Characteristic Wave Amplitudes Research Articles

Amplitudes of characteristic waves and non-reflecting outflow conditions for high-fidelity numerical simulations

Non-reflecting boundary conditions are crucial for aeroacoustic simulations to prevent non-physical reflections at boundaries from contaminating the interior acoustic solutions. Various non-reflecting outflow conditions, mainly based on the characteristic theory, have been developed. By using a locally one-dimensional inviscid approximation, the characteristic wave amplitudes are identified as the projection of flow solutions into the eigenspace of the flux Jacobian matrix. When the weighted transverse terms are included, the definitions are essentially changed and produce different levels of non-physical reflections. This study aims to resolve the ambiguity in defining the amplitudes of characteristic waves. A new analysis in the frequency and wave number domain is proposed to identify the characteristic wave amplitudes in multidimensional space, and a second order in terms of the lateral wave number non-reflecting outflow condition that is more physically reasonable is derived. Numerical experiments are carried out to evaluate the performances of these non-reflecting conditions.

A categorization of marginally stable thermoacoustic modes based on phasor diagrams

Phasor diagrams are utilized to plot and analyze thermoacoustic modes in a duct with ideal closed/open acoustic boundary conditions that contains a velocity-sensitive flame. Inspection of phasor diagrams that represent fluctuations of velocity, pressure, heat release rate and characteristic wave amplitudes at the flame elicits characteristic features of marginally stable, intrinsic thermoacoustic (ITA) modes: the sign of velocity fluctuations and the sign of the gradient of pressure fluctuations change across the flame. These sign changes result from a reversal of direction of the velocity phasor across the flame, affected by unsteady heat release exactly out-of-phase with respect to upstream velocity fluctuations and of sufficient strength. Unlike alternative methods proposed for the identification of ITA modes, the proposed categorization does not involve a parameter sweep, but relies on an analogy with the structure of ITA modes in an anechoic environment. The phasor diagram also elucidates that continuous transitions from acoustic to ITA modes and vice versa can be achieved by an increase or decrease of the gain of the flame transfer function. The representation of acoustic wave propagation in terms of phasors facilitates the formulation of a compact dispersion relation of the thermoacoustic configuration under consideration. The value of the transitional gain of the flame transfer function, where acoustic/ITA transitions occur, may be deduced easily from the dispersion relation. A plot of solution branches of acoustic and ITA modes illustrates how the respective mode transitions, and how they can be related to the well-known quarter wave modes of a closed/open resonator. It is observed that under variation of transfer function gain and phase, marginally stable eigenmodes may occur at almost any frequency, not only at frequencies that correspond to the quarter-wave modes.

Ion-scale Electromagnetic Waves in the Inner Heliosphere

Understanding the physical processes in the solar wind and corona which actively contribute to heating, acceleration, and dissipation is a primary objective of NASA's Parker Solar Probe (PSP) mission. Observations of coherent electromagnetic waves at ion scales suggests that linear cyclotron resonance and non-linear processes are dynamically relevant in the inner heliosphere. A wavelet-based statistical study of coherent waves in the first perihelion encounter of PSP demonstrates the presence of transverse electromagnetic waves at ion resonant scales which are observed in 30-50\% of radial field intervals. Average wave amplitudes of approximately 4 nT are measured, while the mean duration of wave events is of order 20 seconds; however long duration wave events can exist without interruption on hour-long timescales. Though ion scale waves are preferentially observed during intervals with a radial mean magnetic field, we show that measurement constraints, associated with single spacecraft sampling of quasi-parallel waves superposed with anisotropic turbulence, render the measured quasi-parallel ion-wave spectrum unobservable when the mean magnetic field is oblique to the solar wind flow; these results imply that the occurrence of coherent ion-scale waves is not limited to a radial field configuration. The lack of strong radial scaling of characteristic wave amplitudes and duration suggests that the waves are generated {\em{in-situ}} through plasma instabilities. Additionally, observations of proton distribution functions indicate that temperature anisotropy may drive the observed ion-scale waves.

Nonlinear Rossby Wave–Wave and Wave–Mean Flow Theory for Long-term Solar Cycle Modulations

Abstract The Schwabe cycle of solar activity exhibits modulations and frequency fluctuations on slow timescales of centuries and millennia. Plausible physical explanations for the cause of these long-term variations of the solar cycle are still elusive, with possible theories including stochasticity of the alpha effect and fluctuations of the differential rotation. It has been suggested recently in the literature that there exists a possible relation between the spatiotemporal structure of the solar cycle and the nonlinear dynamics of magnetohydrodynamic (MHD) Rossby waves at the solar tachocline, including both wave–wave and wave–mean flow interactions. Here we extend the nonlinear theory of MHD Rossby waves presented in a previous article to take into account long-term modulation effects due to a recently discovered mechanism that allows significant energy transfers throughout different wave triads: the precession resonance mechanism. We have found a large number of Rossby–Hauwirtz wave triads whose frequency mismatches are compatible with the solar cycle frequency. Consequently, by analyzing the reduced dynamics of two triads coupled with a single mode (five-wave system), we have demonstrated that in the amplitude regime in which precession resonance occurs, the energy transfer throughout the system yields significant long-term modulations on the main ∼11 yr period associated with intratriad energy exchanges. We further show that such modulations display an inverse relationship between the characteristic wave amplitude and the period of intratriad energy exchanges, which is consistent with the Waldmeier law for the solar cycle. In the presence of a constant forcing and dissipation, the five-wave system in the precession resonance regime exhibits irregular amplitude fluctuations, with some periods resembling the grand minimum states.

A Comparison Research into Characteristic Waves of the Well Hole II Interface Cement Part Missing Sound Field

Due to construction process and gravity, it forms a part missing in the cased hole cement ring during cementing. For example, in a vertical well, it often forms sector missing parallel to the well axis, or it forms bow missing in the upper layer cement ring of the horizontal well. These part missing are different from traditional cement ring circumferential missing. Study on the relationship between the II interface characteristic wave amplitude and the missing angle in the vertical well or the bow missing in the cement ring upper layer of the horizontal well. It shows that the larger the amount of part loss, the larger the first wave amplitude, which is equivalent to the thickness of the water layer in the circumferential loss. This study helps to establish a quantitative distribution law of part deletions.

The Numerical Simulation of Sector Cement Missing Characteristic Wave in Vertical Well

Numerical simulate the sound field of the Ⅱ interface sector cement missing in the vertical well. And study the influencing factors of the characteristic wave amplitude and travel time by the sector missing angle, the fluid ring thickness, and the formation media and so on. It is considered that the sector missing angle has a great influence on the amplitude of the characteristic wave, but has little influence on the first wave travel time. As the sector missing angle increases, the characteristic wave amplitude also increases. When the thickness of the fluid ring is greater than a certain value (5mm), the thickness of the fluid ring increases. The amplitude of the characteristic wave increases gradually when the sector missing angle is the same. From the influencing factors of characteristic wave amplitude change, we can see that the angle change of sector cement missing is equivalent to the fluid ring thickness change.

Hybrid CFD/low-order modeling of nonlinear thermoacoustic oscillations

This paper proposes and compares two nonlinear time-domain models of self-excited thermoacoustic oscillations of laminar premixed flames. Both models are hybrid formulations, where the flame and its immediate vicinity are resolved with a reactive flow simulation, while the acoustic field is modeled with a low-order model that is coupled to the reactive flow simulation. Firstly, a flame model based on the fully compressible Navier–Stokes equations is investigated. In this case, the flame simulation is coupled to the low-order model via the characteristic wave amplitudes at the inlet boundary. Secondly, the flame is resolved with a low Mach number reactive flow simulation. In order to include two-way thermoacoustic feedback, this flame model is coupled with an acoustic network model via the global heat release rate and the fluctuation of the axial velocity at a reference position upstream of the flame. A bifurcation analysis using the plenum length as bifurcation parameter is conducted. Both models exhibit complex nonlinear oscillations and are in good agreement with each other. Therefore, we conclude that the coupling of a linear acoustic model and a nonlinear flame model via reference velocity and global heat release rate is sufficient to accurately capture thermoacoustic oscillations of the configuration investigated. This implies that the most important nonlinearities can be attributed to hydrodynamic effects and flame kinematics. Furthermore, the study corroborates that premixed flames respond predominantly to fluctuations of the upstream flow velocity.

A Discrete-Time, State-Space Approach for the Investigation of Non-Normal Effects in Thermoacoustic Systems

A low-order, state-space modeling approach for thermoacoustic systems has been developed, which is based on present and past values of nodal characteristic wave amplitudes. The method allows to simulate the time evolution of the system state, but also the efficient computation of the (pseudo-)spectrum of the evolution operator. It is demonstrated by comparison with a frequency-domain “network model” that eigenmodes and asymptotic linear stability are predicted correctly. The influence of various model parameters (downstream reflection coefficient, temperature ratio across the heat source, magnitude and spread of heat source time delays) on transient growth of perturbation energy is explored. The discussion in the present paper is limited to simple test cases, but the approach can be generalized to systems with non-trivial topology.

Effect of the initial spectrum on the spatial evolution of statistics of unidirectional nonlinear random waves

Results of extensive experiments on propagation of unidirectional nonlinear random waves in a large wave tank are presented. The nonlinearity of the wavefield determined by the characteristic wave amplitude and the dominant wave length was retained constant in various series of experimental runs. In each experimental series, initial spectra of different shape and/or width were considered. Every series contained sufficient number of independent realizations to ensure reliable statistics. Evolution of various statistical parameters along the tank was investigated. It is demonstrated that the spectrum width plays an important role in the evolution of the random wavefield and strongly affects the variation of the wave spectrum as well as of parameters that characterize the deviation of the wavefield statistics from that corresponding to the Gaussian distribution. In particular, in a random wavefield that initially contains independent free harmonics within a narrow spectrum, extremely steep waves appear more often in the process of evolutions than predicted by a Rayleigh distribution, while for wider initial wave spectra the probability of those waves decreases sharply and is well below the Rayleigh values.

Long time bounds for the periodic Benjamin–Ono–BBM equation

We consider the periodic Benjamin–Ono equation, regularized in the same way as the Benjamin–Bona–Mahony equation is found from the Korteweg–de Vries one [T.B. Benjamin, J.L. Bona, J.J. Mahony, Model equations for long waves in nonlinear dispersive systems, Philos. Trans. Roy. Soc. London Ser. A 272 (1220) (1972) 47–78], namely the equation u t + u x + α u u x + β H ( u x t ) = 0 , where H is the Hilbert transform, α the quotient between the characteristic wave amplitude and the depth of the waves and β the quotient between this depth and the wavelength. We show that the solution, starting from an initial datum of size ε , remains smaller than ε for a time scale of order ( ε − 1 β / α ) 2 , whereas the local well-posedness gives only a time of order ε − 1 β / α .

Generation of Pc 1 pulsations in the regime of backward wave oscillator

Satellite data [Loto’aniu, T.M., Fraser, B.J., Waters, C.L., 2005. Propagation of electromagnetic ion cyclotron wave energy in the magnetosphere. Journal of Geophysics Research 110 (A07), A07214, doi:10.1029/2004JA010816.] show that EMIC Pc 1 waves demonstrate, in a wide range of L values, bidirectional energy flux propagation at low magnetic latitudes | MLat | < 11 ∘ and unidirectional (downward) propagation for | MLat | > 11 ∘ . Loto’aniu et al. suggested that this fact can be due to generation of Pc 1 waves in the regime of backward wave oscillator (BWO) suggested earlier for ELF/VLF chorus generation. We give a quantitative consideration of this idea. According to the BWO model, waves are generated in the vicinity of the equatorial cross-section of a magnetic flux tube, and the MLat width of the generation region is estimated as | MLat | = ( R 0 k A L ) - 1 / 3 , where R 0 is the Earth radius and k A is the wave number. In the case of Pc 1 waves, for reasonable values of k A ∼ 4 × 10 - 3 km - 1 , | MLat | ≃ 11 ∘ depends only weakly on L. This is in close agreement with observations. We estimate the threshold energetic-ion flux for BWO generation as S thr ∼ 10 7 cm - 2 s - 1 and characteristic wave amplitude as B wave ≈ 0.01 nT at L = 6 .

Wave propagation in light weight profiles with truss-like cores: Wavenumber content, forced response and influence of periodicity perturbations

The wavenumber content of periodic light weight profile strips is investigated. Theory of wave propagation in multi-coupled periodic systems is used to extract the dispersion characteristics of typical configurations. Solving the transfer matrix eigenvalue problem forms a basis for understanding the wave propagation in (infinite) strips; six characteristic waves travelling in each direction occur, either propagating, decaying or complex. Each characteristic wave consists of multiple wavenumbers of different amplitude, forming the so called “space harmonic” series. Typical wave forms of characteristic waves are shown and form the basis for identifying their relative contributions in the space harmonic series. Based on the dynamic stiffness matrix of a single subelement of the periodic system the forced response is calculated for infinite light weight profile strips. The characteristic wave amplitudes for selected force excitations in combination with the corresponding wavenumber spectra form the basis for structural acoustic investigations. Input mobilities for the infinite strip are presented demonstrating the typical pass and stop band behaviour. A brief study of the influence of periodicity perturbations reveals that for typical profiles, even quite high random length variations up to about 10 % have a limited effect on the structural dynamics of the strip.

Characteristic boundary conditions for simulations of compressible reacting flows with multi-dimensional, viscous and reaction effects

A generalized formulation of the characteristic boundary conditions for compressible reacting flows is proposed. The new and improved approach resolves a number of lingering issues of spurious solution behaviour encountered in turbulent reacting flow simulations in the past. This is accomplished (a) by accounting for all the relevant terms in the determination of the characteristic wave amplitudes and (b) by accommodating a relaxation treatment for the transverse gradient terms with the relaxation coefficient properly determined by the low Mach number asymptotic expansion. The new boundary conditions are applied to a comprehensive set of test problems including: vortex-convection; turbulent inflow; ignition front propagation; non-reacting and reacting Poiseuille flows; and counterflow cases. It is demonstrated that the improved boundary conditions perform consistently superior to existing approaches, and result in robust and accurate solutions with minimal acoustic wave interactions at the boundary in hostile turbulent combustion simulation conditions.

Theoretical analysis of tsunami generation by pyroclastic flows

Pyroclastic flows are a common product of explosive volcanism and have the potential to initiate tsunamis whenever thick, dense flows encounter bodies of water. We evaluate the process of tsunami generation by pyroclastic flow by decomposing the pyroclastic flow into two components, the dense underflow portion, which we term the pyroclastic debris flow, and the plume, which includes the surge and coignimbrite ash cloud parts of the flow. We consider five possible wave generation mechanisms. These mechanisms consist of steam explosion, pyroclastic debris flow, plume pressure, plume shear, and pressure impulse wave generation. Our theoretical analysis of tsunami generation by these mechanisms provides an estimate of tsunami features such as a characteristic wave amplitude and wavelength. We find that in most situations, tsunami generation is dominated by the pyroclastic debris flow component of a pyroclastic flow. This work presents information sufficient to construct tsunami sources for an arbitrary pyroclastic flow interacting with most bodies of water.

The Bar‐Mode Instability in Differentially Rotating Neutron Stars: Simulations in Full General Relativity

We study the dynamical stability against bar-mode deformation of rapidly spinning neutron stars with diUerential rotation. We perform fully relativistic three-dimensional simulations of compact stars with M/R 0.1, where M is the total gravitational mass and R the equatorial circumferential radius. We adopt an adiabatic equation of state with adiabatic index ! 2. As in Newtonian theory, we —nd that stars above a critical value of b 4 T /W (where T is the rotational kinetic energy and W the gravita- tional binding energy) are dynamically unstable to bar formation. For our adopted choices of stellar compaction and rotation pro—le, the critical value of is D0.24¨0.25, only slightly smaller than b b dGR the well-known Newtonian value D0.27 for incompressible Maclaurin spheroids. The critical value depends only very weakly on the degree of diUerential rotation for the moderate range we surveyed. All unstable stars form bars on a dynamical timescale. Models with sufficiently large b subsequently form spiral arms and eject mass, driving the remnant to a dynamically stable state. Models with moderately large do not develop spiral arms or eject mass but adjust to form dynamically stable b Z b dGR ellipsoidal-like con—gurations. If the bar-mode instability is triggered in supernova collapse or binary neutron star mergers, it could be a strong and observable source of gravitational waves. We determine characteristic wave amplitudes and frequencies. Subject headings: dense matterrelativitystars: neutronstars: rotation

Ringing loads on a slender vertical cylinder of general cross-section

Third harmonic loads on a vertical cylinder in irregular or regular longcrested waves in deep water are analyzed. Characteristic wave lengths are large relative to the cross-dimensions of the cylinder. Characteristic wave amplitudes are of the same order as the cylinder cross-dimensions. The method is a generalization of the FNV method (Faltinsen, Newman and Vinje [1]) for a circular cross- section. Integral theorems and auxiliary potentials are used to simplify the force expressions. Details are shown for Lewis form sections. Completely analytical expressions are derived for elliptical cross-sections. It is demonstrated that the third harmonic loads are sensitive to the cross-sectional form.

The search for gravitational waves

This article serves as an introduction to the sources of gravitational waves and their detection. The types of sources expected to generate signals detectable by instruments currently planned, together with the theory governing these detectors, are considered. Order of magnitude estimates for the characteristic wave amplitudes are calculated and compared to the sensitivities of the currently prototyped and future detectors.