Hydrodynamic stability theory of double ablation front structures in inertial confinement fusion.

The aim of inertial confinement fusion is the production of energy by the fusion of thermonuclear fuel (deuterium-tritium) enclosed in a spherical target due to its implosion. In the direct-drive approach, the energy needed to spark fusion reactions is delivered by the irradiation of laser beams that leads to the ablation of the outer shell of the target (the so-called ablator). As a reaction to this ablation process, the target is accelerated inwards, and, provided that this implosion is sufficiently strong a symmetric, the requirements of temperature and pressure in the center of the target are achieved leading to the ignition of the target (fusion). One of the obstacles capable to prevent appropriate target implosions takes place in the ablation region where any perturbation can grow even causing the ablator shell break, due to the ablative Rayleigh-Taylor instability. The ablative Rayleigh-Taylor instability has been extensively studied throughout the last 40 years in the case where the density/temperature profiles in the ablation region present a single front (the ablation front). Single ablation fronts appear when the ablator material has a low atomic number (deuterium/tritium ice, plastic). In this case, the main mechanism of energy transport from the laser energy absorption region (low density plasma) to the ablation region is the electron thermal conduction. However, recently, the use of materials with a moderate atomic number (silica, doped plastic) as ablators, with the aim of reducing the target pre-heating caused by suprathermal electrons generated by the laser-plasma interaction, has demonstrated an ablation region composed of two ablation fronts. This fact appears due to increasing importance of radiative effects in the energy transport. The linear theory describing the Rayleigh-Taylor instability for single ablation fronts cannot be applied for the stability analysis of double ablation front structures. Therefore, the aim of this thesis is to develop, for the first time, a linear stability theory for this type of hydrodynamic structures.

GLOBAL WELL-POSEDNESS AND NON-LINEAR STABILITY OF PERIODIC TRAVELING WAVES FOR A SCHRODINGER-BENJAMIN-ONO SYSTEM

The objective of this paper is two-fold: firstly, we develop a local and global (in time) well-posedness theory for a system describing the motion of two fluids with different densities under capillary-gravity waves in a deep water flow (namely, a Schrodinger-Benjamin-Ono system) for low-regularity initial data in both periodic and continuous cases; secondly, a family of new periodic traveling waves for the Schrodinger-Benjamin-Ono system is given: by fixing a minimal period we obtain, via the implicit function theorem, a smooth branch of periodic solutions bifurcating a Jacobian elliptic function called dnoidal, and, moreover, we prove that all these periodic traveling waves are nonlinearly stable by perturbations with the same wavelength.

Discrete linear stability and sensitivity analysis of fluid flows

Este trabajo presenta un método discreto para el cálculo de estabilidad hidrodinámica y análisis de sensibilidad a perturbaciones externas para ecuaciones diferenciales y en particular para las ecuaciones de Navier-Stokes compressible. Se utiliza una aproximación con variable compleja para obtener una precisión analítica en la evaluación de la matriz Jacobiana. Además, mapas de sensibilidad para la sensibilidad a las modificaciones del flujo de base y a una fuerza constante permiten identificar las regiones del campo fluido donde una modificacin (ej. fuerza puntual) tiene un efecto estabilizador del flujo. Se presentan cuatro casos de prueba: (1) un caso analítico para comprobar la derivación discreta, (2) una cavidad cerrada a bajo Reynolds para mostrar la mayor precisión en el cálculo de los valores propios con la aproximación de paso complejo, (3) flujo 2D en un cilindro circular para validar la metodología, y (4) flujo en un cavidad abierta, presentado para validar el método en casos de inestabilidades convectivamente inestables. Los tres últimos casos mencionados (2-4) se resolvieron con las ecuaciones de Navier-Stokes compresibles, utilizando un método Discontinuous Galerkin Spectral Element Method. Se obtuvo una buena concordancia para el caso de validación (3), cuando se comparó el nuevo método con resultados de la literatura. Además, este trabajo muestra que para el cálculo de los modos propios directos y adjuntos, así como para los mapas de sensibilidad, el uso de variables complejas es de suprema importancia para obtener una predicción precisa. El método descrito es aplicado al análisis para la estabilización de la estela generada por un disco actuador, que representa un modelo sencillo para hélices, rotores de helicópteros o turbinas eólicas. Se explora la primera bifurcación del flujo para un disco actuador, y se sugiere que está asociada a una inestabilidad de tipo Kelvin-Helmholtz, cuya estabilidad se controla con en el número de Reynolds y en la resistencia del disco actuador (o fuerza resistente). En primer lugar, se verifica que la disminución de la resistencia del disco tiene un efecto estabilizador parecido a una disminución del Reynolds. En segundo lugar, el análisis hidrodinmico discreto identifica dos regiones para la colocación de una fuerza puntual que controle las inestabilidades, una cerca del disco y otra en una zona aguas abajo. En tercer lugar, se muestra que la inclusión de un forzamiento localizado cerca del actuador produce una estabilización más eficiente que al forzar aguas abajo. El análisis de los campos de flujo controlados confirma que modificando el gradiente de velocidad cerca del actuador es más eficiente para estabilizar la estela. Estos resultados podrían proporcionar nuevas directrices para la estabilización de la estela de turbinas de viento o de marea cuando estén instaladas en un parque eólico y minimizar las interacciones no estacionarias entre turbinas. ABSTRACT A discrete framework for computing the global stability and sensitivity analysis to external perturbations for any set of partial differential equations is presented. In particular, a complex-step approximation is used to achieve near analytical accuracy for the evaluation of the Jacobian matrix. Sensitivity maps for the sensitivity to base flow modifications and to a steady force are computed to identify regions of the flow field where an input could have a stabilising effect. Four test cases are presented: (1) an analytical test case to prove the theory of the discrete framework, (2) a lid-driven cavity at low Reynolds case to show the improved accuracy in the calculation of the eigenvalues when using the complex-step approximation, (3) the 2D flow past a circular cylinder at just below the critical Reynolds number is used to validate the methodology, and finally, (4) the flow past an open cavity is presented to give an example of the discrete method applied to a convectively unstable case. The latter three (2–4) of the aforementioned cases were solved with the 2D compressible Navier–Stokes equations using a Discontinuous Galerkin Spectral Element Method. Good agreement was obtained for the validation test case, (3), with appropriate results in the literature. Furthermore, it is shown that for the calculation of the direct and adjoint eigenmodes and their sensitivity maps to external perturbations, the use of complex variables is paramount for obtaining an accurate prediction. An analysis for stabilising the wake past an actuator disc, which represents a simple model for propellers, helicopter rotors or wind turbines is also presented. We explore the first flow bifurcation for an actuator disc and it suggests that it is associated to a Kelvin- Helmholtz type instability whose stability relies on the Reynolds number and the flow resistance applied through the disc (or actuator forcing). First, we report that decreasing the disc resistance has a similar stabilising effect to an decrease in the Reynolds number. Second, a discrete sensitivity analysis identifies two regions for suitable placement of flow control forcing, one close to the disc and one far downstream where the instability originates. Third, we show that adding a localised forcing close to the actuator provides more stabilisation that forcing far downstream. The analysis of the controlled flow fields, confirms that modifying the velocity gradient close to the actuator is more efficient to stabilise the wake than controlling the sheared flow far downstream. An interesting application of these results is to provide guidelines for stabilising the wake of wind or tidal turbines when placed in an energy farm to minimise unsteady interactions.

Stability analysis of core-annular flow and neutral stability wave number

A general transition criterion is proposed in order to locate the core-annular flow pattern in horizontal and vertical oil-water flows. It is based on a rigorous one-dimensional two-fluid model of liquid-liquid two-phase flow and considers the existence of critical interfacial wave numbers related to a non-negligible interfacial tension term to which the linear stability theory still applies. The viscous laminar-laminar flow problem is fully resolved and turbulence effects on the stability are analyzed through experimentally obtained shape factors. The proposed general transition criterion includes in its formulation the inviscid Kelvin-Helmholtz`s discriminator. If a theoretical maximum wavelength is considered as a necessary condition for stability, a stability criterion in terms of the Eotvos number is achieved. Effects of interfacial tension, viscosity ratio, density difference, and shape factors on the stability of core-annular flow are analyzed in detail. The more complete modeling allowed for the analysis of the neutral-stability wave number and the results strongly suggest that the interfacial tension term plays an indispensable role in the correct prediction of the stable region of core-annular flow pattern. The incorporation of a theoretical minimum wavelength into the transition model produced significantly better results. The criterion predictions were compared with recent data from the literature and the agreement is encouraging. (C) 2007 American Institute of Chemical Engineers.

Global instability of currencies: reasons and perspectives according to the state-corporation hegemonic stability theory

This paper analyses reasons of the instability of the world monetary system. The author considers this problem from historical and contemporary perspectives. According to presented point of view banknotes and electronic money which replaced gold and silver coins in popular circulation are the most important reason of the instability. There are also proven positive and negative consequences of money instability. Reforms of the world monetary system need agreement within the global collective hegemony of state-powers and transnational corporations.

Relevance of sampling schemes in light of Ruelle's linear response theory

We reconsider the theory of the linear response of non-equilibrium steady states to perturbations. We �rst show that by using a general functional decomposition for space-time dependent forcings, we can de�ne elementary susceptibilities that allow to construct the response of the system to general perturbations. Starting from the de�nition of SRB measure, we then study the consequence of taking di�erent sampling schemes for analysing the response of the system. We show that only a speci�c choice of the time horizon for evaluating the response of the system to a general time-dependent perturbation allows to obtain the formula �rst presented by Ruelle. We also discuss the special case of periodic perturbations, showing that when they are taken into consideration the sampling can be �ne-tuned to make the de�nition of the correct time horizon immaterial. Finally, we discuss the implications of our results in terms of strategies for analyzing the outputs of numerical experiments by providing a critical review of a formula proposed by Reick.

Magnetic hyperthermia investigation of cobalt ferrite nanoparticles: Comparison between experiment, linear response theory, and dynamic hysteresis simulations

Considerable effort has been made in recent years to optimize materials properties for magnetic hyperthermia applications. However, due to the complexity of the problem, several aspects pertaining to the combined influence of the different parameters involved still remain unclear. In this paper, we discuss in detail the role of the magnetic anisotropy on the specific absorption rate of cobalt-ferrite nanoparticles with diameters ranging from 3 to 14 nm. The structural characterization was carried out using x-ray diffraction and Rietveld analysis and all relevant magnetic parameters were extracted from vibrating sample magnetometry. Hyperthermia investigations were performed at 500 kHz with a sinusoidal magnetic field amplitude of up to 68 Oe. The specific absorption rate was investigated as a function of the coercive field, saturation magnetization, particle size, and magnetic anisotropy. The experimental results were also compared with theoretical predictions from the linear response theory and dynamic hysteresis simulations, where exceptional agreement was found in both cases. Our results show that the specific absorption rate has a narrow and pronounced maxima for intermediate anisotropy values. This not only highlights the importance of this parameter but also shows that in order to obtain optimum efficiency in hyperthermia applications, it is necessary to carefully tailor the materials properties during the synthesis process. (C) 2012 American Institute of Physics. [http://dx.doi.org/10.1063/1.4729271]

A class of exact Navier-Stokes solutions for homogeneous flat-plate boundary layers and their linear stability

We introduce a new boundary layer formalism on the basis of which a class of exact solutions to the Navier–Stokes equations is derived. These solutions describe laminar boundary layer flows past a flat plate under the assumption of one homogeneous direction, such as the classical swept Hiemenz boundary layer (SHBL), the asymptotic suction boundary layer (ASBL) and the oblique impingement boundary layer. The linear stability of these new solutions is investigated, uncovering new results for the SHBL and the ASBL. Previously, each of these flows had been described with its own formalism and coordinate system, such that the solutions could not be transformed into each other. Using a new compound formalism, we are able to show that the ASBL is the physical limit of the SHBL with wall suction when the chordwise velocity component vanishes while the homogeneous sweep velocity is maintained. A corresponding non-dimensionalization is proposed, which allows conversion of the new Reynolds number definition to the classical ones. Linear stability analysis for the new class of solutions reveals a compound neutral surface which contains the classical neutral curves of the SHBL and the ASBL. It is shown that the linearly most unstable Görtler–Hämmerlin modes of the SHBL smoothly transform into Tollmien–Schlichting modes as the chordwise velocity vanishes. These results are useful for transition prediction of the attachment-line instability, especially concerning the use of suction to stabilize boundary layers of swept-wing aircraft.

The scenario of two-dimensional instabilities of the cylinder wake under EHD forcing: A linear stability analysis

We propose to study the stability properties of an air flow wake forced by a dielectric barrier discharge (DBD) actuator, which is a type of electrohydrodynamic (EHD) actuator. These actuators add momentum to the flow around a cylinder in regions close to the wall and, in our case, are symmetrically disposed near the boundary layer separation point. Since the forcing frequencies, typical of DBD, are much higher than the natural shedding frequency of the flow, we will be considering the forcing actuation as stationary. In the first part, the flow around a circular cylinder modified by EHD actuators will be experimentally studied by means of particle image velocimetry (PIV). In the second part, the EHD actuators have been numerically implemented as a boundary condition on the cylinder surface. Using this boundary condition, the computationally obtained base flow is then compared with the experimental one in order to relate the control parameters from both methodologies. After validating the obtained agreement, we study the Hopf bifurcation that appears once the flow starts the vortex shedding through experimental and computational approaches. For the base flow derived from experimentally obtained snapshots, we monitor the evolution of the velocity amplitude oscillations. As to the computationally obtained base flow, its stability is analyzed by solving a global eigenvalue problem obtained from the linearized Navier–Stokes equations. Finally, the critical parameters obtained from both approaches are compared.

Global Linear Instability at the Dawn of its 4th Decade: A List of Challenges (A Practical Guide on how to Contain the Euphoria and Avoid the Oversell)

Global linear instability theory is concerned with the temporal or spatial development of small-amplitude perturbations superposed upon laminar steady or time-periodic threedimensional flows, which are inhomogeneous in two (and periodic in one) or all three spatial directions.1 The theory addresses flows developing in complex geometries, in which the parallel or weakly nonparallel basic flow approximation invoked by classic linear stability theory does not hold. As such, global linear theory is called to fill the gap in research into stability and transition in flows over or through complex geometries. Historically, global linear instability has been (and still is) concerned with solution of multi-dimensional eigenvalue problems; the maturing of non-modal linear instability ideas in simple parallel flows during the last decade of last century2–4 has given rise to investigation of transient growth scenarios in an ever increasing variety of complex flows. After a brief exposition of the theory, connections are sought with established approaches for structure identification in flows, such as the proper orthogonal decomposition and topology theory in the laminar regime and the open areas for future research, mainly concerning turbulent and three-dimensional flows, are highlighted. Recent results obtained in our group are reported in both the time-stepping and the matrix-forming approaches to global linear theory. In the first context, progress has been made in implementing a Jacobian-Free Newton Krylov method into a standard finite-volume aerodynamic code, such that global linear instability results may now be obtained in compressible flows of aeronautical interest. In the second context a new stable very high-order finite difference method is implemented for the spatial discretization of the operators describing the spatial BiGlobal EVP, PSE-3D and the TriGlobal EVP; combined with sparse matrix treatment, all these problems may now be solved on standard desktop computers.

Linear stability of flow past two circular cylinders in a side-by-side arrangement

The linear stability of flow past two circular cylinders in a side-by-side arrangement is investigated theoretically, numerically and experimentally under the assumption of a two-dimensional flow field, in order to explore the origin of in-phase and antiphase oscillatory flows. Steady symmetric flow is realized at a small Reynolds number, but becomes unstable above a critical Reynolds number though the solution corresponding to the flow still satisfies the basic equations irrespective of the magnitude of the Reynolds number. We obtained the solution numerically and investigated its linear stability. We found that there are two kinds of unstable modes, i.e., antisymmetric and symmetric modes, which lead to in-phase and antiphase oscillatory flows, respectively. We determined the critical Reynolds numbers for the two modes and evaluated the critical distance at which the most unstable disturbance changes from the antisymmetric to the symmetric mode, or vice versa. ©2005 The Physical Society of Japan.

Numerical investigation of the three-dimensional secondary instabilities in the time-developing compressible mixing layer

Mixing layers are present in very different types of physical situations such as atmospheric flows, aerodynamics and combustion. It is, therefore, a well researched subject, but there are aspects that require further studies. Here the instability of two-and three-dimensional perturbations in the compressible mixing layer was investigated by numerical simulations. In the numerical code, the derivatives were discretized using high-order compact finite-difference schemes. A stretching in the normal direction was implemented with both the objective of reducing the sound waves generated by the shear region and improving the resolution near the center. The compact schemes were modified to work with non-uniform grids. Numerical tests started with an analysis of the growth rate in the linear regime to verify the code implementation. Tests were also performed in the non-linear regime and it was possible to reproduce the vortex roll-up and pairing, both in two-and three-dimensional situations. Amplification rate analysis was also performed for the secondary instability of this flow. It was found that, for essentially incompressible flow, maximum growth rates occurred for a spanwise wavelength of approximately 2/3 of the streamwise spacing of the vortices. The result demonstrated the applicability of the theory developed by Pierrehumbet and Widnall. Compressibility effects were then considered and the maximum growth rates obtained for relatively high Mach numbers (typically under 0.8) were also presented.

Verification of a mixed high-order accurate DNS code for laminar turbulent transition by the method of manufactured solutions

This paper presents results on a verification test of a Direct Numerical Simulation code of mixed high-order of accuracy using the method of manufactured solutions (MMS). This test is based on the formulation of an analytical solution for the Navier-Stokes equations modified by the addition of a source term. The present numerical code was aimed at simulating the temporal evolution of instability waves in a plane Poiseuille flow. The governing equations were solved in a vorticity-velocity formulation for a two-dimensional incompressible flow. The code employed two different numerical schemes. One used mixed high-order compact and non-compact finite-differences from fourth-order to sixth-order of accuracy. The other scheme used spectral methods instead of finite-difference methods for the streamwise direction, which was periodic. In the present test, particular attention was paid to the boundary conditions of the physical problem of interest. Indeed, the verification procedure using MMS can be more demanding than the often used comparison with Linear Stability Theory. That is particularly because in the latter test no attention is paid to the nonlinear terms. For the present verification test, it was possible to manufacture an analytical solution that reproduced some aspects of an instability wave in a nonlinear stage. Although the results of the verification by MMS for this mixed-order numerical scheme had to be interpreted with care, the test was very useful as it gave confidence that the code was free of programming errors. Copyright (C) 2009 John Wiley & Sons, Ltd.