Finite-amplitude Waves Research Articles

A robust numerical method for the generation and propagation of periodic finite-amplitude internal waves in natural waters using high-accuracy simulations

Abstract. The design and implementation of boundary conditions for the robust generation and simulation of periodic finite-amplitude internal waves is examined in a quasi two-layer continuous stratification using a spectral-element-method-based incompressible flow solver. The commonly used Eulerian approach develops spurious, and potentially catastrophic small-scale numerical features near the wave-generating boundary in a non-linear stratification when the parameter A/(δc) is sufficiently larger than unity; A and δ are measures of the maximum wave-induced vertical velocity and pycnocline thickness, respectively, and c is the linear wave propagation speed. To this end, an Euler–Lagrange approach is developed and implemented to generate robust high-amplitude periodic deep-water internal waves. Central to this approach is to take into account the wave-induced (isopycnal) displacement of the pycnocline in both the vertical and (effectively) upstream directions. With amplitudes not restricted by the limits of linear theory, the Euler–Lagrange-generated waves maintain their structural integrity as they propagate away from the source. The advantages of the high-accuracy numerical method, whose minimal numerical dissipation cannot damp the above near-source spurious numerical features of the purely Eulerian case, can still be preserved and leveraged further along the wave propagation path through the robust reproduction of the non-linear adjustments of the waveform. The near- and far-source robustness of the optimized Euler–Lagrange approach is demonstrated for finite-amplitude waves in a sharp quasi two-layer continuous stratification representative of seasonally stratified lakes. The findings of this study provide an enabling framework for two-dimensional simulations of internal swash zones driven by well-developed non-linear internal waves and, ultimately, the accompanying turbulence-resolving three-dimensional simulations.

Variable dust charge generates multi solitons, breather soliton structures in Saturn’s ring

In this study, we have investigated nonlinear wave structures that are localized along with the exact stationary wave solutions with oscillating, i.e. the breather structures in an unmagnetized dusty plasma with variable dust charge concentration with two temperatures of ions. We have derived GE from the normalized governing equations employing the reductive perturbative technique (RPT). The GE is the extended Korteweg–de Vries (KdV) equation that includes the united effect of quadratic and cubic nonlinearities. Employing the Hirota bilinear method (HBM), multi-soliton solutions and the breather soliton solutions have been obtained. Breathers (oscillating wave packets) play a significant role in hydrodynamics and optics, and their interaction can change the dynamics of the wave fields. It is also important to propagate finite-amplitude waves in the astrophysical atmosphere, plasma dynamics, ocean, optic fibers, signal processing, etc. In the circumstances of Saturn’s ring, it is noticed that the breather soliton structures are modified significantly with variations in dust charge concentration, ion temperature ratio, and other physical parameters.

Nonclassical wave propagation measurements in the high temperature vapor of D6\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\hbox {D}_{6}$$\\end{document} with the asymmetric shock tube for experiments in rarefaction waves (ASTER)

A novel test setup called the asymmetric shock tube for experiments on nonideal rarefaction waves (ASTER) has been commissioned at Delft University of Technology. The ASTER, which works according to the principle of Ludwieg tubes, is designed to generate and measure the speed of small and finite amplitude waves propagating in the dense vapors of fluids formed by complex organic molecules, therefore in the nonideal compressible fluid dynamics regime. The ultimate goal of the associated research is to prove the existence of nonclassical gasdynamics. The setup consists of a high-pressure charge tube and a vacuum tank separated by a glass disk equipped with a breaking mechanism for rarefaction waves experiments. When the glass disk is broken, an expansion wave propagates into the tube in the direction opposite to the fluid flow. The propagation speed of this wave is measured using a time-of-flight method with the help of four fast-response pressure sensors placed equidistantly in the middle of the tube. The charge tube can withstand pressures and temperatures of up to 15 bar and 400∘C\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$^{\\circ }\\mathrm{C}$$\\end{document}. Preliminary rarefaction experiments were successfully conducted using dodecamethylcyclohexasiloxane, D6\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\hbox {D}_{6}$$\\end{document}, as the working fluid and at pressures and temperatures of up to 9.4 bar and 372∘C\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$^{\\circ }\\mathrm{C}$$\\end{document} , respectively. The results of an experiment featuring the initial state for which a theoretical model predicts the nonclassical acceleration of rarefaction waves show that the propagation is qualitatively different from that put into evidence by experiments for which the propagation is classic. Upcoming setup improvements and experimental campaigns are planned with the objective of experimentally verifying the existence of nonclassical gasdynamics.Graphical abstract

Analytical insights into the behavior of finite amplitude waves in plasma fluid dynamics

This study introduces innovative analytical solutions for the [Formula: see text]-dimensional nonlinear Jaulent–Miodek ([Formula: see text]) equation, a governing model elucidating the propagation characteristics of nonlinear shallow water waves with finite amplitude. Employing analytical methodologies such as the Khater II and unified methods, alongside the Adomian decomposition method as a semi-analytical approach, series solutions are derived with the primary aim of elucidating the fundamental physics dictating the evolution of [Formula: see text] waves. Within the realm of nonlinear fluid dynamics, the [Formula: see text] equation encapsulates the behavior of irrotational, inviscid, and incompressible fluid flow, wherein nonlinear effects and dispersion intricately balance to yield stable propagating waves. This equation encompasses terms representing nonlinear convection, dispersion, and nonlinearity effects. The analytical methodologies employed in this investigation yield solutions for various instances of the [Formula: see text] equation, demonstrating convergence, accuracy, and computational efficiency. The outcomes reveal that the Adomian decomposition method yields solutions congruent with those obtained through analytical techniques, thereby affirming the precision of the derived solutions. Furthermore, this study advances the comprehension of the physical implications inherent in the [Formula: see text] equation, serving as a benchmark for evaluating alternative methodologies. The analytical approaches elucidated in this research furnish accessible tools for addressing a diverse array of nonlinear wave equations in mathematical physics and engineering domains. In summary, the introduction of novel exact and approximate solutions significantly contributes to the advancement of knowledge pertaining to the [Formula: see text]-dimensional [Formula: see text] equation. The ramifications of this research extend to the modeling of shallow water waves, offering invaluable insights for researchers and practitioners engaged in the field.

Nonlinear vibration and acoustic radiation of an internally resonant buckled beam

Although the nonlinear vibration of buckled beam has been thoroughly studied, its acoustic radiation does not get much attention. This paper deals with the nonlinear vibro-acoustic problem of an internally resonant buckled beam immersed in an infinite fluid. A finite element method based on an arbitrary Lagrangian-Eulerian framework is adopted to analyze the nonlinear interaction between the large-deformed buckled beam and the finite-amplitude acoustic waves in the fluid. The effects of acoustic pressure excitation, external harmonic excitation, and internal resonance on the vibro-acoustic responses of the buckled beam are discussed in the first and second primary resonances. It is found that the amplitude of the acoustic pressure can be comparable to the amplitude of the external harmonic force. This leads to an increase in the critical harmonic excitation amplitude for the occurrence of quasi-periodic responses and an increase in the second mode frequency component of quasi-periodic responses compared to the case neglecting the acoustic pressure excitation on the beam. Saturation phenomena are discovered in the second mode frequency components of beam displacement and acoustic pressure. Due to the 2:1 internal resonance, different time-frequency characteristics, quadrupole acoustic directivity patterns with low radiation efficiency, and dipole acoustic directivity patterns with high radiation efficiency can be observed at different harmonic excitation amplitudes and frequencies. Understanding these phenomena will help design loudspeakers and recognize sound sources.

Understanding Stokes Drift Mechanism via Crest and Trough Phase Estimates

Abstract By providing mathematical estimates, this paper answers a fundamental question—“what leads to Stokes drift”? Although overwhelmingly understood for water waves, Stokes drift is a generic mechanism that stems from kinematics and occurs in any nontransverse wave in fluids. To showcase its generality, we undertake a comparative study of the pathline equation of sound (1D) and intermediate-depth water (2D) waves. Although we obtain a closed-form solution x(t) for the specific case of linear sound waves, a more generic and meaningful approach involves the application of asymptotic methods and expressing variables in terms of the Lagrangian phase θ. We show that the latter reduces the 2D pathline equation of water waves to 1D. Using asymptotic methods, we solve the respective pathline equation for sound and water waves, and for each case, we obtain a parametric representation of particle position x(θ) and elapsed time t(θ). Such a parametric description has allowed us to obtain second-order accurate expressions for the time duration, horizontal displacement, and average horizontal velocity of a particle in the crest and trough phases. All these quantities are of higher magnitude in the crest phase in comparison to the trough phase, leading to a forward drift, i.e., Stokes drift. We also explore particle trajectory due to second-order Stokes waves and compare it with linear waves. While finite amplitude waves modify the estimates obtained from linear waves, the understanding acquired from linear waves is generally found to be valid.

Finite amplitude wave propagation through bubbly fluids

The existence of only a few bubbles could drastically reduce the acoustic wave speed in a liquid. Wood’s equation models the linear sound speed, while the speed of an ideal shock waves is derived as a function of the pressure ratio across the shock. The common finite amplitude waves lie, however, in between these limits. We show that in a bubbly medium, the high frequency components of finite amplitude waves are attenuated and dissipate quickly, but a low frequency part remains. This wave is then transmitted by the collapse of the bubbles and its speed decreases with increasing void fraction. We demonstrate that the linear and the shock wave regimes can be smoothly connected through a Mach number based on the collapse velocity of the bubbles.

Developmental mechanism of the SWCV nonlinear inertial waves

Based on the Boussinosq Approximation formulas in the symmetric, cylindric coordinates, the nonlinear effects of the internal inertial gravity waves on the meso-micro scale convective activities of Southwest China Vortex system are analyzed by the multi-scale and perturbation approximation methods. The results obtain two main conclusions: (1) When the atmospheric stratification is stable, the inertial gravity waves for Southwest China Vortex may also develop into finite-amplitude wave packet with a solitonic characteristics of large amplitude and short duration, forming a long-narrow wave band which activates and organizes severe convective activities like high wind and thunderstorm of Southwest China Vortex. When the atmospheric stratification is unstable, the inertial gravity waves exhibits attenuating oscillation characteristics and develops into finite-amplitude wave packet with large amplitude and fast speed, forming queue-type wave band that activates and organizes extreme weather like persistent heavy rainfall of Southwest China Vortex. (2) Under different atmospheric stratifications, the effects of thermal forcing on the inertial gravity waves for Southwest China Vortex are different. In the stable atmospheric stratification, the thermal forcing mainly intensifies the inertial gravity waves and has no significant effect on its duration. And in the unstable atmospheric stratification, the thermal forcing not only strengthens its growth but also obviously extends its duration. The research has revealed the some nonlinear characteristics of the internal inertial gravity waves for Southwest China Vortex, and improved the theoretical understanding about the critical role of the internal inertial gravity waves dynamic processes and its influence mechanism on the meso-micro scale severe convection weather for Southwest China Vortex.

Lagrangian approach to nonlinear waves in non-dispersive and dispersive rotating shallow water magnetohydrodynamics

A Lagrangian approach to both hydrostatic non-dispersive in the short-wave range and non-hydrostatic dispersive rotating shallow-water magnetohydrodynamics is developed, and used to analyse weakly and fully nonlinear waves described by the model. Hyperbolic structure in the non-dispersive case is displayed and Riemann invariants are constructed. Characteristic equations are used to establish criteria of breaking and formation of shocks by magneto-gravity waves, and conditions of the appearance of contact discontinuities in Alfvén waves. As in the case of non-magnetic rotating shallow water, rotation cannot prevent breaking. The Lagrangian equations of the model are reduced to a single partial differential ‘master’ equation, which is used to analyse the propagation of weakly nonlinear waves of both families, with or without weak rotation, and with or without weak short-wave dispersion. Corresponding modulation equations are constructed and their main properties sketched. The same master equation is used to obtain fully nonlinear finite-amplitude wave solutions in particular cases of no short-wave dispersion or no rotation.

Short-wavelength instabilities in a finite-amplitude plane inertial wave

We perform a linear stability analysis of a finite-amplitude plane inertial wave (of frequency $\omega$ in the range $0\le \omega \le f$ , where $f$ is the Coriolis frequency) by considering the inviscid evolution of three-dimensional (3-D), small-amplitude, short-wavelength perturbations. Characterizing the base flow plane inertial wave by its non-dimensional amplitude $A$ and the angle $\varPhi$ that its wavevector makes with the horizontal axis, the local stability equations are solved over the entire range of perturbation wavevector orientations. At sufficiently small $A$ , 3-D parametric subharmonic instability (PSI) is the only instability mechanism, with the most unstable perturbation wavevector making an angle close to $60^{\circ }$ with the inertial wave plane. In addition, the most unstable perturbation is shear-aligned with the inertial wave in the inertial wave plane. Further, at large $\varPhi$ , i.e. $\omega \approx f,$ there exists a wide range of perturbation wavevectors whose growth rate is comparable to the maximum growth rate. As $A$ is increased, theoretical PSI estimates become less relevant in describing the instability characteristics, and the dominant instability transitions to a two-dimensional (2-D) shear-aligned instability, which is shown to be driven by third-order resonance. The transition from 3-D PSI to a 2-D shear-aligned instability is shown to be reasonably captured by two different criteria, one based on the nonlinear time scale in the inertial wave and the other being a Rossby-number-based one.

Optimizing parametric acoustic arrays for high-fidelity low-frequency signals

Parametric acoustic array (PAA) can leverage the nonlinear behavior of sound travelling through the nonlinear medium (e.g., air, water, human tissues) to generate low-frequency broadband high-directivity sound due to the self-demodulation of finite-amplitude modulated ultrasonic waves. However, while propagating, self-demodulated signals (hereon message) interact one with another, leading to message deformation and increase of the total harmonic distortion (THD). This makes it problematic to use powerful PAA to control complex low-frequency signals. This work explores a method for reducing THD by optimizing the input signal using various digital signal processing algorithms. The sustainability of the required spectral components with distance and the spatial boundaries of the operation of the proposed optimization algorithm are also investigated experimentally with a 520-channel hexagonal PAA and numerically. The simulations were done via k-wave acoustic toolbox considering nonlinearities and power law absorption.

Atlantic blocking events in a simplified nonlinear baroclinic model for local finite-amplitude wave activity

To better understand the mechanisms underlying the formation of blocking highs over the North Atlantic as a type of large-amplitude disturbance, this paper reports results from numerical experiments within the framework of local finite-amplitude wave activity (LWA). The numerical model employed in this study explicitly depicts two important atmospheric internal dynamic processes—nonlinear zonal eddy flux and Rossby wave packet propagation—which have been individually emphasized by different previous studies. The simulation results reveal that these two dynamic processes are the dominant contributors to the formation of Atlantic blocking cases. However, they exert different influences over different regions. The southern and northern parts of the primary LWA associated with the blocking cases are mainly induced by the nonlinear zonal eddy flux and Rossby wave packet propagation, respectively. Thus, this study reconciles and integrates insights from previous studies on Atlantic blocking events, providing a cohesive understanding of their formation.摘要为研究北大西洋阻高的形成机制, 本文在局部有限振幅波活动 (LWA) 框架下进行了一系列数值实验. 采用的数值模型能显式地描绘出两种重要的大气内部动力过程, 即非线性纬向位涡通量和Rossby波包传播. 模拟结果显示, 这两种动力学过程均是形成大西洋阻高的重要机理. 具体地, 非线性纬向位涡通量和Rossby波包传播, 分别是大西洋阻高南部和北部LWA形成的主导因子. 因此, 本研究综合了前人关于大西洋阻高的研究成果, 为其形成机理提供了新的认识.

Nonlinear supersonic flutter of a composite panel backed by an acoustic cavity with finite-amplitude sound waves

In this paper, an implicit partitioned fluid-structure-acoustic interaction method is presented for predicting nonlinear aeroelastic response of an elastic composite laminated panel backed by an acoustic cavity and subject to a supersonic flow. The method is formulated in an arbitrary Lagrangian-Eulerian framework based on the unsteady Navier-Stokes equations for the supersonic flow, a geometrical nonlinear dynamics model for the composite laminated panel, and the nonlinear Westervelt equation for the finite-amplitude sound waves in cavity. A theoretical fluid-structure-acoustic model of the supersonic panel is proposed for validating the present numerical method, in which the nonlinear structural model of the panel, the first-order piston aerodynamics model of the supersonic flow and the nonlinear sound wave model of the cavity are coupled in a monolithic manner. It is found that cavity acoustic resonance can appear in the case a vibration mode of the panel coalescing with an acoustic mode of the cavity. Several new physical features of nonlinear acoustic resonance have been discovered, such as the presence of shock wave with high pressure gradients travelling along the resonant cavity in axial direction and the presence of higher-order harmonic wave components, which emphasize a nonlinear acoustic wave model of the cavity must be used to fully characterize these phenomena. In addition, the nonlinearity of the standing wave is quantitatively related to the acoustic modes by means of a proper orthogonal decomposition analysis.

FINITE-AMPLITUDE INTERNAL SOLITARYWAVES IN A SHEAR FLOW OF A TWO-LAYER FLUID

We consider a nonlinear system of equations that describes the propagation of finite-amplitude internal waves in two-layer stratified shallow water under a cover in the Boussinesq approximation. Within the framework of this model, we study solitary waves, taking into account the nonhydrostatic pressure distribution in one or both layers, and also consider the case of weakly nonlinear waves. In the class of traveling waves, this model is reduced to an ordinary differential equation for determining the profile of a solitary wave in a shear flow. This equation admits an analytical study. The conditions for the existence of solitary waves adjacent to a given constant flow are determined by two dimensionless parameters related to the wave speed and the velocity shear of the undisturbed flow. Examples of solitary waves are given. These examples demonstrate the effects of the velocity shear on the waveform.

Modeling and Simulation of Parametric Nonlinear Focused Ultrasound in Three-Dimensional Bubbly Liquids with Axial Symmetry by a Finite-Element Model

This paper presents the development of a numerical model able to track in time the behavior of nonlinear focused ultrasound when interacting with tiny gas bubbles in a liquid. Our goal here is to analyze the frequency components of the waves by developing a model that can easily be adapted to the geometrical restrictions and complexities that come out in several application frameworks (sonochemistry, medicine, and engineering). We thus model the behavior of nonlinear focused ultrasound propagating in a liquid with gas bubbles by means of the finite-element method in an axisymmetric three-dimensional domain and the generalized-α method in the time domain. The model solves a differential system derived for the nonlinear interaction of acoustic waves and gas bubble oscillations. The high nonlinearity and dispersion of the bubbly medium hugely affect the behavior of the finite-amplitude waves. These characteristics are used here to generate frequency components of the signals that do not exist at the source through nonlinear mixing (parametric antenna). The ability of the model to work with complex geometries, which is the main advantage of the method, is illustrated through the simulation of nonlinear focused ultrasound in a medium excited from two spherical sources in opposite directions.

Phase variation of Laguerre-Gaussian vortex beams in a homogeneous atmospheric medium under finite amplitude acoustic wave perturbation

In this article, we have derived the acoustic pressure and medium refractive index expressions in a homogeneous atmospheric medium perturbed by a planar finite amplitude acoustic wave. In a planar finite amplitude acoustic wave perturbation, we developed a Laguerre–Gaussian vortex beam transmission model in a homogeneous atmospheric medium. We investigated the effects of different acoustic source parameters on the phase of the Laguerre–Gaussian vortex beam transmission, considering the atmospheric medium’s viscous effect. The results show that acoustic waves of finite amplitude distort the refractive index distribution of a homogeneous atmospheric medium. At a given distance, the amplitude of the refractive index gradually increases with increasing acoustic wave transmission distance. At the same time, the phase of the Laguerre–Gaussian vortex beam is rotated by the perturbation of the finite-amplitude acoustic wave, and the phase always returns to its initial position. Unlike linear acoustic waves, changes in the homogeneous atmospheric refractive index distribution and the homogeneous phase of the Laguerre–Gaussian vortex light no longer satisfy the periodic variation when perturbed by finite-amplitude acoustic waves. Under the same conditions, the effect of finite-amplitude acoustic waves on the phase of the Laguerre–Gaussian vortex light is stronger than that of linear acoustic waves. Finally, the effects of different acoustic pressure and frequency of the source on the phase of the Laguerre–Gaussian vortex beam transmission are calculated. The results show that different acoustic parameters at the source can be used to achieve phase modulation at different distances and intensities.

Internal resonance induced nonlinear vibration and acoustic radiation of a hyperelastic cantilever structure immersed in fluid

Hyperelastic structures can exhibit peculiar nonlinear vibration and acoustic behavior due to the existence of geometric and material nonlinearities. In order to comprehend the nonlinear vibro-acoustic responses of a hyperelastic cantilever structure configured with internal resonances, a finite element model that considers both the geometric and material nonlinearities in the structure and the finite-amplitude acoustic waves has been developed. The vibro-acoustic problem is described in an arbitrary Lagrangian-Eulerian frame with perfectly matched layers. Based on the finite element model, a loosely coupled serially staggered procedure is applied to solve the nonlinear governing equations. It is found that with large harmonic axial excitation applied to the hyperelastic cantilever structure, the structural vibration undergoes an axial-to-bending transition due to the 2:1 internal resonance, resulting in the variation of acoustic directivity and frequency characteristics. This transition of vibration form occurs quickly when the excitation amplitude is larger or the excitation frequency is closer to the frequency of the axial mode. A threshold of dissipation energy is proposed to determine the transition of the structural and acoustic responses due to nonlinear internal resonance. Saturation of the structural vibration and acoustic responses is observed in the frequency components associated with the first axial mode of the hyperelastic structure, which only exists in the case of the occurrence of the axial-to-bending transition.

Assessing the efficiency of a distensible-tube wave attenuator at three different scales considering aero and hydro-elastic effects

A water-filled floating distensible tube connected to a forward-bent oscillating water column is here considered in the context of harnessing energy from sea waves. Based on wave-tank experiments conducted at three different scales, under intermediate and deep-water incident regular waves of small and finite amplitudes, the present study addresses important aspects that determine the energy capture-width of the system. The comparison between the results obtained at the three scales reveals non-linear and aero-hydroelastic scale effects inherent in modelling the device. The following issues are also tackled: (i) the occurrence of various working modes of the floating tube and their contribution to its performance; (ii) the compressibility of the airflow through the orifice power take-off system; (iii) the viscous-effects associated with the Reynolds and Keulegan-Carpenter numbers. The parameters that govern the system's efficiency are the tube's length, the OWC natural period and the bulge wave tuning period. The system becomes very efficient not only at the OWC resonance, but also when the incident wavelength is equal to or twice the tube's length. Video frames further provide evidence of the relationship between the tube's working modes and its performance. An iterative algorithm based on Buckingham's formula, with an empirical expansibility factor, provides adequate estimates of the compressible flow through the power take-off. Viscous losses closely related to the Reynolds and Keulegan-Carpenter numbers are found to be important even for waves with moderate steepness. Finally, the experiments suggest that a single distensible-tube system in open sea has a maximum capture-width of no more than 2 tube-diameters.

Trajectories of Liquid Particles in a Dark Soliton Field in a Fluid Beneath an Ice Cover

A fluid layer of finite depth described by Euler equations is considered. The ice cover is modeled by a geometrically non-linear elastic Kirchhoff–Love plate. The trajectories of liquid particles under the ice cover are found in the field of a nonlinear surface traveling wave tending to a periodic wave at infinity: the so-called “dark soliton” (which is a nonlinear product of a step-wave and a periodic wave) of small but finite amplitude. The presence of dark solitons in the system is an indicator of the modulation stability of the carrier periodic wave (defocusing). The analysis uses explicit asymptotic expressions for solutions describing wave structures on the water–ice interface such as dark solitons, as well as asymptotic solutions for the velocity field in the liquid column generated by these waves.

Features of Local Finite-Amplitude Wave Activity during Extreme Cold Waves over Eastern China

Abstract The frequent occurrence of extreme cold waves under climate change has attracted widespread attention. Based on the Japanese 55-year Reanalysis daily dataset from 1958 to 2021, we use a newly developed dynamic metric, the local finite-amplitude wave activity (LWA), to explore the precursory signals, outburst conditions, and key dynamic features of extreme cold waves over eastern China from the perspective of synoptic climatology. The statistical results show that approximately 40% of extreme cold waves have the following features. First, the formation of significant positive LWA anomalies over the Balkhash–Baikal region is an evident precursory signal, which is accompanied by significant cold surface air temperature anomalies that accumulate over mid- and high-latitude Eurasia. Second, the appearance of extreme positive LWA anomalies over the region east of Lake Baikal (ELB) is necessary for subsequent outbursts of extreme cold waves. These extreme positive LWA anomalies indicate the meridionally enhanced planetary trough over East Asia and advection of the accumulated cold air masses southeastward to eastern China. Third, the evident positive change in the LWA anomalies over the ELB is mainly attributable to the convergence of the zonal LWA flux due to the zonal wind in the eddy-free state and Stokes drift flux over the eastern area of the ELB and the convergence of the meridional eddy heat flux over the western area. This study demonstrates that the LWA could be used as a simple and feasible metric for monitoring and forecasting extreme cold waves. Significance Statement Enhanced waviness in circulation usually occurs before and during the outburst of extreme cold waves over eastern China. With a state-of-the-art diagnostic tool, the local finite-amplitude wave activity (LWA), the present study reveals both precursory signals and outburst conditions of these extreme cold events from the perspective of synoptic climatology. This study not only deepens our understanding of the dynamic process for extreme cold events over eastern China but also offers a method for monitoring and forecasting those extreme events. Our work also provides a method for studying other extreme climate events that are closely related to large-amplitude circulation waviness over the middle and high latitudes.