Direction Of Inhomogeneity Research Articles

Transient energy transfer and cascade analysis for stratified turbulent channel flows

A comprehensive and fine-grained transient analysis of the kinetic budget equation in the spectral and spatial domains for channel flow subjected to stable stratification is performed, through a series of large eddy simulations (LES) at a bulk Reynolds number of 2200 and for Froude numbers of 0.5, 2.0, 4.5 and 6.8, thereby covering a range of stratification strengths from high to low. The dynamic Smagorinsky eddy viscosity-based sub-grid scale (SGS) model is used for closure. Validation of the methodology is carried out by comparing the turbulent flow LES results to previously published channel flow results. The analysis is focussed on the effect of stratification on the energy cascade process of an initially turbulent flow in a channel configuration. The terms in the kinetic budget equation, in the homogeneous and inhomogeneous directions, are compared for different Froude numbers to assess the effects of weak and strong stratification on turbulent statistics. Transient results are plotted to highlight the role played by different terms in the budget equation and to understand the formation of the gravity waves in the core or outer regions of the wall-bounded flow in the presence of stratification. The energy cascade reveals some interesting observations about the functions of viscous diffusion, pressure diffusion, and inhomogeneous energy transfer in the initial phase of the development of flow, which in turn helps to explain the stationary waves observed in the presence of strong stratification.

Rayleigh Waves Propagating in the Functionally Graded One-Dimensional Hexagonal Quasicrystal Half-Space

For the manufacturing and optimization of quasicrystal structures, Rayleigh waves propagating in the functionally graded one-dimensional hexagonal quasicrystal half-space are investigated. The analytical Laguerre orthogonal polynomial method is employed to solve dynamic equations of wave motion, which greatly improves the computational efficiency. Dispersion curves and displacement distributions are illustrated. The influences of the phonon–phason coupling effect, inhomogeneity, and quasiperiodic direction on wave characteristics are analyzed. Some new results are obtained: (1) Compared with the classical Laguerre polynomial method, the improvement in computational efficiency of the analytical Laguerre polynomial method is more than 99%. (2) The energy penetration depth of phason modes is greater than that of phonon modes. The results lay a theoretical foundation for designing and optimizing SAW devices.

Giant overreflection of magnetohydrodynamic waves from inhomogeneous plasmas with nonuniform shear flows

We theoretically study mode conversion and resonant overreflection of magnetohydrodynamic waves in an inhomogeneous plane-stratified plasma in the presence of a nonuniform shear flow using precise numerical calculations of the reflection and transmission coefficients and the field distributions based on the invariant imbedding method. Cases where the flow velocity and the external magnetic field are directed perpendicularly to the inhomogeneity direction and both the flow velocity and the plasma density vary arbitrarily along it are considered. When there is a shear flow, the wave frequency is modulated locally by the Doppler shift, and resonant amplification and overreflection occur where the modulated frequency is negative and its absolute value matches the local Alfvén or slow frequency. For many different types of the density and flow velocity profiles, we find that, especially when the parameters are such that the incident waves are totally reflected, there arises a giant overreflection where the reflectance is much larger than 10 in a fairly broad range of the incident angles, the frequency, and the plasma β, and its maximum attains values larger than 105. In a finite β plasma, both incident fast and slow magnetosonic waves are found to cause strong overreflection and there appear multiple positions exhibiting both Alfvén and slow resonances inside the plasma. We explain the mechanism of overreflection in terms of the formation of inhomogeneous and open cavities close to the resonances and the strong enhancement of the wave energy due to the occurrence of semi-bound states there. We discuss the observational consequences in magnetized terrestrial and solar plasmas.

Three-dimensional propagation of kink wave trains in solar coronal slabs

ABSTRACT Impulsively excited wave trains are of considerable interest in solar coronal seismology. To our knowledge, however, it remains to examine the three-dimensional (3D) dispersive propagation of impulsive kink waves in straight, field-aligned, symmetric, low-beta, slab equilibria that are structured only in one transverse direction. We offer a study here, starting with an analysis of linear oblique kink modes from an eigenvalue problem perspective. Two features are numerically found for continuous and step structuring alike, one being that the group and phase velocities may lie on opposite sides of the equilibrium magnetic field ($\boldsymbol {B}_0$), and the other being that the group trajectories extend only to a limited angle from $\boldsymbol {B}_0$. We justify these features by making analytical progress for the step structuring. More importantly, we demonstrate by a 3D time-dependent simulation that these features show up in the intricate interference patterns of kink wave trains that arise from a localized initial perturbation. In a plane perpendicular to the direction of inhomogeneity, the large-time slab-guided patterns are confined to a narrow sector about $\boldsymbol {B}_0$, with some wavefronts propagating toward $\boldsymbol {B}_0$. We conclude that the phase and group diagrams lay the necessary framework for understanding the complicated time-dependent behaviour of impulsive waves.

Ascending–descending and direct–inverse cascades of Reynolds stresses in turbulent Couette flow

The interaction between small- and large-scale structures and the coexisting bottom-up and top-down processes are studied in a turbulent plane Couette flow, where space-filling longitudinal rolls appear at relatively low values of the Reynolds number $Re$ . A direct numerical simulation database at $Re_\tau =101$ is built to replicate the highest $Re$ considered in recent experimental work by Kawata & Alfredsson (Phys. Rev. Lett., vol. 120, 2018, 244501). Our study is based on the exact budget equations for the second-order structure function tensor $\left \langle {\delta u_i \delta u_j} \right \rangle$ , i.e. the anisotropic generalized Kolmogorov equations (AGKE). The AGKE study production, redistribution, transport and dissipation of every Reynolds stress tensor component, considering simultaneously the physical space and the space of scales, and properly define the concept of scale in the inhomogeneous wall-normal direction. We show how the large-scale energy-containing motions are involved in the production and redistribution of the turbulent fluctuations. Both bottom-up and top-down interactions occur, and the same is true for direct and inverse cascading. The wall-parallel components $\left \langle {\delta u \delta u} \right \rangle$ and $\left \langle {\delta w \delta w} \right \rangle$ show that both small and large near-wall scales feed the large scales away from the wall. The wall-normal component $\left \langle {\delta v \delta v} \right \rangle$ is different, and shows a dominant top-down dynamics, being produced via pressure-strain redistribution away from the wall and transferred towards near-wall larger scales via an inverse cascade. The off-diagonal component shows a top-down interaction, with both direct and inverse cascades, albeit the latter takes place within a limited range of scales.

Shooting method for linear inviscid bi-global stability analysis of non-axisymmetric jets

The shooting method is commonly used to solve the linear parallel-flow stability problem for axisymmetric jets, i.e., a flow having one inhomogeneous direction. The present extension to two inhomogeneous directions – i.e., a bi-global stability problem – is motivated by inviscid non-axisymmetric jets. The azimuthal direction is Fourier transformed to obtain a set of coupled one-dimensional shooting problems that are solved by two-way integration from both radial boundaries – centreline and far field. The overall problem is formulated as one of iterative root-finding to match the solutions from the two integrations. The approach is validated against results from the well-established matrix method that discretizes the domain to obtain a matrix eigenvalue problem. We demonstrate very good agreement in two jet problems – an offset dual-stream jet, and a jet exiting from a nozzle with chevrons. A disadvantage of the shooting method is its sensitivity to the initial guess of the solution; however, this becomes an advantage when the need arises to track an eigensolution in a sweep over a problem parameter – say with increasing offset in the dual-stream jet, or with downstream distance from the nozzle exit. We demonstrate the performance of the shooting method in such tracking tasks.

Analysis of the instabilities induced by an isolated roughness element in a laminar high-speed boundary layer

Abstract

Physical Origin of Short Scale Plasma Structures in the Auroral F Region

AbstractThe drift instability in the auroral F region of the ionosphere is known to create long scale finger like plasma structures in the presence of a density inhomogeneity and an ambient electric field. These structures elongate mainly along the density inhomogeneity direction. In situ measurements as well as scattering experiments have also revealed the existence of small scale structures in this region. The authors propose that such structures are created due to the breakup of the long scale structures on account of their differential stretching from sheared electric fields. Using heuristic physical arguments and dimensional analysis the authors derive a general criterion for the onset of such breakups. The analytic results are validated from numerical simulations of the full set of basic nonlinear equations describing the instability and should prove useful in the prediction and interpretation of the spread F in the high latitude region.

Structure function tensor equations in inhomogeneous turbulence

Exact budget equations for the second-order structure function tensor ⟨𝛿u$_{i}$𝛿u$_{j}$⟩, where 𝛿u is the difference of the i th fluctuating velocity component between two points, are used to study the two-point statistics of velocity fluctuations in inhomogeneous turbulence. The anisotropic generalised Kolmogorov equations (AGKE) describe the production, transport, redistribution and dissipation of every Reynolds stress component occurring simultaneously among different scales and in space, i.e. along directions of statistical inhomogeneity. The AGKE are effective to study the inter-component and multi-scale processes of turbulence. In contrast to more classic approaches, such as those based on the spectral decomposition of the velocity field, the AGKE provide a natural definition of scales in the inhomogeneous directions, and describe fluxes across such scales too. Compared to the generalised Kolmogorov equation, which is recovered as their half-trace, the AGKE can describe inter-component energy transfers occurring via the pressure–strain term and contain also budget equations for the off-diagonal components of ⟨𝛿u$_{i}$𝛿u$_{j}$⟩. The non-trivial physical interpretation of the AGKE terms is demonstrated with three examples. First, the near-wall cycle of a turbulent channel flow at a friction Reynolds number of Re$_{𝜏}$ = 200 is considered. The off-diagonal component ⟨-𝛿u𝛿υ⟩, which cannot be interpreted in terms of scale energy, is discussed in detail. Wall-normal scales in the outer turbulence cycle are then discussed by applying the AGKE to channel flows at Re$_{𝜏}$ = 500 and 1000. In a third example, the AGKE are computed for a separating and reattaching flow. The process of spanwise-vortex formation in the reverse boundary layer within the separation bubble is discussed for the first time.

Time-dependent study of anisotropy in Rayleigh-Taylor instability induced turbulent flows with a variety of density ratios

This study focuses on understanding the time-dependent anisotropy, mixing, scaling of flows induced by Rayleigh-Taylor instability, and complementing the late-time snapshots reported by Cabot and Zhou [“Statistical measurements of scaling and anisotropy of turbulent flows induced by Rayleigh-Taylor instability,” Phys. Fluids 25, 015107 (2013)]. In particular, we utilize three large datasets with different Atwood numbers (density ratios) from well resolved direct numerical simulations at a moderate Reynolds number with the goal of determining the degree of departure of this inhomogeneous flow from that of homogeneous, isotropic turbulence. Three key time-dependent statistical measurements are considered in detail to delineate the role played by the acceleration. First, a number of directional length scales in this anisotropic turbulence are inspected. Second, the relationship among the outer-scale, the turbulence length, and the Taylor-microscale based Reynolds numbers is also clarified. Finally, the normalized dissipation rate is employed to inspect the distinctive features of the flow in the inhomogeneous direction parallel to gravity and in the homogeneous perpendicular directions.

Stability and receptivity of boundary layers in a swirl flow channel

The analysis of the disturbances on a spiraling base flow is relevant for the design, operation, and control of technological devices such as parallel-disk turbines and swirl flow channel heat sinks. Spiraling inflow inside an annular cavity closed at the top and bottom is analyzed in the framework of modal and nonmodal stability theories. Local and parallel flow approximations are applied, and the inhomogeneous direction is discretized using the Chebyshev collocation method. The optimal growth of initial disturbances and the optimal response to external harmonic forcing are characterized by the exponential and the resolvent of the dynamics matrix. As opposed to plane Poiseuille flow, transient growth is small, and consequently, it does not play a role in the transition mechanism. The transition is attributed to a crossflow instability that occurs because of the change in the shape of the velocity profile due to rotational effects. Agreement is found between the critical Reynolds number predicted in this work and the deviation of laminar behavior observed in the experiments conducted by Ruiz and Carey (J Heat Transfer 137(7):071702, 2015). For the harmonically driven problem, an energy amplification of $$\textit{O}(100)$$ is observed for spiral crossflow waves. Transition to turbulence should be avoided to ensure the safe operation of a parallel-disk turbine, whereas large forcing amplification may be sought to promote mixing in a swirl flow channel heat sink. The analysis presented predicts and provides insight into the transition mechanisms. Due to its easy implementation and low computational cost, it is particularly useful for the early stages of engineering design.

Lattice black branes: sphere packing in general relativity

We perturbatively construct asymptotically {mathrm{mathbb{R}}}^{1,3}times {mathbb{T}}^2 black branes with multiple inhomogeneous directions and show that some of them are thermodynamically preferred over uniform branes in both the microcanonical and canonical ensembles. This demonstrates that, unlike five-dimensional black strings, the instability of some unstable black branes has a plausible endpoint that does not require a violation of cosmic censorship.

Analytical method for analysis of electromagnetic scattering from inhomogeneous spherical structures using duality principles.

In this article, an analytical approach is presented for the analysis of electromagnetic (EM) scattering from radially inhomogeneous spherical structures (RISSs) based on the duality principle. According to the spherical symmetry, similar angular dependencies in all the regions are considered using spherical harmonics. To extract the radial dependency, the system of differential equations of wave propagation toward the inhomogeneity direction is equated with the dual planar ones. A general duality between electromagnetic fields and parameters and scattering parameters of the two structures is introduced. The validity of the proposed approach is verified through a comprehensive example. The presented approach substitutes a complicated problem in spherical coordinate to an easy, well posed, and previously solved problem in planar geometry. This approach is valid for all continuously varying inhomogeneity profiles. One of the major advantages of the proposed method is the capability of studying two general and applicable types of RISSs. As an interesting application, a class of lens antenna based on the physical concept of the gradient refractive index material is introduced. The approach is used to analyze the EM scattering from the structure and validate strong performance of the lens.

Visco-instability of shear viscoelastic collisional dusty plasma systems

In this paper, the stability of Newtonian and non-Newtonian viscoelastic collisional shear-velocity dusty plasmas is studied, using the framework of a generalized hydrodynamic (GH) model. Motivated by Banerjeeet al.’s work (Banerjeeet al.,New J. Phys., vol. 12 (12), 2010, p. 123031), employing linear perturbation theory as well as the local approximation method in the inhomogeneous direction, the dispersion relations of the Fourier modes are obtained for Newtonian and non-Newtonian dusty plasma systems in the presence of a dust–neutral friction term. The analysis of the obtained dispersion relation in the non-Newtonian case shows that the inhomogeneous viscosity force depending on the velocity shear profile can be the genesis of a free energy source which leads the shear system to be unstable. Study of the dust–neutral friction effect on the instability of the considered systems using numerical analysis of the dispersion relation in the Newtonian case demonstrates that the maximum growth rate decreases considerably by increasing the collision frequency in the hydrodynamic regime, while this reduction can be neglected in the kinetic regime. Results show a more significant stabilization role of the dust–neutral friction term in the non-Newtonian cases, through decreasing the maximum growth rate at any fixed wavenumber and construction of the instable wavenumber region. The results of the present investigation will greatly contribute to study of the time evolution of viscoelastic laboratory environments with externally applied shear; where in these experiments the dust–neutral friction process can play a considerable role.

Turbulent energy density in scale space for inhomogeneous turbulence

The energy spectrum is commonly used to describe the scale dependence of the turbulent fluctuations in homogeneous isotropic turbulence. In contrast, one-point statistical quantities, such as the turbulent kinetic energy, are employed for inhomogeneous turbulence modelling. To obtain a better understanding of inhomogeneous turbulence, some attempts have been made to describe its scale dependence by using the second-order structure function and the two-point velocity correlation. However, previous expressions for the energy density in the scale space do not satisfy the requirement that it should be non-negative. In this work, a new expression for the energy density in the scale space is proposed on the basis of the two-point velocity correlation; the integral with a filter function is introduced to satisfy the non-negativity of the energy density. Direct numerical simulation (DNS) data of homogeneous isotropic turbulence were first used to assess the role of the energy density by comparing it with the energy spectrum. DNS data of a turbulent channel flow were then used to investigate the energy density and its transport equation in inhomogeneous turbulence. It was shown that the new energy density is positive in the scale space of the homogeneous direction. The energy transfer was successfully examined in the scale space both in the homogeneous and inhomogeneous directions. The energy cascade from large to small scales was clearly observed. Moreover, the inverse energy cascade from large to very large scales was observed in the scale space of the spanwise direction.

Resonant absorption of electromagnetic waves in transition anisotropic media.

We study the mode conversion and resonant absorption phenomena occurring in a slab of a stratified anisotropic medium, optical axes of which are tilted with respect to the direction of inhomogeneity, using the invariant imbedding theory of wave propagation. When the tilt angle is zero, mode conversion occurs if the longitudinal component of the permittivity tensor, which is the one in the direction of inhomogeneity in the non-tilted case, varies from positive to negative values within the medium, while the transverse component plays no role. When the tilt angle is nonzero, the wave transmission and absorption show an asymmetry under the sign change of the incident angle in a range of the tilt angle, while the reflection is always symmetric. We calculate the reflectance, the transmittance and the absorptance for several configurations of the permittivity tensor and find that resonant absorption is greatly enhanced when the medium from the incident surface to the resonance region is hyperbolic than when it is elliptic. For certain configurations, the transmittance and absorptance curves display sharp peaks at some incident angles determined by the tilt angle.

Terahertz waves propagation through an inhomogeneous collisional magnetized plasma slab

Propagation of terahertz waves through an inhomogeneous collisional magnetized plasma layer is studied. The plasma has bell-like electron density distributions, but collision frequency is constant. The transmission, reflection and absorption of s-polarized wave obliquely incident on the plasma slab, are found using the impedance matching method. Here the external magnetic field is uniform and its direction is perpendicular to inhomogeneity direction and parallel with the plasma surface. The effects of the incident wave characteristics, such as frequency of the electromagnetic wave and its incident angle, and plasma parameters, such as the inhomogeneity coefficient, cyclotron frequency and collision frequency on transmission, reflection and absorption are investigated.

Heisenberg-Euler effective action in slowly varying electric field inhomogeneities of Lorentzian shape

We use a locally constant field approximation (LCFA) to study the one-loop Heisenberg-Euler effective action in a particular class of slowly varying inhomogeneous electric fields of Lorentzian shape with $0\leq d\leq 4$ inhomogeneous directions. We show that for these fields, the LCFA of the Heisenberg-Euler effective action can be represented in terms of a single parameter integral, with the constant field effective Lagrangian with rescaled argument as integration kernel. The imaginary part of the Heisenberg-Euler effective action contains information about the instability of the quantum vacuum towards the formation of a state with real electrons and positrons. Here, we in particular focus on the dependence of the instantaneous vacuum decay rate on the dimension $d$ of the field inhomogeneity. Specifically for weak fields, we find an overall parametric suppression of the effect with $(E_0/E_{\rm cr})^{d/2}$, where $E_0$ is the peak field strength of the inhomogeneity and $E_{\rm cr}$ the critical electric field strength.

Heterogeneous creep behavior of a CrMoV multi-pass weld metal

Effect of inhomogeneous microstructure of a CrMoV multi-pass weld metal on creep behavior was investigated experimentally. Four subzones in the multi-pass weld metal were identified in terms of the grain size and morphology. Compared to the micro-hardness and tensile strength, a remarkable different creep behavior was achieved for different subzones. Especially, the heterogeneous creep deformation was observed during the tertiary creep stage. Such a heterogeneous creep behavior of multi-pass weld metal was ascribed to the coupling effect of inhomogeneous microstructure and loading direction.

An inhomogeneous direction selective map in the superior colliculus

An inhomogeneous direction selective map in the superior colliculus