effect do not eliminate this discrepancy. Most likely, in the experiments of Gaillard et al., we face with an unknown effect that does not fit to the concept of transition arising from linear instability.

Thermosolutal LTNE Porous Mixed Convection Under the Influence of the Soret Effect

The effects of horizontal pressure gradient and Soret coefficient on the onset of double-diffusive convection in a fluid-saturated porous layer under the influence of local thermal nonequilibrium (LTNE) temperatures are analyzed. Darcy's law with local acceleration term, which involves the two-field temperature model describing the fluid and solid phases separately and the approximation of Oberbeck-Boussinesq, is used. The dynamics of small-amplitude perturbations on the basic mixed convection flow is studied numerically. Using the Galerkin method along with the QZ-algorithm, the eighth order eigenvalue differential equation obtained by employing linear stability analysis is solved. The solution provides the neutral stability curves and determines the threshold of linear instability, and the critical values of thermal Darcy-Rayleigh number, wave number, and the frequency at the onset of instability are determined for various values of control parameters. It is found that, rather than the stationary motion, the instability is found to be via oscillatory motion. Besides, the contribution to each parameter on stability characteristics is explored in detail, and some relevant findings have been described that have not been reported hitherto in the literature.

Thermal convection with generalized friction

A model for thermal convection with generalized friction is investigated. It is shown that the linear instability threshold is the same as the global stability one. In addition, decay of the energy in the $$L^2$$ L 2 norm is shown for the perturbation velocity and temperature fields. However, due to the presence of the generalized friction we establish exponential decay in the $$L^{\beta +1}$$ L β + 1 norm for the perturbation temperature, where $$\beta >1$$ β > 1 .

Linear instability of lid- and pressure-driven flows in channels textured with longitudinal superhydrophobic grooves

It is known that an increased flow rate can be achieved in channel flows when smooth walls are replaced by superhydrophobic surfaces. This reduces friction and increases the flux for a given driving force. Applications include thermal management in microelectronics, where a competition between convective and conductive resistance must be accounted for in order to evaluate any advantages of these surfaces. Of particular interest is the hydrodynamic stability of the underlying basic flows, something that has been largely overlooked in the literature, but is of key relevance to applications that typically base design on steady states or apparent-slip models that approximate them. We consider the global stability problem in the case where the longitudinal grooves are periodic in the spanwise direction. The flow is driven along the grooves by either the motion of a smooth upper lid or a constant pressure gradient. In the case of smooth walls, the former problem (plane Couette flow) is linearly stable at all Reynolds numbers whereas the latter (plane Poiseuille flow) becomes unstable above a relatively large Reynolds number. When grooves are present our work shows that additional instabilities arise in both cases, with critical Reynolds numbers small enough to be achievable in applications. Generally, for lid-driven flows one unstable mode is found that becomes neutral as the Reynolds number increases, indicating that the flows are inviscidly stable. For pressure-driven flows, two modes can coexist and exchange stability depending on the channel height and slip fraction. The first mode remains unstable as the Reynolds number increases and corresponds to an unstable mode of the two-dimensional Rayleigh equation, while the second mode becomes neutrally stable at infinite Reynolds numbers. Comparisons of critical Reynolds numbers with the experimental observations for pressure-driven flows of Daniello et al. (Phys. Fluids, vol. 21, issue 8, 2009, p. 085103) are encouraging.

Long-wave equation for a confined ferrofluid interface: periodic interfacial waves as dissipative solitons

We study the dynamics of a ferrofluid thin film confined in a Hele-Shaw cell, and subjected to a tilted non-uniform magnetic field. It is shown that the interface between the ferrofluid and an inviscid outer fluid (air) supports travelling waves, governed by a novel modified Kuramoto–Sivashinsky-type equation derived under the long-wave approximation. The balance between energy production and dissipation in this long-wave equation allows for the existence of dissipative solitons. These permanent travelling waves’ propagation velocity and profile shape are shown to be tunable via the external magnetic field. A multiple-scale analysis is performed to obtain the correction to the linear prediction of the propagation velocity, and to reveal how the nonlinearity arrests the linear instability. The travelling periodic interfacial waves discovered are identified as fixed points in an energy phase plane. It is shown that transitions between states (wave profiles) occur. These transitions are explained via the spectral stability of the travelling waves. Interestingly, multi-periodic waves, which are a non-integrable analogue of the double cnoidal wave, are also found to propagate under the model long-wave equation. These multi-periodic solutions are investigated numerically, and they are found to be long-lived transients, but ultimately abruptly transition to one of the stable periodic states identified.

Double-diffusive Magnetic Layering

Double-diffusive systems, such as thermosolutal convection, in which the density depends on two components that diffuse at different rates, are prone to both steady and oscillatory instabilities. Such systems can evolve into layered states, in which both components, and also the density, adopt a “staircase” profile. Turbulent transport is enhanced significantly in the layered state. Here we exploit an analogy between magnetic buoyancy and thermosolutal convection in order to demonstrate the phenomenon of magnetic layering. We examine the long-term nonlinear evolution of a vertically stratified horizontal magnetic field in the so-called “diffusive regime,” where an oscillatory linear instability operates. Motivated astrophysically, we consider the case where the viscous and magnetic diffusivities are much smaller than the thermal diffusivity. We demonstrate that diffusive layering can occur even for subadiabatic temperature gradients. Magnetic layering may be relevant for stellar radiative zones, with implications for the turbulent transport of heat, magnetic field, and chemical elements.

Understanding core tungsten (W) transport and control in an improved high-performance fully non-inductive discharge on EAST

The behavior of heavy/high-Z impurity tungsten (W) in an improved high-performance fully non-inductive discharge on EAST with ITER-like divertor (ILD) is analyzed. It is found that W could be well controlled. The causes of no W accumulation are clarified by analyzing the background plasma parameters and modeling the W transport. It turns out that the electron temperature (T_e) and its gradient are usually high while the toroidal rotation and density peaking of the bulk plasma are small. In this condition, the modeled W turbulent diffusion coefficient is big enough to offset the total turbulent and neoclassical pinch, so that W density profile for zero particle flux will not be very peaked. Combining NEO and TGLF for the W transport coefficient and the impurity transport code STRAHL, not only the core W density profile is predicted but also the radiated information mainly produced by W in the experiment can be closely reconstructed. At last, the physics of controlling W accumulation by electron cyclotron resonance heating (ECRH) is illustrated considering the effects of changed T_e by ECRH on ionization balance and transport of W. It shows that the change of ionization and recombination balance by changed T_e is not enough to explain the experimental observation of W behavior, which should be attributed to the changed W transport. By comparing the W transport coefficients in two kinds of plasmas with different T_e profiles, it is shown that high T_e and its gradient play a key role to generate large turbulent diffusion through increasing the growth rate of linear instability so that W accumulation is prevented.

Thermohaline staircase formation in the diffusive convection regime: a theory based upon stratified turbulence asymptotics

We describe a mechanism that leads to the spontaneous formation of a thermohaline staircase in the high-latitude oceans. Our analysis of this mechanism is based upon a model in which uniform gradients of temperature and salinity are assumed and is applied to a simplified mean-field model of stratified turbulence. Detailed analysis employs a parametrization of turbulent diapycnal diffusivities (Bouffard & Boegman, Dyn. Atmos. Oceans, vol. 61, 2013, pp. 14–34). This parametrization is apparently unique in that it distinguishes between the diapycnal diffusivities for heat and salt on the basis of their Prandtl (Schmidt) numbers. Our model predicts that the temperature and salinity profiles will be susceptible to linear instability if the buoyancy Reynolds number lies in the range 0.18–91, and a nonlinear mean-field model simulation demonstrates that it evolves into a well-defined thermohaline staircase that matches the characteristics of those found in the high-latitude oceans. The criterion for initial instability is furthermore shown to be consistent with the observed regional variability of staircase occurrence in the Arctic Ocean as determined by the most recent observational datasets.