Anomalous Wave Research Articles

Atmospheric Circumglobal Teleconnection Triggered by Spring Land Thermal Anomalies Over West Asia and Its Possible Impacts on Early Summer Climate Over Northern China

AbstractEurasian continent experienced significant warming during the past decades. West Asia locates in arid/semi-arid zone and its warming amplification has drawn lots of attention. However, the climatic effect of such a warming is not clear yet. In this study, we explored the possible impacts of recent land surface warming over West Asia on the atmospheric general circulation and climate. Results show that abnormal spring land surface warming over West Asia tends to increase precipitation over North China but decrease (increase) precipitation (air temperature) over Northeast China in early summer (June). It is noted that the precipitation anomalies are much stronger over the eastern region of North/Northeast China. Further analysis suggests abnormal spring land surface warming can trigger eastward-propagating disturbance via diabatic heating, which benefits intensified the atmospheric circumglobal teleconnection (CGT) pattern, causing anomalous circulation and climate in early summer over northern China. Sensitivity experiments demonstrate that abnormal spring land surface warming can increase the atmospheric baroclinic instability and trigger Rossby waves that propagate along the westerly jet stream (WJS), resulting in the formation of CGT. Due to persistent land surface thermal forcing and the interaction between the basic flow (especially WJS) and CGT, the CGT tends to be intensified. The anomalous wave center over East Asia in early summer is responsible for the precipitation increases (decreases) over North (Northeast) China and the evident warming in Northeast China. Our results suggest that the spring land surface thermal anomalies over West Asia can be a potential signal for short-term prediction of early summer climate over northern China.

On the anomalous development of the extremely intense positive Arctic Oscillation of the 2019–2020 winter

Numerous extreme climate anomalies were recorded in the northern extratropics in January–March (JFM) 2020, significantly impacting human lives and ecosystems in the affected areas. Those anomalies were caused by an extreme positive Arctic Oscillation (AO) event, with the JFM 2020 AO index of 2.8 being the highest on the record. However, all well-established autumn precursors pointed towards the following wintertime AO phase being negative. Indeed, a negative AO phase was developing until late December when a sudden shift to the strong positive AO event occurred in the troposphere. The geopotential anomalies associated with positive AO spread into the lower stratosphere, and were steadily enhancing throughout JFM resulting in an extreme positive AO event. We show that the strong positive AO event was a result of the destructive interference of the anomalous planetary waves with climatological ones, which led to wave flattening and enhancement of the polar vortex.

Anomalous wave statistics following sudden depth transitions: application of an alternative Boussinesq-type formulation

Recent studies of water waves propagating over sloping seabeds have shown that sudden transitions from deeper to shallower depths can produce significant increases in the skewness and kurtosis of the free surface elevation and hence in the probability of rogue wave occurrence. Gramstad et al. (Phys. Fluids 25 (12): 122103, 2013) have shown that the key physics underlying these increases can be captured by a weakly dispersive and weakly nonlinear Boussinesq-type model. In the present paper, a numerical model based on an alternative Boussinesq-type formulation is used to repeat these earlier simulations. Although qualitative agreement is achieved, the present model is found to be unable to reproduce accurately the findings of the earlier study. Model parameter tests are then used to demonstrate that the present Boussinesq-type formulation is not well-suited to modelling the propagation of waves over sudden depth transitions. The present study nonetheless provides useful insight into the complexity encountered when modelling this type of problem and outlines a number of promising avenues for further research.

Impacts of Tropical North Atlantic and Equatorial Atlantic SST Anomalies on ENSO

AbstractThe Sea Surface Temperature Anomaly (SSTA) in tropical Atlantic during boreal spring and summer shows two dominant modes: a basin-warming and a meridional dipole mode, respectively. Observational and coupled model simulations indicate that the former induces a Pacific La Niña in the succeeding winter whereas the latter cannot. The basin-warming forcing induces a La Niña through a Kelvin wave response and the associated wind-evaporation-SST-convection (WESC) feedback over the northern Indian Ocean (NIO) and Maritime Continent (MC). Anomalous Kelvin wave easterly interacts with the monsoonal westerly, leading to a warm SSTA and a northwest-southeast oriented heating anomaly in NIO/MC, which further induces easterly and cold SSTA over the equatorial Pacific. In contrast, the dipole forcing has little impact on the Indian and Pacific Oceans due to the offsetting of the Kelvin wave to the asymmetric Atlantic heating.Further observational and modeling studies towards the Tropical North Atlantic (TNA) and Equatorial Atlantic (EA) SSTA modes indicate that the TNA (EA) forcing induces a CP- (EP-) type ENSO. In both cases, the Kelvin wave response and the WESC feedback over the NIO/MC are important in conveying the Atlantic’s impact. The difference lies in distinctive Rossby wave responses – A marked westerly anomaly appears in the equatorial eastern Pacific (EEP) for the TNA forcing (due to its westward location) while no significant wind response is observed in EEP for the EA forcing. The westerly anomaly prevents a cooling tendency in EEP through anomalous zonal and vertical advection according to a mixed-layer heat budget analysis.

Anomalous Tropical Instability Wave activity hindered the development of the 2016/2017 La Niña

AbstractAlthough the 1997/98 and 2015/16 El Niño events are considered to be the strongest on record, their subsequent La Niña events exhibited contrasted evolutions. In this study, we demonstrate that the extremely strong period of Tropical Instability Waves (TIWs) at the beginning of boreal summer of 2016 played an important role in hindering the subsequent La Niña’s development by transporting extra off-equatorial heat into the Pacific cold tongue. By comparing the TIWs contribution based on an oceanic mixed-layer heat budget analysis for the 1998 and 2016 episodes, we establish that TIW-induced nonlinear dynamical heating (NDH) is a significant contributor to the El Niño-Southern Oscillation (ENSO) phase transition in 2016. TIW-induced NDH contributed to around 0.4°C per month warming during the early boreal summer (May-June) following the 2015/16 El Niño’s peak, which is found to be an essential inhibiting factor that prevented the subsequent La Niña’s growth. A time-mean eddy kinetic energy analysis reveals that anomalous TIWs during 2016 mainly gained their energy from the baroclinic instability conversion due to a strong SST warming in the northeastern off-equatorial Pacific that promoted an increased meridional SST gradient. This highlights the importance of accurately reproducing TIW activity in ENSO simulation and the benefit of off-equatorial SST anomalies in the eastern Pacific as an independent precursor for ENSO predictions.

What induces the interdecadal shift of the dipole patterns of summer precipitation trends over the Tibetan Plateau?

AbstractPrecipitation on the Tibetan Plateau (TP) exert great impacts on the energy, water cycle, and regional ecosystem. But due to the wide differences in climate regimes and complicated topography, TP precipitation is characterized as greater spatial diversity and lower confidence of temporal tendency. Based on the precipitation datasets from in situ observations, reanalysis, and satellites, this study identifies the interdecadal shift of the summer precipitation trends in the southern and northern TP, which corresponds well with the remarkable changes of TP lakes area in recent years. The statistical results indicate that the TP summer precipitation has experienced an interdecadal transition in the late 1990s, with precipitation increasing and then decreasing in the southern TP, and decreasing and then increasing in the northern TP. Further analyses suggest that the changes in moisture budget and convection activities play an important role in the interdecadal variations of precipitation in the northern and southern TP, respectively. More specifically, the variations in the southern TP are contributed largely by the persistent weakening sensible heat source, which can depress the ascending motion and hinder the northward moisture transport in the southern TP. While in the northern TP, both observations and model sensitivity experiments indicate that the co‐effect of the cold interdecadal Pacific oscillation (IPO) and warm Atlantic multidecadal oscillation (AMO) has profound impacts on the decadal shift of the net moisture budget in the northern TP. Specifically, the AMO can impact the Lake Baikal anticyclone through the anomalous wave propagation and then decrease the moisture output in the eastern TP. While the IPO can weaken the climatological westerlies and prompt the moisture to get stuck in the northern TP. Consequently, the variations in the net moisture budget can give rise to the decadal variations in summer precipitation in the northern TP.

Intermittent but Rapid Changes to Coastal Landscapes: The Tsunami and El Niño Wave-Formed Sea Arch at Laie Point, Oahu, Hawaii, U.S.A.

Kukuiho’olua Island is an islet that lies 164 m due north of Laie Point, a peninsula of cemented, coastal, Pleistocene and Holocene sand dunes. Kukuiho’olua Island consists of the same dune deposits as Laie Point and is cut by a sea arch, which, documented here for first time, may have formed during the 1 April 1946 “April Fools’s Day Tsunami.” The tsunami-source of formation is supported by previous modeling by other authors, which indicated that the geometry of overhanging sea cliffs can greatly strengthen and focus the force of tsunami waves. Additional changes occurred to the island and arch during the 2015–2016 El Niño event, which was one of the strongest on record. During the event, anomalous wave heights and reversed wind directions occurred across the Pacific. On the night of 24–25 February 2016, large storm waves, resulting from the unique El Niño conditions washed out a large boulder that had lain within the arch since its initial formation, significantly increasing the open area beneath the arch. Large waves also rose high enough for seawater to flow over the peninsula at Laie Point, causing significant erosion of its upper surface. These changes at Laie Point and Kukuio’olua Island serve as examples of long-term, intermittent change to a coastline—changes that, although infrequent, can occur quickly and dramatically, potentially making them geologic hazards.

Seascape genomics reveals candidate molecular targets of heat stress adaptation in three coral species.

Anomalous heat waves are causing a major decline of hard corals around the world and threatening the persistence of coral reefs. There are, however, reefs that have been exposed to recurrent thermal stress over the years and whose corals appear to have been tolerant against heat. One of the mechanisms that could explain this phenomenon is local adaptation, but the underlying molecular mechanisms are poorly known. In this work, we applied a seascape genomics approach to study heat stress adaptation in three coral species of New Caledonia (southwestern Pacific) and to uncover the molecular actors potentially involved. We used remote sensing data to characterize the environmental trends across the reef system, and sampled corals living at the most contrasted sites. These samples underwent next generation sequencing to reveal single nucleotide polymorphisms (SNPs), frequencies of which were associated with heat stress gradients. As these SNPs might underpin an adaptive role, we characterized the functional roles of the genes located in their genomic region. In each of the studied species, we found heat stress‐associated SNPs located in proximity of genes involved in pathways well known to contribute to the cellular responses against heat, such as protein folding, oxidative stress homeostasis, inflammatory and apoptotic pathways, and DNA damage‐repair. In some cases, the same candidate molecular targets of heat stress adaptation recurred among species. Together, these results underline the relevance and the power of the seascape genomics approach for the discovery of adaptive traits that could allow corals to persist across wider thermal ranges.

Soliton-Like Waves in the Vicinity of the Southern Kuril Islands

urpose. This paper focuses on modulated solitons detected in time series of observational data on sea level oscillations in the Sea of Okhotsk, verifying the presence of nonstationary processes within a quantitative framework of methods. Methods and Results. The paper reports an analysis of wave observation data collected using ARW-type, bottom-mounted pressure sensors in the area of the Capes Castricum, Van-der-Lind and Lovtsova in the southern Kuril Islands. The time series obtained were bandpass filtered using hardware with a passband of 20 minutes to 2.5 hours. Residual time series show the presence of wave packets generated at the beginning of the K1 (diurnal) tide, which consistently appear as a group consisting of 5–7 packets. It is shown that the synchronicity between each wave packet and the K1 wave initiation is associated with the cyclic separation of the tidal flow of the K1 oscillation at the elevation in the Urup Strait located between the islands, along with a concomitant spawning of vortices. It is speculated that the vortices generate the detected wave packets, which are each found to encase a cluster of waves with an average period of about 1.6 hours that are attributed to either edge waves or shelf seiches or a combination of both. A numerical model simulation of the detected wave packets was performed using the Korteweg – de Vries equation, confirming that the envelope of the observed wave packets is close to the modeled one and behaves like a soliton. Conclusions. It is shown that synchronous initiation of a wave packet and a K1 wave is associated with the cyclic separation of the tidal flow of the K1 oscillations at a subsurface elevation in the Urup Strait located between the islands, with a concomitant spawning of vortices. The vortices are assumed to generate the detected wave packets. Each packet contains a cluster of waves with an average period of about 1.6 hours, which is conditioned by the period of the edge wave or shelf seiche. Spectral analysis performed for the 4.5-day-long time series with and without the groups of solitons, showed that the wave energy increases in the 0.5–5.5 hour period range when solitons occur. Application of a simple amplitude-based criterion permitted the authors to identify the waves detected in the wave packets as anomalous. Transformation of the time series into normalized time and normalized amplitude coordinates show that all the examples of anomalous wave packets could be modeled using the Korteweg – de Vries time equation

Longitudinal wave steering using beam-type elastic metagratings

Metagratings have recently received much attention for effective realization of anomalous wave steering. Governed by the diffraction grating theory and the concept of metamaterials, metagratings allow to suppress superfluous propagations of high-order scattering modes in a selective manner such that wavefronts are accurately steered as designated. While numerous metagratings have been reported in electromagnetic wave research field, little has been explored in the elastic wave regime because of difficulties caused by complicatedly coupled motions among various types of elastic waves. In this circumstance, we newly propose a novel elastic metagrating model to realize anomalous steering of longitudinal waves in elastic continuum medium. Modeled by a periodic arrangement of a single or array of so-called beam-type elastic members, the present elastic metagratings resolve the difficulties in steering a specific scattered mode of elastic longitudinal waves by suppressing undesired modes in the scattered wave field. As the metagratings are attached to a boundary of elastic continuum, both longitudinal and flexural motions in the beam-type members are so coupled with elasticity wave solutions in the elastic medium as to thoroughly manipulate the reflected longitudinal waves from the interface. A set of appropriate geometric parameters of the beam-type members are searched for a direct control of the scattered modes quantitatively. As practical applications, the proposed elastic metagratings are applied to realize anomalous reflections and asymmetric splitting of longitudinal elastic waves. As well as experimental verifications, performance of the designed elastic metagratings are physically interpreted in the perspective of phase modulation.

Anomalous Dynamics of QBO Disruptions Explained by 1D Theory with External Triggering

AbstractThe quasi-biennial oscillation (QBO) is an alternating, descending pattern of zonal winds in the tropical stratosphere with a period averaging 28 months. The QBO was disrupted in 2016, and arguably again in 2020, by the formation of an anomalous easterly shear zone, and unprecedented stagnation and ascent of shear zones aloft. Several mechanisms have been implicated in causing the 2016 disruption, most notably triggering by horizontal eddy momentum flux divergence, but also anomalous upwelling and wave stress. In this paper, the 1D theory of the QBO is used to show how seemingly disparate features of disruptions follow directly from the dynamics of the QBO response to triggering. The perturbed QBO is interpreted using a heuristic version of the 1D model, which establishes that 1) stagnation of shear zones aloft resulted from wave dissipation in the shear zone formed by the triggering, and 2) ascent of shear zones aloft resulted from climatological upwelling advecting the stagnant shear zones. Obstacles remain in the theory of triggering. In the 1D theory, the phasing of the triggering is key to determining the response, but the dependence on magnitude is less steep. Yet in MERRA-2, there are triggering events only 20% weaker than the 2016 triggering and equal to the 2020 triggering that did not lead to disruptions. Complicating matters further, MERRA-2 has record-large analysis tendencies during the 2016 disruption, reducing confidence in the resolved momentum budget.

Anomalous Wave Transmission through a Thin Channel Connecting Two Acoustic Waveguides

Anomalous Wave Transmission through a Thin Channel Connecting Two Acoustic Waveguides

Different impacts of spring tropical Atlantic SST anomalies on Eurasia spring climate during the periods of 1970–1995 and 1996–2018

We investigate impacts of spring tropical Atlantic sea surface temperature anomalies (SSTAs) on Eurasian spring climate during the period of 1961–2018, using both observations and Community Atmosphere Model (CAM) simulations. Observations during the study period show that the tropical Atlantic sea surface temperature (SST) experienced an abrupt warming around 1995. Distinctive impacts of spring tropical Atlantic SSTAs on Eurasian spring surface air temperature (SAT) and precipitation during the period 1970–1995 (P1) and 1996–2018 (P2) are revealed. During P1, spring tropical Atlantic SSTAs were highly correlated with spring SAT anomalies over Northern Europe, Southeast China, and Indochina Peninsula. These high correlations disappeared during P2; instead, high correlations dominated over North-Northeastern China, and Central Siberia in spring. The high correlation patterns between spring tropical Atlantic SSTAs and spring Eurasian precipitation of these two periods also differed. The interannual relationship between spring tropical Atlantic SSTAs and Eurasian SAT/precipitation during P2 was mainly due to the existence of an anomalous atmospheric wave train across the tropical Atlantic and Eurasia, which was absent during P1. These observational results are confirmed by a set of CAM simulations.

The role of transient eddies and diabatic heating in the maintenance of European heat waves: a nonlinear quasi-stationary wave perspective

European heat waves result from large-scale stationary waves and have major impacts on the economy and mortality. However, the dynamical processes leading to and maintaining heat waves are still not well understood. Here we use a nonlinear stationary wave model (NSWM) to examine the role played by anomalous stationary waves and how they are forced during heat waves. For our study, we use the Japanese Reanalysis (JRA-55) data for the period 1958 through 2017. We show that the NSWM can successfully reproduce the main features of the observed anomalous stationary waves in the upper troposphere. Our results indicate that the dynamics of heat waves are nonlinear, and transient momentum fluxes are the primary drivers of the observed anomalous stationary waves. The contribution from orographic forcing is moderate and mainly through nonlinear interactions with diabatic heating. Further decomposition of the transients indicates that the high-frequency transient vorticity fluxes make dominant contributions. Furthermore, our results reveal that the response to heating located in the tropical Indian Ocean and the west Pacific region is primarily responsible for maintaining the observed anomalous stationary waves linked to European heat waves. This is confirmed by exploring the relationship between heat waves and the Indian Ocean Dipole strength. The heating in the mid-latitude and tropical Atlantic region plays a secondary role. Our results suggest that European heat waves are potentially predictable by considering the nonlinear effects involved in anomalous stationary waves and the heating sources in the nearby and remote tropical region.

Wave propagation improvement in two-dimensional bond-based peridynamics model

In this study, methods to mitigate anomalous wave propagation in 2-D Bond-Based Peridynamics (PD) are presented. Similarly to what happens in classical non-local models, an irregular wave transmission phenomenon occurs at high frequencies. This feature of the dynamic performance of PD, limits its potential applications. A minimization method based on the weighted residual point collocation is introduced to substantially extend the frequency range of wave motion modeling. The optimization problem, developed through inverse analysis, is set up by comparing exact and numerical dispersion curves and minimizing the error in the frequency-wavenumber domain. A significant improvement in the wave propagation simulation using Bond-Based PD is observed.

Addressing the meteotsunami risk in the united states

Meteotsunamis are created by transitory weather disturbances moving over water, have a long history of impacting the United States (U.S.) and have resulted in loss of life and property. Many of these events have been historically mischaracterized as seiches, anomalous weather-related waves, or ignored altogether. In this paper, we review meteotsunami generation mechanisms common in the U.S. and highlight several classic historical cases of U.S. meteotsunami formation and impact. We then describe recent advances in sensing and understanding that led to the establishment of initial, rudimentary alerting capabilities for the U.S. Great Lakes and U.S. East Coast. Finally, we describe the major challenges and gaps that must be overcome to move the U.S. toward a comprehensive meteotsunami forecast and warning capability. We also discuss how we envision the various relevant offices of the national oceanic and atmospheric administration (NOAA) working together to achieve this vision. These offices include the NOAA research laboratories, national weather service (NWS) Weather Forecast Offices and National Centers, National Ocean Service Center for Operational Oceanographic Products and Services and NWS Tsunami Warning Centers.

Iba: The First Pure Tropical Cyclogenesis Over the Western South Atlantic Ocean

AbstractIn March 2019, the tropical western South Atlantic Ocean (∼16.5°S) registered the first pure tropical cyclogenesis since the beginning of the satellite era, which the Brazilian Navy named Iba. This study presents a description of the synoptic features and meteorological mechanisms contributing to Iba's initial cyclonic vorticity as well as the anomalous synoptic patterns linked to this unprecedented tropical cyclogenesis. Moreover, a general description of Iba's lifecycle is provided. The genesis of Iba was as a pure tropical cyclone (00:00 UTC on March 22), and it underwent subtropical (18:00 UTC on March 25) and extratropical (06:00 UTC on March 29) transitions. Anomalies for a 5‐day period prior to the genesis relative to the March climatology show environmental features appropriate for tropical cyclogenesis: (a) vertical wind shear in the 850–200 hPa lower than 10 m s−1, (b) intense initial cyclonic relative vorticity at 925 hPa (−10 × 10−5 s−1), (c) latent and sensible heat fluxes near the climatological values (∼150 W m−2), (d) warmer sea surface temperature (+2°C), and (e) relative humidity at 700 hPa 20% higher than the climatology. These features were associated with an anomalous wave pattern at 500 hPa, resembling a blocking structure over the southeastern South Pacific Ocean, and an anticyclonic circulation at upper levels over southeastern Brazil. This environment propitiated a weak vertical wind shear and convective cloud organization. Near the surface, the horizontal wind shear between the postfrontal southwesterly winds and the northeasterly winds of the South Atlantic subtropical anticyclone helped to generate Iba's initial cyclonic vorticity.

Dependence of the magneto-optical signal on the Co layer thickness asymmetry in Co/Pt/Co films

We have studied the magneto-optical response of $\mathrm{Co}({t}_{1})/\mathrm{Pt}(d)/\mathrm{Co}({t}_{2})$ trilayer structures, in which the total Co thickness $({t}_{1}+{t}_{2})$ was held constant, but the split between the top and bottom layer made variable to investigate the impact of the Co layer thickness asymmetry ${a}_{t}=({t}_{1}\ensuremath{-}{t}_{2})/({t}_{1}+{t}_{2})$ as well as the influence of the Pt interlayer thickness $d$. The optical and magneto-optical properties of these films were measured using generalized magneto-optical ellipsometry. A set of specifically designed inverted double-wedge structures were characterized to determine the influence of $d$ and especially of ${a}_{t}$, which should be significant if quantum-well states are relevantly modified by the Co layer thickness asymmetry. In addition to a Co/Pt interface proximity effect that leads to an overall enhancement of the magneto-optical response, we do not find the expected quadratic ${a}_{t}$ effect, but instead observe a strong linear ${a}_{t}$ effect. We also compare our experimental results to a classical optics description based upon the transfer matrix method, but we can achieve agreement in between these calculations and our experimental data only if we assume massively anomalous optical wave attenuation in Pt. This perceived anomalous attenuation of Pt is not observed for Co/Pt/Co trilayer structures with much thicker Co films, in which quantum-well states should not be relevant anymore. Thus, the origin of the unexpected strong linear ${a}_{t}$ effect in ultrathin Co/Pt/Co trilayers cannot be a local materials modification, but instead must be associated with the collective nature of quantum-mechanical electronic states in asymmetric trilayers.

Fermi-Pasta-Ulam-Tsingou recurrence of periodic anomalous waves in the complex Ginzburg-Landau and in the Lugiato-Lefever equations.

The complex Ginzburg-Landau (CGL) equation, an envelope model relevant in the description of several natural phenomena like binary-fluid convection and second-order phase transitions, and the Lugiato-Lefever (LL) equation, describing the dynamics of optical fields in pumped lossy cavities, can be viewed as nonintegrable generalizations of the nonlinear Schrödinger (NLS) equation, including diffusion, linear and nonlinear loss or gain terms, and external forcing. In this paper we treat the nonintegrable terms of both equations as small perturbations of the integrable focusing NLS equation, and we study the Cauchy problem of the CGL and LL equations corresponding to periodic initial perturbations of the unstable NLS background solution, in the simplest case of a single unstable mode. Using the approach developed in a recent paper by the authors with P. G. Grinevich [Phys. Rev. E 101, 032204 (2020)10.1103/PhysRevE.101.032204], based on the finite gap method and the theory of perturbations of soliton PDEs, we construct the proper analytic models describing quantitatively how the solution evolves, after a suitable transient, into a Fermi-Pasta-Ulam-Tsingou (FPUT) recurrence of anomalous waves (AWs) described by slowly varying lower dimensional patterns (attractors) in the (x,t) plane, characterized by Δx=L/2 or Δx=0 in the case in which loss or gain, respectively, effects prevail, where Δx is the x-shift of the position of the AW during the recurrence and L is the period. We also obtain, in the CGL case, the analytic condition for which loss and gain exactly balance, stabilizing the ideal FPUT recurrence of periodic NLS AWs; such a stabilization is not possible in the LL case due to the external forcing. These processes are described, to leading order, in terms of elementary functions of the initial data in the CGL case, and in terms of elementary and special functions of the initial data in the LL case.

Inverse design of topological metaplates for flexural waves with machine learning

The mechanical analog to the topological insulators brings anomalous elastic wave properties which diversifies classic wave functions for potential broad applications. To obtain topological mechanical wave states with good quality at desired frequency ranges, it needs repetitive trials of different geometric parameters with traditional forward designs. In this work, we develop an inverse design of topological edge states for flexural wave using machine learning method which is promising for instantaneous design. Nonlinear mapping function from input targets to output desired parameters are adopted in artificial neural networks where the data sets for training are generated by the plane wave expansion method. Topological edge states are then realized and compared for different bandgap width conditions with such inverse designs, proving that wide bandgap can promote the confinement of the topological edge states. Finally, direction selective propagations with sharp turns are further demonstrated as anomalous wave behaviors. The machine learning inverse design of topological states for flexural wave provides an efficient way to design practical devices with targeted needs for potential applications such as signal processing, sensing and energy harvesting.