Mean-Flow Correction as Non-Linear Saturation Mechanism

The flow in a cylinder driven by time-harmonic oscillations of the rotation rate, called longitudinal librations, is investigated. Using a theoretical approach and axisymmetric numerical simulations, we study two distinct phenomena appearing in this librating flow. First, we investigate the occurrence of a centrifugal instability near the oscillating boundary, leading to the so-called Taylor-Görtler vortices. A viscous stability criterion is derived and compared to numerical results obtained for various libration frequencies and Ekman numbers. The strongly nonlinear regime well above the instability threshold is also documented. We show that a new mechanism of spontaneous generation of inertial waves in the bulk could exist when the sidewall boundary layer becomes turbulent. Then, we analyse the librating flow below the instability threshold and characterize the mean zonal flow correction induced by the nonlinear interaction of the boundary layer flow with itself. In the frequency regime where inertial modes are not excited, we show that the mean flow correction in the bulk is a uniform rotation, independent of the Ekman number and cylinder aspect ratio, in perfect agreement with the analytical results of Wang [“Cylindrical tank of fluid oscillating about a state of steady rotation,” J. Fluid. Mech. 41, 581 (1970)]. When inertial modes are resonantly excited, the mean flow correction is found to have a more complex structure. Its amplitude still scales as the square of the libration amplitude but now depends on the Ekman number.

A one-dimensional steady-state model for stimulated Raman backscatter (SRS) and stimulated Brillouin backscatter (SBS) processes in laser-irradiated plasmas is presented. Based on a novel “predictor-corrector” method, the model is capable to deal with broadband scattered light and inhomogeneous plasmas, exhibiting robustness and high efficiency. Influences of the electron density and temperature on the linear gains of both SRS and SBS are investigated, which indicates that the SRS gain is more sensitive to the electron density and temperature than that of the SBS. For the low-density case, the SBS dominates the scattering process, while the SRS exhibits much higher reflectivity in the high-density case. The nonlinear saturation mechanisms and competition between SRS and SBS are included in our model by a phenomenological method. The typical anti-correlation between SRS and SBS versus electron density is reproduced in the model. Calculations of the reflectivities are qualitatively in agreement with the typical results of experiments and simulations.

Precise and predictable propagation and deposition of laser energy in high energy density (HED) plasma is threatened by the breakup of the beam into filaments. Such filaments can be deflected and sprayed but also locally intensify the light, increasing the likelihood of other problematic interactions with the plasma. Adequately modeling, anticipating, and avoiding such processes in HED experiments requires a thorough understanding of the thresholds and nonlinear saturation mechanisms, particularly for the weakly collisional, high temperature plasmas achieved at the National Ignition Facility (NIF).

A nonlinear saturation mechanism for reversed shear Alfvén eigenmode (RSAE) is proposed and analyzed, and is shown to be of relevance to typical reactor parameter region. The saturation is achieved through the generation of high-frequency quasi-mode due to nonlinear coupling of two RSAEs, which is then damped due to coupling with the shear Alfvén continuum, and leads to the nonlinear saturation of the primary RSAEs. An estimation of the nonlinear damping rate is also provided.

Phase change processes or any heat transfer processes are controlled by different parameters like the flow and thermal boundary conditions, thermo-physical properties, area, and shape of medium and cavity. In this study, the melting process of paraffin wax is studied in 60 mm and 80 mm diameter spherical cavity and 50 mm × 40 mm (H × W) rectangular cavity. Enthalpy-porosity model with volume-of-fluid is used for numerical simulation of the process. The study reports that the melting process is faster in the spherical cavity compared to the rectangular cavity. The effect of shape and area of the cavity on melt fraction is expressed for proper justification of the phase change process. The nonlinear relation between melting time and area for rectangular and spherical cavity shapes is calculated.

The rectangular cavity structure was applied to edges of the rear view mirror, numerical computation was conducted for aerodynamic noises of the rear view mirror, and the results of optimized structure were compared with those of the original structure to verify optimized effects. Wind tunnel test was then conducted on the rear view mirror to verify correctness of the computational model. Sound pressure levels of each observation point between experimental test and numerical simulation were basically consistent, where only parts of the peak frequency points were different. The computational accuracy was very high. Two large-size vortexes were in this region behind the common rear view mirror. Vortexes above the rear part of the rear view mirror rotated anticlockwise, while vortexes under it rotated clockwise. There were two vortexes in the region behind the optimized rear view mirror, but the energy intensity of this vortex near the side window panel was very weak. Pressures on the front part of the optimized rear view mirror were also smaller than those of the original structure. In addition, it could be found that radiation noise distribution of the rear view mirror on the lateral window presented symmetry. When lateral window effects were considered, the aerodynamic noise was more than results without considering the lateral window effects. Total noises of each observation point without considering the lateral window effects were 56.7 dB, 59.2 dB, 58.6 dB, 58.9 dB, 62.3 dB and 63.1 dB, respectively. Total noises at each observation point with consideration of the lateral window effects were 65.3 dB, 66.5 dB, 68.7 dB, 69.2 dB, 70.1 dB and 70.8 dB, respectively. Therefore, when aerodynamic noises of the rear view mirror were computed, impacts of lateral window effects must be considered, otherwise the computation would be seriously deviated from actual situations. The frequency corresponding to maximum peaks of the aerodynamic noise after optimization approached the self-oscillation frequency of the rectangular cavity. The result indicates that aerodynamic noises in the rectangular cavity were fluid self-oscillation caused by the cavity structure. In addition, within the analyzed frequency band, the aerodynamic noises of the optimized rear view mirror were smaller than those of the original structure. The maximum decrease rate of total noises of the optimized rear view mirror was 15.62 %, and minimum decrease rate was 8.90 %. Optimized effects were very significant, especially in the low frequency bands.

Convective behaviour of a uniformly Joule-heated liquid pool in a rectangular cavity

Wave-filter-based approach for generation of a quiet space in a rectangular cavity

Flow pattern evolution in natural convection cooling from an array of discrete heat sources in a rectangular cavity at various orientations

In the present work, the effects of nonlinear saturations on the dynamics of three excitons in the protein chain are investigated. Extending the Davydov Hamiltonian to three excitons, it is shown that the system reduces to three-coupled nonlinear Schrodinger equations with three additional saturation terms. Then, it is proved that nonlinear saturations may be used to stabilize the system under modulational instability. Besides, many solutions of the three-coupled nonlinear Schrodinger equations with saturation terms are constructed and classified in three families, i.e., hyperbolic functions which includes bright, kink and dark solitary waves, triangular periodic and generalized Jacobi elliptic functions. The analytical predictions are confirmed by numerical simulations with a good accuracy. It appears that nonlinear saturations profoundly affect the dynamics of the solutions. These solutions may be used to explain the energy transfer and flow through proteins chains.

Magnetorotational instability (MRI) is one of the fundamental processes in astrophysics, driving angular momentum transport and mass accretion in a wide variety of cosmic objects. Despite much theoretical/numerical and experimental efforts over the last decades, its saturation mechanism and amplitude, which sets the angular momentum transport rate, remains not well understood, especially in the limit of high resistivity, or small magnetic Prandtl numbers typical to interiors (dead zones) of protoplanetary disks, liquid cores of planets and liquid metals in laboratory. Using direct numerical simulations, in this paper we investigate the nonlinear development and saturation properties of the helical magnetorotational instability (HMRI)—a relative of the standard MRI—in a magnetized Taylor–Couette flow at very low magnetic Prandtl number (correspondingly at low magnetic Reynolds number) relevant to liquid metals. For simplicity, the ratio of azimuthal field to axial field is kept fixed. From the linear theory of HMRI, it is known that the Elsasser number, or interaction parameter determines its growth rate and plays a special role in the dynamics. We show that this parameter is also important in the nonlinear problem. By increasing its value, a sudden transition from weakly nonlinear, where the system is slightly above the linear stability threshold, to strongly nonlinear, or turbulent regime occurs. We calculate the azimuthal and axial energy spectra corresponding to these two regimes and show that they differ qualitatively. Remarkably, the nonlinear state remains in all cases nearly axisymmetric suggesting that this HMRI-driven turbulence is quasi two-dimensional in nature. Although the contribution of non-axisymmetric modes increases moderately with the Elsasser number, their total energy remains much smaller than that of the axisymmetric ones.

This paper presents a numerical study of the linear and nonlinear evolution of the electromagnetic electron-cyclotron (EMEC) instability in a bi-Kappa distributed plasma. Distributions with high energy tails described by the Kappa power-laws are often observed in collision-less plasmas (e.g., solar wind and accelerators), where wave-particle interactions control the plasma thermodynamics and keep the particle distributions out of Maxwellian equilibrium. Under certain conditions, the anisotropic bi-Kappa distribution gives rise to plasma instabilities creating low-frequency EMEC waves in the whistler branch. The instability saturates nonlinearly by reducing the temperature anisotropy until marginal stability is reached. Numerical simulations of the Vlasov-Maxwell system of equations show excellent agreement with the growth-rate and real frequency of the unstable modes predicted by linear theory. The wave-amplitude of the EMEC waves at nonlinear saturation is consistent with magnetic trapping of the electrons.

The nonlinear evolution of dust waves generated by a low-frequency Hall current instability in a collisional dusty plasma is investigated with theory and nonlinear numerical simulations. The instability is driven by an electron E × B current and is an analog of the well-known Farley–Buneman instability in the dust acoustic type wave regime. This instability is believed to have broad applications to irregularity production in regions where dust is present in the earth’s ionosphere such as noctilucent clouds and meteor trails. The results indicate that the instability nonlinearly saturates with dust heating and the production of secondary waves that propagate in a direction perpendicular to the primary dust acoustic type waves. Results of the investigation also indicate that dust-neutral collisions increase the amplitude of the unstable dust waves after nonlinear saturation. Possible mechanisms for the production of the secondary waves as well as implications of these waves are described.

<p indent="0mm">In this paper, using a recently proposed sharp-interface method for compressible multiphase flows with phase change, we numerically study the Richtmyer-Meshkov instability problem of the vapor-liquid interface, both with and without phase change. The wave structures and the interfacial evolution mechanism of a single-mode sinusoidally perturbed interface under the impact of a shock wave are analyzed. First, the classical air-SF6 interface Richtmyer-Meshkov instability and shock water column interaction are simulated in the paper to validate the feasibility of the numerical method. The numerical simulations and experimental results are generally in good agreement, indicating that the present method can accurately capture the interface flow evolution characteristics during the development of Richtmyer-Meshkov instability. Next, we investigate the similarities and differences in Richtmyer-Meshkov instability at the vapor-liquid interface under thirteen conditions: no phase change, evaporation, and condensation with three different Mach numbers. It is shown that, unlike the air-SF6, a double spike structure is formed during the development of interfacial instability due to the large acoustic impedance difference at the vapor-liquid interface. And the phase change process affects the local deformation of the interface, as the evaporation effect inhibits the development of the interfacial instability, while the condensation effect promotes the development of the interfacial instability. Finally, we compare the numerical simulation data with the existing linear model and find that the impulsive model can predict the linear growth of the early stage, while the nonlinear growth of the later stage will be investigated further.

The three-dimensional nonlinear evolution of moderate wavelength pressure-driven edge-localized instabilities is calculated in divertor tokamaks. The evolution consists of several stages: linear growth, nonlinear saturation and turbulence, shear flow generation, pressure outflow to the outboard divertor, and finally, outflow to the inboard divertor. The shear flow generation appears to be an important factor in transporting pressure perturbations to the inboard side, and in causing pressure loss to the inboard divertor. The physical model consists of dissipative compressional reduced magnetohydrodynamics which includes the important effect of sound wave propagation. A novel numerical discretization, using a poloidal unstructured mesh and a staggered toroidal mesh, has been implemented on a parallel, distributed memory computer. Nonlinear, three-dimensional numerical computations include a separatrix X-point in the computational domain.