Secondary Waves Research Articles

Towards predicting COVID-19 infection waves: A random-walk Monte Carlo simulation approach

Phenomenological and deterministic models are often used for the estimation of transmission parameters in an epidemic and for the prediction of its growth trajectory. Such analyses are usually based on single peak outbreak dynamics. In light of the present COVID-19 pandemic, there is a pressing need to better understand observed epidemic growth with multiple peak structures, preferably using first-principles methods. Along the lines of our previous work [Physica A 574, 126014 (2021)], here we apply 2D random-walk Monte Carlo calculations to better understand COVID-19 spread through contact interactions. Lockdown scenarios and all other control interventions are imposed through mobility restrictions and a regulation of the infection rate within the stochastically interacting population. The susceptible, infected and recovered populations are tracked over time, with daily infection rates obtained without recourse to the solution of differential equations.The simulations were carried out for population densities corresponding to four countries, India, Serbia, South Africa and USA. In all cases our results capture the observed infection growth rates. More importantly, the simulation model is shown to predict secondary and tertiary waves of infections with reasonable accuracy. This predictive nature of multiple wave structures provides a simple and effective tool that may be useful in planning mitigation strategies during the present pandemic.

INTERACTION OF BENDING WAVES PROPAGATING IN AN INHOMOGENEOUS PLATE WITH AN OBSTACLE, WHICH IS A ROD RESTING ON A VISCOELASTIC FOUNDATION

A single interaction of a wave propagating in an inhomogeneous plate in the form of an infinite strip with a one-dimensional distributed mechanical object is considered. A distributed object is understood as a rod lying on a viscoelastic foundation that performs bending and torsional vibrations. It is considered that the plate has different parameters to the left and to the right of the rod. Physically and mathematically correct conditions at the interface between a plate and a rod are obtained as a consequence of the formulation of contact problems of the dynamics of two-dimensional elastic systems with one-dimensional loads, based on the variational principle of Hamilton – Ostrogradsky. The frequencies and wave numbers of the secondary (reflected and transmitted) waves, as well as the critical frequency, below which the wave does not propagate in the plate, are determined. Based on the solution of the kinematics problem from a system of linear algebraic equations obtained from the boundary conditions, the coefficients of reflection and transmission of bending waves are found. These coefficients resonantly depend on the frequency of the incident wave. Calculated graphs of the transmission coefficient versus the frequency of the incident wave are given for various parameters of the rod. The conditions for self-isolation and reflectionless passage of a wave through an obstacle are determined. It has been established that the frequency of the maximum vibration isolation is located above the frequencies at which the waves completely pass through the obstacle. An expression is obtained for the force due to the pressure of bending waves on a one-dimensional object. Its constant component is calculated, which vanishes (for a homogeneous plate) in the absence of waves reflected from the obstacle. It is shown that in degenerate cases the results obtained coincide with previous studies by other authors.

Primary Versus Secondary Gravity Wave Responses at F‐Region Heights Generated by a Convective Source

AbstractA 2D nonlinear, compressible model is used to simulate the acoustic‐gravity wave (AGW, i.e., encompassing the spectrum of acoustic and gravity waves) response to a thunderstorm squall‐line type source. We investigate the primary and secondary neutral AGW response in the thermosphere, consistent with waves that can couple to the F‐region ionospheric plasma, and manifest as Traveling Ionospheric Disturbances (TIDs). We find that primary waves at z = 240 km altitude have wavelengths and phase speeds in the range 170–270 km, and 180–320 m/s, respectively. The secondary waves generated have wavelengths ranging from ∼100 to 600 km, and phase speeds from 300 to 630 m/s. While there is overlap in the wave spectra, we find that the secondary waves (i.e., those that have been nonlinearly transformed or generated secondarily/subsequently from the primary wave) generally have faster phases than the primary waves. We also assess the notion that waves with fast phase speeds (that exceed proposed theoretical upper limits on passing from the mesosphere to thermosphere) observed at F‐region heights must be secondary waves, for example, those generated in situ by wave breaking in the lower thermosphere, rather than directly propagating primary waves from their sources. We find that primary waves with phase speeds greater than this proposed upper limit can tunnel through a deep portion of the lower/middle atmosphere and emerge as propagating waves in the thermosphere. Therefore, comparing a TID's/GWs phase speed with this upper limit is not a robust method of identifying whether an observed TID originates from a primary versus secondary AGW.

Dynamics and 2D temperature distribution of plasma obtained by femtosecond laser-induced breakdown

Recently, plasma produced by focusing femtosecond laser in gases has been introduced as an etching tool in materials processing. Proper control of the plasma in this application necessitates the apt understanding of the different morphological features of the plasma. In this contribution we show that, the plasma produced in air goes through several stages of morphological development–from ellipsoidal to spherical to toroidal plasma, whereas in argon, axial compression of an ellipsoidal plasma is observed. To explain this dissimilarity, we have quantified the temperature by emission spectroscopy (Planck analysis with Wien’s approximation). The evolution of temperature shows a triple exponential dependence in time which can be correlated with different stages of morphological changes of the plasma. Open Source Field Operation and Manipulation simulations using experimentally determined temperature values show that—(i) the reverse pressure gradient propagates radially inwards and compresses the plasma in both air and argon and forms a localized high pressure zone at the center that generates a secondary pressure wave in air, but not in argon, and (ii) the baroclinic torque that is generated because of the Richtmyer–Meshkov instability, dominates the rate of vorticity in air, whereas effects of flow compressibility and velocity gradients dominate the vortices in argon. Knowledge of the initial state and the dynamics of the subsequent stages of the plasma formation can be utilized for control and optimization of laser-induced plasma applications.

Mesospheric Short‐Period Gravity Waves in the Antarctic Peninsula Observed in All‐Sky Airglow Images and Their Possible Source Locations

AbstractThis study presents an analysis of OH airglow images observed from an all‐sky camera (ASC) at King Sejong Station (KSS), Antarctic for the 2012–2016 period. The two‐dimensional power spectra of short‐period gravity waves (<1 hr) as a function of phase velocities are obtained using the M‐transform method that employs the time sequence of ASC images. The amplitudes of the power spectral densities show that the mesospheric wave activity is the largest during winter (May, June, and July) and is the smallest in fall (February, March, and April). Wind‐blocking diagrams are constructed on the same two‐dimensional domain as in the two‐dimensional spectra using horizontal winds obtained from MERRA‐2 reanalysis at z = 0–80 km and from KSS meteor radar data at z = 80–90 km. Climatologically, the spectral regions of slowly propagating gravity waves (<30 m s−1) are overlaid by the wind‐blocking areas, which suggests the filtering of gravity waves with small phase speeds by winds below the upper stratosphere. Eastward propagating gravity waves in winter and intense south‐eastward waves in spring (October) are found to be unfiltered by the stratospheric winds. It is also found from the spectral analysis that these unfiltered gravity waves can originate from the upper stratosphere or the lower mesosphere, and not from the troposphere, which suggests the possibility of ASC observation of the secondary gravity waves generated near the stratopause.

Primordial black holes and secondary gravitational waves from string inspired general no-scale supergravity

The formation of primordial black hole (PBH) dark matter and the generation of scalar induced secondary gravitational waves (SIGWs) have been studied in the generic no-scale supergravity inflationary models. By adding an exponential term to the K\"ahler potential, the inflaton experiences a period of ultraslow-roll and the amplitude of primordial power spectrum at small scales is enhanced to $\mathcal{O}({10}^{\ensuremath{-}2})$. The enhanced power spectra of primordial curvature perturbations can have both sharp and broad peaks. A wide mass range of PBHs can be produced in our model, and the frequencies of the accompanied SIGWs are ranged form nanohertz to kilohertz. We show four benchmark points where the generated PBH masses are around $\mathcal{O}({10}^{\ensuremath{-}16}\text{ }\text{ }{M}_{\ensuremath{\bigodot}})$, $\mathcal{O}({10}^{\ensuremath{-}12}\text{ }\text{ }{M}_{\ensuremath{\bigodot}})$, $\mathcal{O}({10}^{\ensuremath{-}2}\text{ }\text{ }{M}_{\ensuremath{\bigodot}})$ and $\mathcal{O}({10}^{2}\text{ }\text{ }{M}_{\ensuremath{\bigodot}})$. The PBHs with masses around $\mathcal{O}({10}^{\ensuremath{-}16}\text{ }\text{ }{M}_{\ensuremath{\bigodot}})$ and $\mathcal{O}({10}^{\ensuremath{-}12}\text{ }\text{ }{M}_{\ensuremath{\bigodot}})$ can make up almost all the dark matter, and the accompanied SIGWs can be probed by the upcoming space-based gravitational wave observatory. Also, the SIGWs accompanied with the formation of stellar mass PBHs can be used to interpret the stochastic GW background in the nanohertz band, detected by the North American Nanohertz Observatory for Gravitational Waves, and can be tested by future interferometric gravitational wave observatory.

Spall and recompression processes with double shock loading of polycrystalline copper

Spall fracture induced by interaction of multiple shockwaves in shock-loaded material is a key issue for both basic science and practical application. Here, shock induced spall and subsequent recompression process of polycrystalline copper are investigated using molecular dynamics simulations. Two significant velocity peaks are observed from the velocity history of free surface, which is explained through the complex propagation of waves and dynamic damage processes. The overshoot feature is also noted in the free-surface velocities on account of the shock response of the damaged region. Recrystallization occurs after secondary shock passes through the spall region. Meanwhile, the differences in recrystallization processes are observed for the different shock response states of the spall region induced by secondary shock waves. What's more, the reduction of grain sizes in the spall region is also revealed in our simulation, which is consistent with experiments.

Asymmetric vortex pair induces secondary traveling wave vibration of a flexible cylinder from still water to incoming flow

As one of the fundamental problems in fluid mechanics, the flow-induced vibration of a flexible cylinder helps shed light on various complex fluid–structure interaction phenomena, such as the coupling effect of the cross-flow and in-line motions in the relationship between external fluid forces and vortical wake patterns. This paper devised a non-uniform in-flow condition (partially uniform flow and partially still water) for flexible cylinders in experimental and numerical conditions. Consistently, a new phenomenon is observed in different scale experiments and simulations where secondary traveling wave vibration of the flexible cylinder is excited from the still water part to the uniform inflow part due to the positive external fluid energy input in the still water. Furthermore, the detailed flow visualization on the vortical wake patterns around the vibrating flexible cylinders reveals that the external fluid force sources in the still water are due to the existence of the attached vortex pair with an uneven strength, which has been observed before in the still rigid cylinder in the oscillatory flow or the rigid cylinder oscillating in the still water at Keulegan–Carpenter number from 4 to 7.

Using GAM functions and Markov-Switching models in an evaluation framework to assess countries\u2019 performance in controlling the COVID-19 pandemic

BackgroundThe COVID-19 pandemic has initiated several initiatives to better understand its behavior, and some projects are monitoring its evolution across countries, which naturally leads to comparisons made by those using the data. However, most “at a glance” comparisons may be misleading because the curve that should explain the evolution of COVID-19 is different across countries, as a result of the underlying geopolitical or socio-economic characteristics. Therefore, this paper contributes to the scientific endeavour by creating a new evaluation framework to help stakeholders adequately monitor and assess the evolution of COVID-19 in countries, considering the occurrence of spikes, "secondary waves" and structural breaks in the time series.MethodsGeneralized Additive Models were used to model cumulative and daily curves for confirmed cases and deaths. The Root Relative Squared Error and the Percentage Deviance Explained measured how well the models fit the data. A local min-max function was used to identify all local maxima in the fitted values. The pure Markov-Switching and the family of Markov-Switching GARCH models were used to identify structural breaks in the COVID-19 time series. Finally, a quadrants system to identify countries that are more/less efficient in the short/long term in controlling the spread of the virus and the number of deaths was developed. Such methods were applied in the time series of 189 countries, collected from the Centre for Systems Science and Engineering at Johns Hopkins University.ResultsOur methodology proves more effective in explaining the evolution of COVID-19 than growth functions worldwide, in addition to standardizing the entire estimation process in a single type of function. Besides, it highlights several inflection points and regime-switching moments, as a consequence of people’s diminished commitment to fighting the pandemic. Although Europe is the most developed continent in the world, it is home to most countries with an upward trend and considered inefficient, for confirmed cases and deaths.ConclusionsThe new outcomes presented in this research will allow key stakeholders to check whether or not public policies and interventions in the fight against COVID-19 are having an effect, easily identifying examples of best practices and promote such policies more widely around the world.

Interaction of Irregular Waves with Vertical Breakwater and Characteristics of Secondary Wave Generated by Overtopping

Interaction of Irregular Waves with Vertical Breakwater and Characteristics of Secondary Wave Generated by Overtopping

Nonlinear stability of diffusive contact wave for a chemotaxis model

We consider a 2×2 system of hyperbolic-parabolic balance laws. Our system is the converted form under inverse Hopf-Cole transformation of a Keller-Segel type chemotaxis model with logistic growth, logarithmic sensitivity, non-diffusive chemical signal and density-dependent production/consumption rate. We study Cauchy problem when the Cauchy data are near a diffusive contact wave. The contact wave connects two different end-states as x→±∞, reflecting the situation when the logarithmic singularity plays an intrinsic role in the original chemotaxis model. We establish global existence of solution and study time asymptotic behavior of the solution. Consequently, we obtain nonlinear stability of the diffusive contact wave. Our result shows a significant difference when comparing our model to Euler equations with damping. In our case, there exists a secondary wave in the asymptotic ansatz. Therefore, the solution to Cauchy problem converges to the diffusive contact wave slower than in the case of Euler equations with damping. Besides its own physical relevance, our model is a prototype of a general system of hyperbolic-parabolic balance laws. Our results shed light on the future study of nonlinear stability of elementary waves for a general system.

Fast gravitational wave bursts from axion clumps

The axion objects such as axion miniclusters and axion clouds around spinning black holes induce parametric resonances of electromagnetic waves through the axion-photon interaction. In particular, it has been known that the resonances from the axion with the mass around ${10}^{\ensuremath{-}6}\text{ }\text{ }\mathrm{eV}$ may explain the observed fast radio bursts (FRBs). Here we argue that similar bursts of high frequency gravitational waves, which we call fast gravitational wave bursts (FGBs), are generated from axion clumps with the presence of gravitational Chern-Simons (CS) coupling. The typical frequency is half of the axion mass, which in general can range from kHz to GHz. We also discuss the secondary gravitational wave production associated with FRB, as well as the possible host objects of the axion clouds, such as primordial black holes with typical masses around ${10}^{\ensuremath{-}5}\text{ }\text{ }{M}_{\ensuremath{\bigodot}}$. Future detections of FGBs together with the observed FRBs are expected to provide more evidence for the axion.

Q2DW-Tide and -Ionosphere Interactions as Observed From ICON and Ground-Based Radars.

A quasi-2-day wave (Q2DW) event during January-February, 2020, is investigated in terms of its propagation from 96 to 250 km as a function of latitude (10°S to 30°N), its nonlinear interactions with migrating tides to produce 16 and 9.6-h secondary waves (SWs), and the plasma drift and density perturbations that it produces in the topside F-region (590-607 km) between magnetic latitudes 18°S and 18°N. This is accomplished through analysis of coincident Ionospheric Connections Explorer (ICON) measurements of neutral winds, plasma drifts and ion densities, and wind measurements from four low-latitude (±15°) specular meteor radars (SMRs). The Q2DW westward-propagating components that existed during this period consist of zonal wavenumbers s = 2 and s = 3, that is, Q2DW+2 and Q2DW+3 (e.g., He, Chau et al., 2021, https://doi.org/10.1029/93jd00380). SWs in the ICON measurements are inferred from Q2DW+2 and Q2DW+3 characteristics derived from traditional longitude-UT fits that potentially contain aliasing contributions from SWs ("apparent" Q2DWs), from fits to space-based zonal wavenumbers that each reflect the aggregate signature of either Q2DW+2 or Q2DW+3 and its SWs combined ("effective" Q2DWs), and based on information contained in published numerical simulations. The total Q2DW ionospheric responses consists of F-region field-aligned and meridional drifts of order ±25 ms-1 and ±5-7 ms-1, respectively, and total ion density perturbations of order (±10%-25%). It is shown that the SWs can sometimes make substantial contributions to the Q2DW winds, drifts, and plasma densities.

Secondary Faraday waves in microgravity

Recent microgravity experiments have demonstrated that Faraday waves can arise in a secondary instability over the primary columnar patterns that develop after the frozen wave instability. While some numerical studies have investigated this phenomenon, theoretical analyses are only found in the works of Shevtsova et al. (2016) [1] and Lyubimova et al. (2019) [2]. Here, we extend these efforts by analysing the stability of a three-layer system, and derive the critical onset of Faraday waves, which appear via Hopf bifurcation. Numerical simulations — based on a model that reproduces the frozen wave mode with lowest wavenumber — are carried out to test this result and to analyse the character of the bifurcation. The predicted Hopf bifurcation is confirmed, which constitutes the first observation of modulated secondary Faraday waves. The abrupt growth of these modulated waves above onset indicates that the primary bifurcation is subcritical and is accompanied by a saddle-node bifurcation of periodic orbits that stabilises the (branch of) unstable solutions created in the subcritical Hopf bifurcation. Further above onset, these modulated waves are destroyed via a saddle-node heteroclinic bifurcation. Results for an N-layer configuration, which represents a more general frozen wave pattern, are also presented and compared with the three-layer case.

Temperature of Polymethyl Methacrylate in a Secondary Shock Wave

Temperature of Polymethyl Methacrylate in a Secondary Shock Wave

Azimuthal anisotropy from eikonal tomography: example from ambient-noise measurements in the AlpArray network

SUMMARY Ambient-noise records from the AlpArray network are used to measure Rayleigh wave phase velocities between more than 150 000 station pairs. From these, azimuthally anisotropic phase-velocity maps are obtained by applying the eikonal tomography method. Several synthetic tests are shown to study the bias in the Ψ2 anisotropy. There are two main groups of bias, the first one caused by interference between refracted/reflected waves and the appearance of secondary wave fronts that affect the phase traveltime measurements. This bias can be reduced if the amplitude field can be estimated correctly. Another source of error is related to the incomplete reconstruction of the traveltime field that is only sparsely sampled due to the receiver locations. Both types of bias scale with the magnitude of the velocity heterogeneities. Most affected by the spurious Ψ2 anisotropy are areas inside and at the border of low-velocity zones. In the isotropic velocity distribution, most of the bias cancels out if the azimuthal coverage is good. Despite the lack of resolution in many parts of the surveyed area, we identify a number of anisotropic structures that are robust: in the central Alps, we find a layered anisotropic structure, arc-parallel at mid-crustal depths and arc-perpendicular in the lower crust. In contrast, in the eastern Alps, the pattern is more consistently E–W oriented which we relate to the eastward extrusion. The northern Alpine forleand exhibits a preferential anisotropic orientation that is similar to SKS observations in the lowermost crust and uppermost mantle.

Long-Term Study on Medium-Scale Traveling Ionospheric Disturbances Observed over the South American Equatorial Region

Using data collected by the GNSS dual-frequency receivers network, de-trended TEC maps were generated to identify and characterize the medium-scale traveling ionospheric disturbances (MSTIDs) over the South American equatorial region (latitude: 0∘ to 15∘ S and longitude: 30∘ to 55∘ W) during solar cycle 24 (from January 2014 to December 2019). A total of 712 MSTIDs were observed during quiet geomagnetic conditions. The Frequency of occurrence of MSTID is high during the solar maximum and low in the minimum phase. This might be due to the solar cycle dependence of gravity wave activity in the lower atmosphere and gravity wave propagation conditions in the thermosphere. The predominant daytime MSTIDs, representing 80% of the total observations, occurred in winter (June-August season in the southern hemisphere) with the secondary peak in the equinox; while the evening time MSTIDs, representing 18% of the entire events, occurred in summer (December to February season) and equinox (March to May and September to November), and the remaining 2% of the MSTIDs were observed during nighttime. The seasonal variation of the MSTID events was attributed to the source mechanisms generating them, the wind filtering and dissipation effects, and the local time dependency. The horizontal wavelengths of the MSTIDs were mostly concentrated between 500 and 800 km, with the mean value of 667 ± 131 km. The observed periods ranged from 30 to 45 min with the mean value of 36 ± 7 min. The observed horizontal phase speeds were distributed around 200 to 400 m/s, with the corresponding mean of 301 ± 75 m/s. The MSTIDs in the winter solstice and equinoctial months preferentially propagated northeastward and northwestward. Meanwhile, during the summer solstice, they propagated in all directions. The anisotropy of the propagation direction might be due to several reasons: the wind and dissipative filtering effects, ion drag effects, the primary source region, and the presence of the secondary or tertiary gravity waves in the thermosphere. Atmospheric gravity waves from strong convective sources might be the primary precursor for the observed equatorial MSTIDs. In all seasons, we noted that the MSTIDs propagating southeastward were probably excited by the likely gravity waves generated by the intertropical convergence zone (ITCZ).

Gravity wave instability structures and turbulence from more than 1.5 years of OH* airglow imager observations in Slovenia

Abstract. We analysed 286 nights of data from the OH* airglow imager FAIM 3 (Fast Airglow IMager) acquired at Otlica Observatory (45.93∘ N, 13.91∘ E), Slovenia, between 26 October 2017 and 6 June 2019. Measurements have been performed with a spatial resolution of 24 m per pixel and a temporal resolution of 2.8 s. A two-dimensional fast Fourier transform is applied to the image data to derive horizontal wavelengths between 48 m and 4.5 km in the upper mesosphere/lower thermosphere (UMLT) region. In contrast to the statistics of larger-scale gravity waves (horizontal wavelength up to ca. 50 km; Hannawald et al., 2019), we find a more isotropic distribution of directions of propagation, pointing to the presence of wave structures created above the stratospheric wind fields. A weak seasonal tendency of a majority of waves propagating eastward during winter may be due to instability features from breaking secondary gravity waves that were created in the stratosphere. We also observe an increased southward propagation during summer, which we interpret as an enhanced contribution of secondary gravity waves created as a consequence of primary wave filtering by the meridional mesospheric circulation. We present multiple observations of turbulence episodes captured by our high-resolution airglow imager and estimated the energy dissipation rate in the UMLT from image sequences in 25 cases. Values range around 0.08 and 9.03 W kg−1 and are on average higher than those in recent literature. The values found here would lead to an approximated localized maximum heating of 0.03–3.02 K per turbulence event. These are in the same range as the daily chemical heating rates for the entire atmosphere reported by Marsh (2011), which apparently stresses the importance of dynamical energy conversion in the UMLT.

Disturbances of the Thermosphere and the Ionosphere during a Meteorological Storm

Determination of the physical mechanisms of energy transfer of tropospheric disturbances to the ionosphere is one of the fundamental problems of atmospheric physics. This article presents the results of observations carried out using two-wavelength lidar sensing at tropospheric altitudes and satellite GPS measurements during a meteorological storm in Kaliningrad (Russia, 54.7° N, 20.5° E) on 1 April 2016. During lidar sensing, it was found that the amplitudes of variations in atmospheric parameters with periods of acoustic (AWs) and internal gravity (IGWs) waves significantly increased. As a result of numerical modeling using the AtmoSym software package, it was shown that there is a noticeable increase in the period of temperature disturbances from 6–12 min to 10–17 min at altitudes from 150 km up to 230 km during the vertical propagation of acoustic waves and internal gravity waves from the troposphere. Nonlinear and dissipative processes in this layer lead to the formation of sources of secondary waves in the thermosphere with periods longer than those of primary ones. In this case, the unsteady nature of the wave source and the short duration of its operation does not lead to significant heating of the thermosphere. Simultaneous satellite observations demonstrate the response of the ionosphere (total electron content (TEC) disturbance) to tropospheric disturbances. Analysis of the time series of the amplitudes of the reflected lidar signal and TEC made it possible to determine that the response time of the ionosphere to tropospheric disturbances is 30–40 min.

Triadic resonances in internal wave modes with background shear

In this paper, we use asymptotic theory and numerical methods to study resonant triad interactions among discrete internal wave modes at a fixed frequency ( $\omega$ ) in a two-dimensional, uniformly stratified shear flow. Motivated by linear internal wave generation mechanisms in the ocean, we assume the primary wave field as a linear superposition of various horizontally propagating vertical modes at a fixed frequency $\omega$ . The weakly nonlinear solution associated with the primary wave field is shown to comprise superharmonic (frequency $2\omega$ ) and zero frequency wave fields, with the focus of this study being on the former. When two interacting primary modes $m$ and $n$ are in triadic resonance with a superharmonic mode $q$ , it results in the divergence of the corresponding superharmonic secondary wave amplitude. For a given modal interaction $(m, n)$ , the superharmonic wave amplitude is plotted on the plane of primary wave frequency $\omega$ and Richardson number $Ri$ , and the locus of divergence locations shows how the resonance locations are influenced by background shear. In the limit of weak background shear ( $Ri\to \infty$ ), using an asymptotic theory, we show that the horizontal wavenumber condition $k_m + k_n = k_q$ is sufficient for triadic resonance, in contrast to the requirement of an additional vertical mode number condition ( $q = |m-n|$ ) in the case of no shear. As a result, the number of resonances for an arbitrarily weak shear is significantly larger than that for no shear. The new resonances that occur in the presence of shear include the possibilities of resonance due to self-interaction and resonances that occur at the seemingly trivial limit of $\omega \approx 0$ , both of which are not possible in the no shear limit. Our weak shear limit conclusions are relevant for other inhomogeneities such as non-uniformity in stratification as well, thus providing an understanding of several recent studies that have highlighted superharmonic generation in non-uniform stratifications. Extending our study to finite shear (finite $Ri$ ) in an ocean-like exponential shear flow profile, we show that for cograde–cograde interactions, a significant number of divergence curves that start at $Ri\to \infty$ will not extend below a cutoff $Ri$ $\sim O(1)$ . In contrast, for retrograde–retrograde interactions, the divergence curves extend all the way from $Ri\to \infty$ to $Ri = 0.5$ . For mixed interactions, new divergence curves appear at $\omega = 0$ for $Ri\sim O(10)$ and extend to other primary wave frequencies for smaller $Ri$ . Consequently, the total ( $\text {cograde} + \text {retrograde} + \text {mixed}$ ) number of resonant triads is of the same order for small $Ri\approx 0.5$ as in the limit of weak shear ( $Ri\to \infty$ ), although it attains a maximum at $Ri\sim O(10)$ .