Gravity Wave Speed Research Articles

The effect of vertical temperature gradient on the equivalent depth in thin atmospheric layers

AbstractThe equivalent depth of an atmospheric layer is of importance in determining the phase speed of gravity waves and characterizing wave phenomena. The value of the equivalent depth can be obtained from the eigenvalues of the vertical structure equation (the vertical part of the primitive equations) where the mean temperature profile is a coefficient. Both numerical solutions of the vertical structure equation and analytical considerations are employed to calculate the equivalent depth, , as a function of the atmospheric layer's thickness, . Our solutions for layers of thickness 100 2000 m show that for baroclinic modes, can be over two orders of magnitudes smaller than . Analytic expressions are derived for in layers of uniform temperature and numerical solutions are derived for layers in which the temperature changes linearly with height. A comparison between the two cases shows that a slight temperature gradient (of say 0.65 K across a 100 m layer) decreases by a factor of 3 (but can reach a factor of 10 for larger gradients) compared with its value in a layer of uniform temperature, while a change of 10 K in the layer's uniform temperature hardly changes . The baroclinic mode exists in all combinations of boundary conditions top and bottom while the barotropic mode only exists when the vertical velocity vanishes at both boundaries of the layer.

A Semi-implicit Finite Volume Scheme for Incompressible Two-Phase Flows

This paper presents a mass and momentum conservative semi-implicit finite volume (FV) scheme for complex non-hydrostatic free surface flows, interacting with moving solid obstacles. A simplified incompressible Baer-Nunziato type model is considered for two-phase flows containing a liquid phase, a solid phase, and the surrounding void. According to the so-called diffuse interface approach, the different phases and consequently the void are described by means of a scalar volume fraction function for each phase. In our numerical scheme, the dynamics of the liquid phase and the motion of the solid are decoupled. The solid is assumed to be a moving rigid body, whose motion is prescribed. Only after the advection of the solid volume fraction, the dynamics of the liquid phase is considered. As usual in semi-implicit schemes, we employ staggered Cartesian control volumes and treat the nonlinear convective terms explicitly, while the pressure terms are treated implicitly. The non-conservative products arising in the transport equation for the solid volume fraction are treated by a path-conservative approach. The resulting semi-implicit FV discretization of the mass and momentum equations leads to a mildly nonlinear system for the pressure which can be efficiently solved with a nested Newton-type technique. The time step size is only limited by the velocities of the two phases contained in the domain, and not by the gravity wave speed nor by the stiff algebraic relaxation source term, which requires an implicit discretization. The resulting semi-implicit algorithm is first validated on a set of classical incompressible Navier-Stokes test problems and later also adds a fixed and moving solid phase.

Tsunami Triggered by the Lamb Wave From the 2022 Tonga Volcanic Eruption and Transition in the Offshore Japan Region

AbstractThe 2022 volcanic eruption in Tonga caused an unusually large tsunami around the Pacific. It travels with a faster apparent velocity and has larger amplitudes at long distances than what would be expected from a conventional tsunami from the volcanic source. This tsunami was generated by the moving atmospheric Lamb wave and traveled at the speed of the Lamb wave (0.31 km/s). Japanese data showed the amplitude of this first tsunami becomes small when approaching the coast, due to the weaker air‐sea coupling at the shallow depth. This wave split when passing the continental slope, and traveled at the speed of the ocean gravity wave. Therefore, the tsunami observed at the coast is delayed by thousands of seconds from the passage of the Lamb wave. Tsunamis generated by this atmospheric mechanism have not been previously observed by modern digital recording systems and should be considered in the tsunami warning systems.

The Compressional Beta Effect and Convective System Propagation

Abstract The compressional beta effect (CBE) arises in a compressible atmosphere with the nontraditional Coriolis terms (NCTs), the Coriolis force from the locally horizontal part of the planetary rotation. Previous studies proposed that the CBE speeds up the eastward propagation and slows down the westward propagation of zonal vertical circulations in a dry atmosphere. Here, we examine how the CBE affects the propagation of convectively coupled tropical waves. We perform 2D (x, z), large-domain cloud-resolving simulations with and without NCTs. This model setup mimics the atmosphere along Earth’s equator, and differences between the simulations highlight the role of the CBE. We analyze precipitation, precipitable water, and surface and upper-level winds from our simulations. Gravity wave signals emerge in all fields. In the no-NCT simulation, eastward and westward gravity waves propagate at the same speed. With NCTs, eastward gravity waves propagate faster than westward gravity waves. To quantify the strength of the CBE, we then measure the difference in gravity wave speed and find that it linearly increases with the system rotation rate. This result is consistent with our theoretical prediction and suggests that the CBE can induce zonal asymmetry in propagation behaviors of convectively coupled waves. Significance Statement The rotation of Earth turns eastward motion upward and upward motion westward, and vice versa. This effect is called the nontraditional Coriolis effect and is omitted in most of the current atmospheric models for predicting weather and climate. Using an idealized model with cloud physics, this study suggests that the inclusion of the nontraditional Coriolis effect speeds up eastward-moving rainy systems and slows down westward-moving ones. The speed change agrees with a theory without cloud physics. This study encourages restoring the nontraditional Coriolis effect to the atmospheric models since it increases the accuracy of tropical large-scale weather prediction while the cost is low.

Imager observation of concentric mesospheric gravity waves over Srinagar, Jammu and Kashmir, India

Using the NARL airglow imager in the Indian subtropical station of Srinagar, Kashmir, India, we report the characteristics of the concentric deformed circular pattern of gravity waves detected at ∼85 km height. OH molecular emission intensities from the height of ∼85 km as observed by the imager in the wide band optical filter of centre wavelength of 840 nm show concentric deformed circular gravity waves drifting northwestward. Using Atmospheric Infrared Sounder (AIRS) image at the centre wavelength of 8.1 µm, deep convective activity around the imager site in the lower atmosphere is recognized as the source mechanism of the observed concentric gravity waves in the mesosphere. The determined phase speed, direction and period of these concentric gravity waves (CGWs) is ∼47 m/s, 150° north of east and ∼10 min (intrinsic period ∼8 min) respectively. At heights of ∼97 km [OI (1S)] and ∼250 km [OI (1D)], these concentric gravity waves are sporadically visible depending on the possible vertical movement of airglow layer height. The dissipated portions of these concentric gravity waves get converted into turbulence at these heights. Using anelastic gravity wave dispersion relation, decreasing horizontal wavelength from the centre of concentric gravity waves is explained. This result is novel in the sense that it disagrees with most of the earlier interpretations of such observations.

Waves on the equatorial β-plane in the presence of a uniform zonal flow: Beyond the Doppler shift

Analytical and numerical solutions of the eigenvalue equation associated with zonally propagating waves of the linearized rotating shallow water equations are derived in a channel on the equatorial β-plane in the presence of a uniform mean zonal flow. The meridionally varying mean height field is in geostrophic balance with the prescribed mean zonal flow. In addition to the trivial Doppler shift of the free waves' phase speeds, the mean state causes the dispersion curves of each of the free Rossby and Poincaré waves to nearly coalesce in pairs of modes when the zonal wavenumber increases. For large zonal wavenumber or large mean flow, the latitudinal variation of the waves' amplitudes differs from that of free waves, i.e., Hermite functions (in wide channels) and harmonic functions (in narrow channels) do not describe the amplitude structure. For large mean speed and for large zonal wavenumber, the eigenvalue problem loses its Sturm–Liouville structure and the eigenfunctions have multiple extrema between successive zeros of the function itself. In contrast to free Kelvin waves, in the presence of a mean flow the meridional velocity component of these waves does not vanish identically. For zonal winds of order 20 m s−1 and for gravity wave speed of order 25 m s−1, conditions relevant to Earth's stratosphere, the phase speed with mean wind can be twice that of the classical theory with no mean zonal wind.

Effect of depth discontinuity on interfacial stability of tangential-velocity discontinuity in shallow-water flow

It is well known that an interface of tangential velocity discontinuity is necessarily unstable, regardless of the velocity difference's strength, so-called the Kelvin-Helmholtz instability (KHI). However, the instability is suppressed for shallow water flows if the Froude number, defined by the ratio of the velocity difference to the gravity wave's speed, is sufficiently large. In this investigation, we examine the effect of the depth difference of two fluid layers on the KHI. The depth difference enhances instability. The dispersion equation is obtained in a sextic polynomial, the interface is thus linearly stable if the dispersion equation has enough six real roots. Given the Froude number M1 in the instability range, the growth rate sensitively depends on the depth ratio r=H1/H2 and increases monotonically with the depth ratio difference from unity. The critical value of the Froude number for stabilization varies with the depth ratio and attains the minimum value 8 for equal depth. This behavior is verified by asymptotic and numerical analysis. Numerically, we illustrate that if the depth ratio r=0.5, the Froude number is equal or greater than 33≈5.745 to stabilize the interface and it is 4.08 for r=2.

Scaling Law for Boundary Layer Inner Eyewall Pumping in Concentric Eyewalls

AbstractThis study explains why observed storms with long concentric eyewall (CE) duration often have a large moat size. A series of slab boundary layer model experiments are conducted with the free atmosphere forcing from different CE structures. The experimental results indicate that the inner eyewall pumping (IEP), the maximum vertical motion at the inner eyewall region, increases with the increase in moat size d and vortex maximum wind vm, the decrease in the inner eyewall radius rm, and increase in inner eyewall vorticity. A scaling law is derived from hundreds of SBL experiments with four variables: IEP win, vortex inner radius rm, vortex maximum wind vm, and moat size d. The dimensionless scaling law is where w∗ = win/vm, d∗ = ζd/c, ζ is the vorticity 2vm/rm, and c is a constant gravity wave speed. The moat size divided by the Rossby length c/ζ, the dimensionless moat size d∗, combines the effect of the moat size and the vortex pressure gradient force to accelerate the inflow and to enlarge the IEP for inner eyewall convection maintenance. A phase diagram of IEP with vortex structure dimensionless moat ζd/c and vortex intensity vm is constructed based on the scaling law for the aircraft and satellite observations. The eyewall replacement cycle may be viewed as the process to reduce the IEP from the decrease of the vortex intensity and the vortex size of the dimensionless moat. This leads to the ultimate disappearance of the inner eyewall.

Generalized Horndeski-like Einstein Gauss-Bonnet inflation with massless primordial gravitons

In this work we shall introduce a theoretical framework comprised by a non-minimal coupled canonical scalar field, a non-minimal coupling to the Gauss-Bonnet invariant and a non-minimal kinetic coupling. This theoretical framework is basically a non-minimally coupled Einstein-Gauss-Bonnet theory with extra corrections of the form of a non-minimal kinetic coupling. In order to comply with the GW170817 event, we shall impose a constraint on the propagation speed of the primordial tensor perturbations that it is equal to that of light's in vacuum, and this constraint basically specifies the way that the scalar potential and the non-minimal couplings of the theory can be chosen. The whole theoretical framework, which belongs to the larger class of Horndeski theories, cannot yield viable results, due to the fact that the primordial gravitational wave speed is not equal to that of light's. Thus we study this theory by also imposing the constraint of having gravity wave speed equal to the light speed. We directly examine the inflationary phenomenology of our theoretical framework and by assuming the slow-roll conditions, we derived the equations of motion in such a way so that analytical results may be extracted. By using several well motivated models we demonstrate the framework leads to a viable phenomenology.

Balance in non-hydrostatic rotating shallow-water flows

Unsteady nonlinear shallow-water flows typically emit inertia-gravity waves through a process called “spontaneous adjustment-emission.” This process has been studied extensively within the rotating shallow-water model, the simplest geophysical model having the required capability. Here, we consider what happens when the hydrostatic assumption underpinning the shallow-water model is dropped. This assumption is in fact not necessary for the derivation of a two-dimensional or single-layer flow model. All one needs is that the horizontal flow field be independent of height in the fluid layer. Then, vertical averaging yields a single-layer flow model with the full range of expected conservation laws, similar to the shallow-water model yet allowing for non-hydrostatic effects. These effects become important for horizontal scales comparable to or less than the depth of the fluid layer. In a rotating flow, such scales may be activated if the Rossby deformation length (the ratio of the characteristic gravity-wave speed to the Coriolis frequency) is comparable to the depth of the fluid layer. Then, the range of frequencies supporting inertia-gravity waves is compressed, and the group velocity of these waves is reduced. We find that this change in wave properties has the effect of strongly suppressing spontaneous adjustment-emission and trapping inertia-gravity waves near regions of relatively strong circulation.

Distilling the mechanism for the Madden–Julian Oscillation into a simple translating structure

AbstractThis article presents a minimal model of the Madden–Julian Oscillation (MJO), isolating a robust mechanism that leads to the observed characteristic pattern and eastward propagation. A localized heat source at the Equator leads to a Gill‐like pattern in the geopotential, with moist air converging toward the heat source. Over a fairly wide range of parameters, the moisture convergence is found to be slightly to the east of the heat source, with moist air advected in from the east along the Kelvin lobe meeting slightly drier air advected meridionally around the Rossby lobes. The associated condensation then gives rise to a heat source that also is east of the original one, thus causing the pattern itself to propagate east with dryer regions both to the east and west of the region of precipitation. The speed of the propagation is limited by the ability of the moisture advection to move the condensational heat source; it thus scales with the fluid speed which is induced by the convective heat source, and so with the strength of the convective heating, and not with a gravity wave speed. The propagation speed also increases with the nominal offset between the centre of the pattern and the subsequent moistening and condensation. In the real world this distance, as well as the level and coherence of condensation, are determined not only by the location of moisture convergence but also by the complex physics of convection in the tropical environment. Thus, even though the underlying MJO mechanism is itself not complicated, its reproduction will depend rather sensitively on model parameters in simulations with comprehensive numerical models.

Total Surface Current Vector and Shear From a Sequence of Satellite Images: Effect of Waves in Opposite Directions

AbstractThe total surface current velocity (TSCV)—the horizontal vector quantity that advects seawater—is an essential climate variable, with few observations available today. The TSCV can be derived from the phase speed of surface gravity waves, and the estimates of the phase speeds of different wavelengths could give a measure of the vertical shear. Here, we combine 10‐m resolution Level‐1C of the Sentinel‐2 Multispectral Instrument, acquired with time lags up to 1 s, and numerical simulation of these images. Retrieving the near‐surface shear requires a specific attention to waves in opposing directions when estimating a single‐phase speed from the phase difference in an image pair. Opposing waves lead to errors in phase speeds that are most frequent for shorter wavelengths. We propose an alternative method using a least squares fit of the current speed and amplitudes of waves in opposing directions to the observed complex amplitudes of a sequence of three images. When applied to Sentinel‐2, this method generally provides more noisy estimate of the current. A byproduct of this analysis is the “opposition spectrum” which is a key quantity in the sources of microseisms and microbaroms. For future possible sensors, the retrieval of TSCV and shear can benefit from increased time lags, resolution, and exposure time of acquisition. These findings should allow new investigations of near‐surface ocean processes including regions of freshwater influence or internal waves, using existing satellite missions such as Sentinel‐2, and provide a basis for the design of future optical instruments.

Planetary, inertia-gravity and Kelvin waves on the f-plane and -plane in the presence of a uniform zonal flow.

A linear wave theory of the Rotating Shallow‐Water Equations (RSWE) is developed in a channel on the midlatitude f‐plane or β‐plane in the presence of a uniform mean zonal flow that is balanced geostrophically by a meridional gradient of the fluid surface height. Here we show that this surface height gradient is a potential vorticity (PV) source that generates Rossby waves even on the f‐plane similar to the generation of these waves by PV sources such as the β‐effect, shear of the mean flow and bottom topography. Numerical solutions of the RSWE show that the resulting Rossby, Poincaré and “Kelvin‐like” waves differ from their counterparts without mean flow in both their phase speeds and meridional structures. Doppler shifting of the “no mean‐flow” phase speeds does not account for the difference in phase speeds, and the meridional structure is often trapped near one of the channel's boundaries and does not oscillate across the channel. A comparison between the phase speeds of Rossby waves of the present theory and those of the Quasi‐Geostrophic Shallow‐Water (QG‐SW) theory shows that the former can be 2.5 times faster than those of the QG‐SW theory. The phase speed of “Kelvin‐like” waves is modified by the presence of a mean flow compared to the classical gravity wave speed, and furthermore their meridional velocity does not vanish. The gaps between the dispersion curves of adjacent Poincaré modes are not uniform but change with the zonal wave number, and the convexity of the dispersion curves also changes with the zonal wave number. These results have implications for the propagation of Rossby wave packets: QG theory overestimates the zonal group velocity.

A mass and momentum‐conservative semi‐implicit finite volume scheme for complex non‐hydrostatic free surface flows

AbstractIn this article, a novel mass and momentum conservative semi‐implicit method is presented for the numerical solution of the incompressible free‐surface Navier–Stokes equations. This method can be seen as an extension of the semi‐implicit mass‐conservative scheme presented by Casulli. The domain is covered by the fluid, by potential solid obstacles, and by the surrounding void via a scalar volume fraction function for each phase, according to the so‐called diffuse interface approach. The semi‐implicit finite volume discretization of the mass and momentum equations leads to a mildly nonlinear system for the pressure. The nonlinearity on the diagonal of the system stems from the nonlinear definition of the volume, while the remaining linear part of the pressure system is symmetric and at least positive semi‐definite. Hence, the pressure can be efficiently obtained with the family of nested Newton‐type techniques recently introduced and analyzed by Brugnano and Casulli. The time step size is only limited by the flow speed and eventually by the velocity of moving rigid obstacles contained in the computational domain, and not by the gravity wave speed. Therefore, the method is efficient also for low Froude number flows. Moreover the scheme is formulated to be locally and globally conservative: for this reason it fits well in the presence of shock waves, too. In the special case of only one grid cell in vertical direction, the proposed scheme automatically reduces to a mass and momentum conservative discretization of the shallow water equations. The proposed method is first validated against the exact solution of a set of one‐dimensional Riemann problems for inviscid flows. Then, some computational results are shown for non‐hydrostatic flow problems and for a simple fluid‐structure interaction problem.

A Shallow-Water Model for Convective Self-Aggregation

AbstractRandomly distributed convective storms can self-aggregate in the absence of large-scale forcings. Here we present a 1D shallow-water model to study the convective self-aggregation. This model simulates the dynamics of the planetary boundary layer and represents convection as a triggered process. Once triggered, convection lasts for finite time and occupies finite length. We show that the model can successfully simulate self-aggregation, and that the results are robust to a wide range of parameter values. In the simulations, convection excites gravity waves. The gravity waves then form a standing wave pattern, separating the domain into convectively active and inactive regions. We analyze the available potential energy (APE) budget and show that convection generates APE, providing energy for self-aggregation. By performing dimensional analysis, we develop a scaling theory for the size of convective aggregation, which is set by the gravity wave speed, damping time scale, and number density of convective storms. This paper provides a simple modeling framework to further study convective self-aggregation.

Occurrence and Development of an Extreme Precipitation Event in the Ili Valley, Xinjiang, China and Analysis of Gravity Waves

We used observational data and the results from a high-resolution numerical simulation model to analyze the occurrence and development of an extreme precipitation event in the Ili Valley, Xinjiang, China on 26 June 2015. We analyzed the horizontal wavelength, period, speed, ducting, energy propagation and feedback mechanism of inertial gravity waves. A low-level convergence line was formed in the valley by the northerly and westerly winds as a result of Central Asian vortices and the trumpet-shaped topography of the Ili Valley. There was sufficient water vapor in the valley for the precipitation event to develop. A mesoscale vortex formed and developed on the low-level convergence line and the rainfall was distributed either near the convergence line or the mesoscale vortex. The low-level convergence line and the uplift caused by the terrain triggered convection, and then the convection triggered waves at lower levels. The combination of ascending motion induced by the lower level waves and the mesoscale vortex led to the development of convection, causing the precipitation to intensify. When the convection moved eastward to Gongliu County, it was coupled with the ascending phase of upper level waves, causing both the convection and precipitation to intensify again. We applied spectral analysis methods to verify that the waves were inertial gravity waves. The upper level inertial gravity waves propagated westward at a mean speed of −12 m s−1 with periods of 73–179 min and horizontal wavelengths of 50–55 km. The lower level inertial gravity waves propagated eastward at a mean speed of 8 m s−1 with periods of 73–200 min and a horizontal wavelength of 85 km. The more (less) favorable waveguide conditions determined whether the gravity waves persisted for a long (short) time and propagated for a longer (shorter) distance. Based on the mesoscale Eliassen–Palm flux theory, the wave energy of inertial gravity waves had an important effect on the maintenance and development of convection and precipitation by affecting wind strength and wind divergence. Feedback was mainly through the meridional and vertical transport of zonal momentum and the meridional transport of heat.

An Artificial Compressibility Method for 1D Simulation of Open-Channel and Pressurized-Pipe Flow

Piping systems (e.g., storm sewers) that transition between free-surface flow and surcharged flow are challenging to model in one-dimensional (1D) networks as the continuity equation changes from hyperbolic to elliptic as the water surface reaches the pipe ceiling. Previous network models are known to have poor mass conservation or unpredictable convergence behavior at such transitions. To address this problem, a new algorithm is developed for simulating unsteady 1D flow in closed conduits with both free-surface and surcharged flow. The shallow-water (hydrostatic) approximation is used as the governing equations. The artificial compressibility (AC) method is implemented as a dual-time-stepping discretization for a finite-volume solver with timescale interpolation used for face reconstruction. A new formulation for the AC celerity parameter is proposed such that the AC celerity matches the equivalent gravity wave speed for the local hydraulic head—which has some similarities to the classic Preissmann Slot used to approximate pressurized flow in conduits. The new approach allows the AC celerity to be set locally by the flow (i.e., non-uniform in space) and removes it as a free parameter of the AC solution method. The derivation of the AC method provides for only a minor change in the form of the solution equations when a computational element switches from free-surface to surcharged. The new solver is tested for both unsteady free-surface (supercritical, subcritical) and surcharged flow transitions in a circular pipe and is implemented in an open-source Python code available under the name “PipeAC.” The results are compared to laboratory experiments that include rapid flow changes due to opening/closing of gates. Results show that the new algorithm is satisfactory for 1D representation of unsteady transition behavior with two caveats: (i) sufficient grid resolution must be applied, and (ii) the shallow-water equation approximations (hydrostatic, single-fluid) limit the accuracy of the solution with regards to the celerity of the turbulent unsteady bore that propagates upstream. This research might benefit any piping network model that must smoothly handle unsteady transitions from free surface to surcharged flow.

Observations of Shoaling Density Current Regime Changes in Internal Wave Interactions

AbstractWe present in situ and remote observations of a Mississippi plume front in the Louisiana Bight. The plume propagated freely across the bight, rather than as a coastal current. The observed cross-front circulation pattern is typical of density currents, as are the small width (≈100 m) of the plume front and the presence of surface frontal convergence. A comparison of observations with stratified density current theory is conducted. Additionally, subcritical to supercritical transitions of frontal propagation speed relative to internal gravity wave (IGW) speed are demonstrated to occur. That is in part due to IGW speed reduction with decrease in seabed depth during the frontal propagation toward the shore. Theoretical steady-state density current propagation speed is in good agreement with the observations in the critical and supercritical regimes but not in the inherently unsteady subcritical regime. The latter may be due to interaction of IGW with the front, an effect previously demonstrated only in laboratory and numerical experiments. In the critical regime, finite-amplitude IGWs form and remain locked to the front. A critical to supercritical transition eventually occurs as the ambient conditions change during frontal propagation, after which IGWs are not supported at the front. The subcritical (critical) to critical (supercritical) transition is related to Froude number ahead (under) the front, consistently with theory. Finally, we find that the front-locked IGW (critical) regime is itself dependent on significant nonlinear speed enhancement of the IGW by their growth to finite amplitude at the front.

The Matsuno baroclinic wave test case

Abstract. The analytic wave solutions obtained by Matsuno (1966) in his seminal work on equatorial waves provide a simple and informative way of assessing the performance of atmospheric models by measuring the accuracy with which they simulate these waves. These solutions approximate the solutions of the shallow-water equations on the sphere for low gravity-wave speeds such as those of the baroclinic modes in the atmosphere. This is in contrast to the solutions of the non-divergent barotropic vorticity equation, used in the Rossby–Haurwitz test case, which are only accurate for high gravity-wave speeds such as those of the barotropic mode. The proposed test case assigns specific values to the wave parameters (gravity-wave speed, zonal wave number, meridional wave mode and wave amplitude) for both planetary and inertia-gravity waves, and suggests simple assessment criteria suitable for zonally propagating wave solutions. The test is successfully applied to a spherical shallow-water model in an equatorial channel and to a global-scale model. By adding a small perturbation to the initial fields it is demonstrated that the chosen initial waves remain stable for at least 100 wave periods. The proposed test case can also be used as a resolution convergence test.

Banded Convective Activity Associated With Mesoscale Gravity Waves Over Southern China

AbstractBanded convective activity that occurred near the south coast of China on 30 January 2018 was investigated through convection‐allowing simulations using a nonhydrostatic mesoscale model. The simulations capture reasonably well the observed characteristics of this event. The convective bands are found to be closely related to an episode of mesoscale gravity waves propagating northeastward with a wave speed of around 12 m/s and a primary wavelength of about ~40–50 km. Further analyses and sensitivity experiments reveal that the environment provides a wave duct for these gravity waves, with a thick low‐level stable layer below 850 hPa capped by a low‐stability reflecting layer with a critical level. The strength and depth of the low‐level stable layer determine the intrinsic phase speed and wavelength of the ducted gravity waves. In the sensitivity tests that the stable layer depth is reduced, the wave characteristics change according to what are predicted with the wave duct theory. The convective bands collocate and propagate in phase with the peak updraft regions of the gravity waves, suggesting strong interactions of convection and gravity waves, in which the ducted gravity waves can trigger and modulate convection, while latent heating from convection enhances the waves. In essence, both wave ducting and wave‐convection interaction are jointly responsible for the banded convective activity.