Traveling Wave Packets Research Articles

On the generation of near-wall dilatational motions in hypersonic turbulent boundary layers

Dilatational motions in the shape of travelling wave packets have been identified recently to be dynamically significant in hypersonic turbulent boundary layers. The present study investigates the mechanisms of their generation and their association with the solenoidal motions, especially the well-recognized near-wall self-sustaining process of the regeneration cycle between the velocity streaks and quasi-streamwise vortices. By exploiting the direct numerical simulation databases and orchestrating numerical experiments, we explore systematically the near-wall flow dynamics in the processes of the formation and transient growth of low-speed streaks. We conclude via theoretical ansatz that the nonlinearity related to the parallel density and pressure gradients close to the wall due to the restriction of the isothermal boundary condition is the primary cause of the generation of the dilatational structures at small scales. In fully developed turbulence, the formation and the existence of healthy dilatational travelling wave packets require the participation of the turbulence at scales larger than those of the near-wall regeneration cycles, especially the occurrence of the bursting events that generate vortex clusters. This is proven by the less intensified dilatational motions in the numerical experiments in which the Orr mechanism is alleviated and the vortical structures and turbulent bursts are weakened.

Compressibility effects in supersonic and hypersonic turbulent boundary layers subject to wall disturbances

In the present study, we investigate the compressibility effects in supersonic and hypersonic turbulent boundary layers under the influence of wall disturbances by exploiting direct numerical simulation databases at Mach numbers up to 6. Such wall disturbances enforce extra Reynolds shear stress on the wall and induce mean streamline curvature in rough wall turbulence that leads to the intensification of turbulent motions in the outer region. The turbulent and fluctuating Mach numbers, the density and the velocity divergence fluctuation intensities suggest that the compressibility effects are enhanced by the increment of the free-stream Mach number and the implementation of the wall disturbances. The differences between the Reynolds and Favre average due to the density fluctuations constitute approximately $9\,\%$ of the mean velocity close to the wall and $30\,\%$ of the Reynolds stress near the edge of the boundary layer, indicating their non-negligibility in turbulent modelling strategies. The comparatively strong compressive events behaving as eddy shocklets are observed at the free-stream Mach number of $6$ only in the cases with wall disturbances. By further splitting the velocity into the solenoidal and dilatational components with the Helmholtz decomposition, we found that the dilatational motions are organized as travelling wave packets in the wall-parallel planes close to the wall and as forward inclined structures in the form of radiated waves in the vertical planes. Despite their increased magnitudes and higher portion in the Reynolds normal and shear stresses, the dilatational motions show no tendency of contributing significantly to the skin friction and the production of turbulent kinetic energy due to their mitigation by the cross-correlation between the solenoidal and dilatational velocity components.

Wall temperature effects on wall heat flux in high-enthalpy turbulent boundary layers

The wall temperature significantly varies the turbulent statistics and coherent structures in high-speed wall-bounded turbulence under the low-enthalpy condition. The present study set out to investigate whether this is also the case for high-enthalpy turbulent boundary layers that incorporate the chemical reactions of multi-species gas mixture. For that purpose, we perform direct numerical simulations for high-enthalpy turbulent boundary layers at the Mach number of 4.5 and the momentum Reynolds number of 2400 with three groups of wall temperature. Statistical results show that the effects of wall temperature on the mean flow properties are similar to those of low-enthalpy flows, and the chemical reactions only affect the mean temperature without leaving strong impacts on the statistics of velocity. The wall heat flux and the physical processes thereof are further analyzed. The mass diffusion effects are increased by the rising wall temperature due to the more sufficient dissociation of the molecules. The wall heat flux fluctuations are also slightly enhanced, with the lower skewness and the higher kurtosis, and show more prominent structures of traveling wave packets and weaker streaks, as well as the less coherent vortices in the vicinity of the extreme positive wall heat flux events. The organizations of the mass species are also altered substantially by the rising wall temperature due to the stronger impacts of chemical reactions on the flow dynamics.

Nonlinear dynamics of modulated waves on graphene like quantum graphs

AbstractWe consider cubic Klein–Gordon equations on infinite two‐dimensional periodic metric graphs having for instance the form of graphene. At non‐Dirac points of the spectrum, with a multiple scaling expansion Nonlinear Schrödinger (NLS) equations can be derived in order to describe slow modulations in time and space of traveling wave packets. Here we justify this reduction by proving error estimates between solutions of the cubic Klein–Gordon equations and the associated NLS approximations. Moreover, we discuss the validity of the modulation equations appearing by the same procedure at the Dirac points of the spectrum.

Wall heat transfer in high-enthalpy hypersonic turbulent boundary layers

In this paper, we investigate the differences in wall heat transfer between the low- and high-enthalpy turbulent boundary layers by exploiting direct numerical simulation databases of hypersonic turbulent boundary layers at the free-stream Mach number of 4.5 and the friction Reynolds number of 800. For that purpose, we refine the integral formula of decomposing the wall heat flux proposed by Sun et al. [“A decomposition formula for the wall heat flux of a compressible boundary layer,” Adv. Aerodyn. 4, 1–13 (2022)], enabling us to scrutinize the contribution of different physical processes. Statistical results show that the mean wall heat transfer is primarily contributed by the heat conduction, the turbulent heat transfer, viscous dissipation of mean kinetic energy, and turbulent kinetic energy production. Among these processes, the contribution of the turbulent heat flux in the high-enthalpy case is 10% higher than that in the low-enthalpy case. Such discrepancy is caused by the turbulent–chemistry interaction consisting of velocity and species mass fraction fluctuations. Coherent structures in the conditionally averaged fields related to this process reveal that the sweep in the viscous sublayer and ejection in the logarithmic layer bringing the hot fluid downward and upward, respectively, significantly alter the distribution of the species mass fraction. The wall heat flux fluctuations are slightly enhanced in the high-enthalpy flows, which is ascribed to be the intensification of traveling wave packets.

Wall shear stress, pressure, and heat flux fluctuations in compressible wall-bounded turbulence, part I: One-point statistics

This two-part study investigates the effects of Mach number and wall temperature on the statistics of wall shear stress, pressure, and heat flux fluctuations in compressible wall-bounded turbulence. In the first part, we focus on their one-point statistics, including the root mean square (r.m.s.), skewness factor (third-order moment), flatness factor (fourth-order moment), and their correlations. By exploiting the direct numerical simulation databases, we found that the r.m.s. of the streamwise wall shear stress and pressure, the skewness factor of all the flow quantities considered, and the flatness factor of streamwise wall shear stress monotonically vary with the friction Mach number (Mτ), while for the rest, the wall heat flux and global temperature parameters should be taken into account as well for a monotonic trend of variation. The correlation coefficients between wall shear stress, pressure, and heat flux fluctuations increase with the Mach number Mτ, suggesting the underlying interactions between dynamic and thermodynamic processes. The distributions of spectra and probability density functions indicate that the increased correlation is induced by the highly intermittent traveling wave packets among the streaky structures, as reflected by the “double-peak” feature of the spectra that gradually emerges with the increasing compressibility effects. The probability density distribution also manifests the alteration of the occurrence of extreme events caused by these structures. By accordingly decomposing the fluctuations with cutoff filtering, it is found that the root mean squares of streamwise wall shear stress and heat flux fluctuations related to the streaky structures are Mach number-independent, while those related to the traveling wave packets monotonically increase with the friction Mach number.

Wall shear stress, pressure and heat flux fluctuations in compressible wall-bounded turbulence. II. Spectra, correlation and nonlinear interactions

Wall shear stress, pressure, and heat flux are of significant importance in engineering applications. In this two-part study, we investigate the compressibility effects on wall shear stress, pressure, and heat flux fluctuations in compressible wall-bounded turbulence by exploiting direct numerical simulation databases. In Paper I, we primarily deal with the one-point statistics, whereas in this second part, we report the effects of compressibility on the frequency spectra, wavenumber-frequency spectra of these flow quantities, and the two-point cross-correlations between them. It is found that the scaling laws of the spectra at low and high frequencies are retained as those of incompressible flows, whereas the spectra intensities at mid frequencies increase with the enhancement of compressibility effects, which is identified to be related to the ever-predominating traveling wave packets. These wave packets are convected downstream at the same velocity of 0.87Ub as that of pressure fluctuations, higher than that of the streaky structures 0.65Ub (Ub the bulk velocity), and enhance the space and time cross correlation between wall shear stress, pressure, and heat flux fluctuations. By extracting the envelopes of the traveling wave packets and inspecting the time and space correlations between the envelopes and the streaky structures, we found that the emergence of traveling wave packets comes later than the streaky structures, both in time and space. Based on these observations, we provide a depiction of the physical processes regarding the formation and evolution of the traveling wave packets.

A Variety of New Traveling Wave Packets and Conservation Laws to the Nonlinear Low-Pass Electrical Transmission Lines via Lie Analysis

This research is based on computing the new wave packets and conserved quantities to the nonlinear low-pass electrical transmission lines (NLETLs) via the group-theoretic method. By using the group-theoretic technique, we analyse the NLETLs and compute infinitesimal generators. The resulting equations concede two-dimensional Lie algebra. Then, we have to find the commutation relation of the entire vector field and observe that the obtained generators make an abelian algebra. The optimal system is computed by using the entire vector field and using the concept of abelian algebra. With the help of an optimal system, NLETLs convert into nonlinear ODE. The modified Khater method (MKM) is used to find the wave packets by using the resulting ODEs for a supposed model. To represent the physical importance of the considered model, some 3D, 2D, and density diagrams of acquired results are plotted by using Mathematica under the suitable choice of involving parameter values. Furthermore, all derived results were verified by putting them back into the assumed equation with the aid of Maple software. Further, the conservation laws of NLETLs are computed by the multiplier method.

Transient aspects of the Hadley circulation forced by an idealized off‐equatorial ITCZ

AbstractThis paper presents analytical solutions of large‐scale, zonally symmetric overturning circulations in the tropical free troposphere forced by transient diabatic heating in the off‐equatorial intertropical convergence zone (ITCZ). The dynamics are discussed in the context of the time‐dependent meridional circulation equation arising in an equatorial β‐plane model. The solutions of these differential equations contain terms for the slow, quasi‐balanced part of the response and terms for the transient, zonally symmetric, inertia‐gravity wave part of the response. When the off‐equatorial (north of the equator) ITCZ diabatic heating is switched on at various rates, both parts of the response reveal a basic asymmetry between the southern and northern hemispheres, with the southern hemisphere side containing most of the quasi‐balanced compensating subsidence and transient inertia‐gravity wave activity. The inertia‐gravity waves travel in wave packets that bounce off a spectrum of turning latitudes and are analyzed in the context of an average conservation law approach. These traveling wave packets cause the mass flux in the southern and northern Hadley cells to pulsate on timescales of about 1, 2, and 3 days for diabatic heating of the external, first internal, and second internal vertical modes, respectively. The spectral characteristics of the vertical motion in the ITCZ and subsidence regions are slightly more complicated and depend on ITCZ location.

Atomic wave packets in amplitude-modulated vertical optical lattices

We report on the realization of dynamical control of transport for ultra-cold 88Sr atoms loaded in an accelerated amplitude-modulated one-dimensional (1D) optical lattice. We show that the behavior of the dynamical system can be viewed as if traveling wave packets were moving in a static lattice whose energy dispersion can be tailored at will in width, amplitude and phase. One basic control operation is a reversible switch between Wannier–Stark localization and driven transport based on coherent tunneling. Performing modulation sequences of this operation within a Loschmidt-echo scheme, we are able to reverse the atomic group velocities at once. We then apply the technique to demonstrate a novel mirror for matter waves working independently of the momentum state. We finally discuss advantages of amplitude over previously reported phase modulation techniques for applications in force measurements at micrometric scales.

Travelling wave packets generated by the solar terminator in the upper atmosphere

For the first time, the morphology of a new type of midlatitude, medium scale, travelling ionospheric disturbances—travelling wave packets (TWPs)—is presented with the use of total electron content (TEC) measurements from the data of a global net of GPS receivers over a long time period from 1998 to 2007. The total amount of registered TWPs exceeds 275 000. In the context of time, TWPs are narrow-band TEC oscillations of an hour length with a period of about 10–20 min. TWPs are predominantly observed within 3 h after passing the morning solar terminator, when the TEC derivatives reach their maximum.

MHD nature of ionospheric wave packets generated by the solar terminator

We obtained the first experimental evidence for the magnetohydrodynamic (MHD) nature of ionospheric medium-scale travelling wave packets (MSTWP). We used data on total electron content (TEC) measurements obtained at the dense Japanese network GPS/GEONET (1220 stations) in 2008-2009. We found that the diurnal, seasonal and spectral MSTWP characteristics are specified by the solar terminator (ST) dynamics. MSTWPs are the chains of narrow-band TEC oscillations with single packet's duration of about 1-2 hours and oscillation periods of 10-20 minutes. Their total duration is about 4--6 hours. The MSTWP spatial structure is characterized by a high degree of anisotropy and coherence at the distance of more than 10 wavelengths. The MSTWP direction of travelling is characterized by a high directivity regardless of seasons. Occurrence rate of daytime MSTWPs is high in winter and during equinoxes. Occurrence rate of nighttime MSTIDs has its peak in summer. These features are consistent with previous MS travelling ionosphere disturbance (TID) statistics obtained from 630-nm airglow imaging observations in Japan. In winter, MSTWPs in the northern hemisphere are observed 3-4 hours after the morning ST passage. In summer, MSTWPs are detected 1.5-2 hours before the evening ST occurrence at the point of observations, at the moment of the evening ST passage in the magneto-conjugate point. Both the high Q-factor of oscillatory system and synchronization of MSTWP occurrence with the solar terminator passage at the point of observations and in the magneto-conjugate area testify the MHD nature of ST-excited MSTWP generation. The obtained results are the first experimental evidence for the hypothesis of the ST-generated ion sound waves.

Algebraically decaying modes and wave packet pseudo-modes in swept Hiemenz flow

The modal structure of the swept Hiemenz flow, a model for the flow near the attachment line of a swept wing, consists of eigenfunctions which exhibit (super-)exponential or algebraic decay as the wall-normal coordinate tends to infinity. The subset of algebraically decaying modes corresponds to parts of the spectrum which are characterized by a significant sensitivity to numerical discretization. Numerical evidence further suggests that a continuous spectrum covering a two-dimensional range of the complex plane exists. We investigate the family of uniform swept Hiemenz modes using eigenvalue computations, numerical simulations and the concept of wave packet pseudo-modes. Three distinct branches of the family of algebraically decaying eigenmodes are identified. They can be superimposed to produce wavefronts propagating towards or away from the boundary layer and standing or travelling wave packets in the free stream. Their role in the exchange of information between the free stream and the attachment-line boundary layer for the swept Hiemenz flow is discussed. The concept of wave packet pseudo-modes has been critical in the analysis of this problem and is expected to lead to further insights into other shear flows in semi- or bi-infinite domains.

Spatiotemporal evolution of Poiseuille-Rayleigh-Bénard flows in binary fluids with Soret effect under initial pulselike disturbances

The spatiotemporal evolution of Poiseuille-Rayleigh-Bénard flows in binary fluids with Soret effect is investigated by carrying out fully nonlinear two-dimensional numerical simulations initiated by a pulselike disturbance. The traveling wave packets for positive as well as negative separation factors psi are obtained numerically for ethanol-water-like mixtures (Prandtl number Pr=10 , Lewis number Le=0.01) and selected combinations of Rayleigh and Reynolds numbers at psi=0.01, 0.1 and psi=-0.1. The characteristics of the wave fronts and the transitions observed between absolute and convective instabilities when changing the parameters are compared with the results previously obtained by linear spatiotemporal stability analysis. The simulations are in very good agreement with the stability results, which confirms the validity of both approaches. Finally, in order to characterize the possible interaction between the two wave packets of the so-called downstream and upstream modes for psi<0, the spatiotemporal stability analysis is used to detect a boundary curve in the (Re, Ra) parameter region beyond which the two wave packets will never completely separate. Numerical simulations illustrate the different evolutions of the wave packets on both sides of this boundary.

Spatio-temporal structure of the wave packets generated by the solar terminator

Using long-term (1998--2009) total electron content (TEC) measurements from the GPS global network including dense network of GPS sites in USA and Japan, we have obtained the first data regarding the spatio-temporal structure and the statistics of medium-scale traveling wave packets (MS TWPs) excited by the solar terminator (ST). Total amount of the detected TWPs exceeds 565,000. There is no correlation between TWPs occurrence and geomagnetic and solar activity. We found that the diurnal, seasonal and spectral MS TWPs characteristics are specified by the solar terminator (ST) dynamics. MS TWPs are the chains of narrow-band TEC oscillations with single packet’s duration of about 1–2 h and oscillation periods of 10–20 min. The total duration of chain is about 4–6 h. The MS TWPs spatial structure is characterized by a high degree of anisotropy and coherence at the distance of more than 10 wavelengths. Occurrence rate of daytime MS TWPs is high in winter and during equinoxes. Occurrence rate of nighttime MS TWPs has its peak in summer. These features are consistent with previous MS travelling ionosphere disturbance (TID) statistics obtained from 630-nm airglow imaging observations in Japan. In winter, MS TWPs in the northern hemisphere are observed 3–4 h after the morning ST passage. In summer, MS TWPs are detected 1.5–2 h before the evening ST appearance at the point of observations, but at the moment of the evening ST passage in the magneto-conjugate point. The obtained results are the first experimental evidence for the hypothesis of the ST-generated ion sound waves.

The first GPS-TEC imaging of the space structure of MS wave packets excited by the solar terminator

Abstract. Using TEC measurements from the dense network of GPS sites GEONET, we have obtained the first GPS-TEC image of the space structure of medium-scale traveling wave packets (MS TWP) excited by the morning solar terminator (ST). We found that ST-generated wave packets have duration of about 1–2 h and time shift of about 1.5–6 h after the morning ST appearance at an altitude of 300 km. The TWP wave front extends along the morning ST line with the angular shift of about 20°. The time period and wave-length of ST-generated wave packets are about 10–20 min and 200–300 km, respectively. The velocity of the TWP phase front traveling is of about 300 m/s. The space image of MS TWP manifests itself in pronounced anisotropy and high coherence over a long distance of about 2000 km.

Controlled quantum-state transfer in a spin chain

Control of the transfer of quantum information encoded in quantum wave packets moving along a spin chain is demonstrated. Specifically, based on a relationship with control in a paradigm of quantum chaos, it is shown that wave packets with slow dispersion can automatically emerge from a class of initial superposition states involving only a few spins, and that arbitrary unspecified traveling wave packets can be nondestructively stopped and later relaunched with perfection. The results establish an interesting application of quantum chaos studies in quantum information science.

Publisher's Note: Controlling the capture dynamics of traveling wave packets into a quantum dot [Phys. Rev. B73, 125334 (2006)

Publisher's Note: Controlling the capture dynamics of traveling wave packets into a quantum dot [Phys. Rev. B<b>73</b>, 125334 (2006)

Controlling the capture dynamics of traveling wave packets into a quantum dot

An analysis of the control of capture processes from a traveling wave packet in a semiconductor quantum wire into localized states of a quantum dot is presented. On ultrafast time scales this capture in general leads to occupations of the discrete states as well as to coherences among these states. We show that both occupations and coherences can be efficiently controlled by excitation with a pair of spatially localized laser pulses which are spatially, temporally, or spectrally displaced with respect to each other. The coherences between discrete dot states are controlled by spatially nonoverlapping pulses by varying either their spatial or their temporal displacement. For spatially overlapping pulses an effective pulse shaping occurs which modifies both occupations and coherences. By using two-color laser pulses the dot states can be selectively addressed which may result in particularly pronounced coherences.

Thermal escape and capture processes in quantum wire–dot structures

We study the dynamics of an electronic wave packet in a quantum wire with an embedded quantum dot interacting with an LO-phonon bath at room temperature. Two different cases are studied: in the first scenario (escape scenario), we determine the probability for the electrons to leave the dot by absorption of an LO-phonon. In the second scenario (capture and escape scenario), we study the capture process from the delocalized states of the wire into the localized states of the dot accompanied by re-emission into the delocalized states. These scenarios are analysed by using a quantum kinetic theory for the electron LO-phonon interaction. The thermal escape scenario shows a continuous flow of density directed with equal probabilities to both sides from the dot accompanied by small oscillations in the density of bound carriers. For the capture and escape scenario, we find an interplay between thermal escape and a coherent escape process, the latter being present even at zero temperature. In the coherent escape, a part of the captured density re-escapes and forms additional travelling wave packets following the original wave packet.