Generation Of Internal Waves Research Articles

Flexural-gravity wave scattering due to a crack in a floating ice sheet in the perspective of wave blocking in a three-layer fluid

Flexural-gravity wave blocking is demonstrated in a three-layer fluid having a floating ice-covered surface in the water of finite depth. The study reveals that wave blocking occurs for higher values of compressive force in either of the modes, which depends on the density ratio and the wave frequency. Two (three) roots of the dispersion relation coalesce at the blocking (saddle) frequencies. Further, within the blocking frequencies, the dispersion relation possesses five propagating wave modes, of which three are affiliated with the layer where blocking occurs, whilst the other two modes are connected with the wave motion propagating in the respective layers. Dead water analogue is established due to the propagation of internal waves along the interface when the thickness of an individual layer is either thin or the density of two consecutive layers is close to each other. Subsequently, the role of blocking dynamics on the flexural-gravity wave scattering by a linear crack in an ice sheet floating in a three-layer fluid is studied. The canonical energy balance relation is generalized to account for multiple propagating wave modes. The velocity potentials are expanded in terms of a scattering matrix to account for the multiple incidents and scattered wave modes within the blocking frequencies. The study depicts the occurrence of removable/jump discontinuities in the scattering coefficients, both at the points where blocking/mode conversion takes place. Irregularities in the ice sheet's deflection and interface elevations are due to the superposition of multiple propagating wave modes within the blocking frequencies.

Characterization of singular flows of zeroth-order pseudo-differential operators via elliptic eigenfunctions: A numerical study

The propagation of internal gravity waves in stratified media, such as those found in ocean basins and lakes, leads to the development of geometrical patterns called “attractors”. These structures accumulate much of the wave energy and make the fluid flow highly singular. In more analytical terms, the cause of this phenomenon has been attributed to the presence of a continuous spectrum in some nonlocal zeroth-order pseudo-differential operators. In this work, we analyse the generation of these attractors from a numerical analysis perspective. First, we propose a high-order pseudo-spectral method to solve the evolution problem (whose long-term behaviour is known to be not square-integrable). Then, we use similar tools to discretize the corresponding eigenvalue problem. Since the eigenvalues are embedded in a continuous spectrum, we compute them using viscous approximations. Finally, we explore the effect that the embedded eigenmodes have in the long-term evolution of the system.

Observations of Internal Wave Interactions in a Southern Ocean Standing Meander

Abstract We characterize the internal wave field at a standing meander of the Antarctic Circumpolar Current (ACC) where strong winds, bathymetry, and a strong eddy field combine to form a dynamic environment for the generation and dissipation of internal waves. We use Electromagnetic Autonomous Profiling Explorer float data spanning 0–1600 m depth collected from a meander near the Macquarie Ridge, south of Australia. Of the 112 internal waves identified, 69% are associated with upward energy propagation. Most of the upward propagating waves (35%) are found near the Polar Front and are likely generated by mean flow–topography interactions. Generation by wind forcing at the sea surface is likely responsible for more than 40% of the downward propagating waves. Our results highlight advection of the waves and wave–mean flow interactions within the ACC as the dominant processes affecting the wave dynamics. The larger dissipation time scales of the waves compared to advection suggests they are likely to dissipate away from the generation site. We find that about 79% (66%) of the waves in cyclonic eddies (the Subantarctic Front) are influenced by horizontal strain, whereas 92% of the waves in the slower Polar Front are influenced by the relative vorticity of the background flow. There is energy exchange between internal waves and the mean flow, in both directions. The mean energy transfer (1.4 ± 1.0 × 10−11 m2 s−3) is from the mean flow to the waves in all dynamic regions except in anticyclonic eddies. The strongest energy exchange (5.0 ± 3.7 × 10−11 m2 s−3) is associated with waves in cyclonic eddies.

Generation of nonlinear internal waves on the northern continental shelf south of Hainan Island

Nonlinear internal waves (NLIWs) are prevalent on the northern continental shelf south of Hainan Island in the South China Sea. However, our understanding of these NLIWs is still in a preliminary state. In the study, we take a step toward fully elucidating the generation and propagation process of the NLIWs on the northern continental shelf south of Hainan Island through a synergistic analysis of satellite observations, in situ measurements, and numerical simulations. Both mooring and satellite observations suggest that the Xisha Islands remotely generate the NLIWs on the northern continental shelf south of Hainan Island; moreover, more than one source exists in the Xisha Islands. Based on the realistic topography, stratification, and tidal forcing, two-dimensional numerical simulations using the MITgcm reveal that the NLIWs observed on the continental shelf can be generated from the Xisha Islands through the internal tidal beam regime. Furthermore, the internal tide energy flux estimation shows that the locally generated internal tides that arise from the continental shelf break mostly carry their energy toward the deep water and have little effect on the generation of NLIWs on the shelf.

Highly nonlinear internal solitary waves with a free surface

A new mathematical model is derived for internal wave propagation in a two-layer fluid domain with a free surface in which the lower layer is of finite depth. The mathematical model consists of three coupled nonlinear equations for displacement of the interface and velocity potentials of the two layers, each of which is expressed as the convex combination of their values at two arbitrary depths. Model equations are correct up to O(μ4) terms, where μ is the ratio of harmonic mean of the depths of the two layers to double of a typical wavelength. Finite amplitude internal solitary wave profiles as well as free surface wave profiles are obtained numerically for different wave speeds, density ratios and depth ratios. Interfacial solitary wave profiles obtained here are in very good agreement with recent experimental observations of Zhao et al. (2020). The figures presented here demonstrate how the interfacial wave profile predicted by the free surface model differs from predictions of rigid-lid two-layer fluid models.

Short Standing and Propagating Internal Waves in an Ice-Covered Shallow Lake

The intensity of vertical heat and mass transfer remains among the challenging topics in the study of ice-covered lakes. Presumably, internal waves (IWs) make a significant contribution to the heat transfer in the water column. However, the mechanisms of mixing enhancement by generation, interaction, and breaking of IWs of different scales, especially short-wavelength ones, have not been sufficiently studied. Furthermore, the experimental data required for estimating the key parameters of IWs (wavelengths, propagation velocities) are rather fragmentary, which makes it difficult to quantify the turbulent transfer caused by IWs. This paper presents the estimates of these IW parameters based on data obtained in the winter months of 2014 and 2016 in a small boreal ice-covered lake. Having analyzed horizontally spaced thermistor chain data, we managed to detect the presence of short standing and propagating IWs, and to estimate their length (from several meters to several tens of meters) and phase and group velocities (from several mm/s to several tens of mm/s). Also, their vertical mode structure was detected. It was shown that IW generation events were characterized by a high degree of spatial localization, and the IW energy was unevenly distributed through the water column.

Simple two-layer dispersive models in the Hamiltonian reduction formalism

A Hamiltonian reduction approach is defined, studied, and finally used to derive asymptotic models of internal wave propagation in density stratified fluids in two-dimensional domains. Beginning with the general Hamiltonian formalism of Benjamin (1986 J. Fluid Mech. 165 445–74) for an ideal, stably stratified Euler fluid, the corresponding structure is systematically reduced to the setup of two homogeneous fluids under gravity, separated by an interface and confined between two infinite horizontal plates. A long-wave, small-amplitude asymptotics is then used to obtain a simplified model that encapsulates most of the known properties of the dynamics of such systems, such as bidirectional wave propagation and maximal amplitude travelling waves in the form of fronts. Further reductions, and in particular devising an asymptotic extension of Dirac’s theory of Hamiltonian constraints, lead to the completely integrable evolution equations previously considered in the literature for limiting forms of the dynamics of stratified fluids. To assess the performance of the asymptotic models, special solutions are studied and compared with those of the parent equations

Strongly non-linear Boussinesq-type model of the dynamics of internal solitary waves propagating in a multilayer stratified fluid

We propose a system of first-order balance laws that describe the propagation of internal solitary waves in a multilayer stratified shallow water with non-hydrostatic pressure in the upper and lower layers. The construction of this model is based on the use of additional variables, which make it possible to approximate the Green–Naghdi-type dispersive equations by a first-order system. In the Boussinesq approximation, the governing equations allow one to simulate the propagation of non-linear internal waves, taking into account fine density stratification, a weak velocity shear in the layers, and uneven topography. We obtain smooth steady-state soliton-like solutions of the proposed model in the form of symmetric and non-symmetric waves of mode-2 adjoining to a given multilayer constant flow. Numerical calculations of the generation and propagation of large-amplitude internal waves are carried out using both the proposed first-order system and Green–Naghdi-type equations. It is established that the solutions of these models practically coincide. The advantage of the first-order equations is the simplicity of numerical implementation and a significant reduction in the calculation time. We show that the results of numerical simulation are in good agreement with the experimental data on the evolution of mode-2 solitary waves in tanks of constant and variable height.

Traveling internal waves in a two-layer shallow medium with variable bathymetry and current: Surface and near-bottom flows

In the linear approximation, we examine the one-dimensional problem of long internal wave propagation without reflection in a stationary two-layer flow with a free boundary in a channel of variable depth and width, in the limiting cases of surface and near-bottom currents. We use the shallow-water approximation and assume that liquids in the layers are ideal, immiscible, and having a small relative density difference, and that the flow is only in one of the layers. To filter fast processes (such as surface gravity waves), the flow velocity is assumed to have the same order of magnitude as the speed of internal waves. Both surface and near-bottom flows are divided into three classes, in accordance with conditions providing wave propagation without reflection. The properties of the flows in each of the classes are examined, and it is shown that the global reflectionless near-bottom flows do exist. The main results and conclusions are illustrated by a few particular solutions. A detailed comparison with the first part of the study concerning the flows with currents in both layers made it possible to clarify and refine some of the results obtained there, and to formulate questions for further investigation. The results obtained may be of interest for understanding of those natural processes in surface and near-bottom flows, which are significantly influenced by internal waves.

Abnormal high tides and flooding induced by the internal surge in Hiroshima Bay due to a remote typhoon

The Itsukushima Shrine is located in northern Hiroshima Bay in the Seto Inland Sea (SIS). This structure of great cultural value is preserved as one of the World Heritage Sites in Japan. The shrine was built seaside, 30 cm above the highest tide, to prevent it from submerging. However, from 2011 to 2019, the shrine was submerged four times during September due to internal surges. To study the abnormal tide event on 29 September 2011, a high-resolution numerical ocean circulation model was established using Semi-implicit Cross-scale Hydroscience Integrated System Model (SCHISM). Observed subtidal components of surface elevation in the northern part of the bay decreased due to northerly winds when the typhoon passed east off the bay. After 7–8 days of typhoon passage, the component increased abnormally in the northern part of the bay. Simulation results revealed that a destabilized density stratification by the typhoon winds most likely caused bay-scale internal waves. The internal wave developed after the typhoon passed and was caught from the kinetic energy filtered in the possible internal wave periods. The internal wave propagated southward after the typhoon passage and returned to the northern bay, causing the subtidal component to increase after 7–8 days. Sensitivity tests with various scales of the typhoon were performed, and the test results exhibited a positive relationship between the abnormal tide level and typhoon intensity to some extent. The results can be generally applied to a semi-closed bay or closed water body for internal wave generation and propagation under specific meteorological conditions for coastal protection and disaster prevention.

Path Loss and Auxiliary Communication Analysis of VANET in Tunnel Environments

Vehicular ad hoc network (VANET) communications face severe fading problems due to the signal reflections and diffractions within tunnels. Unlike the open road, the space of a tunnel is very limited, so VANET communication performance in a tunnel is seriously affected. In the process of signal transmission, the reflected signal is symmetrical with the incident signal after it is reflected by the road and the wall. In this paper, we establish a mathematical model of path loss for V2V (Vehicle-to-Vehicle) communication based on the principle of signal reflection symmetry in tunnels and considering several factors, such as the tunnel surface and the color of the tunnel wall. In addition, we use cooperative communication to form a virtual multiple-input multiple-output (V-MIMO) system, to improve the communication quality in tunnels. In the proposed system, the OBU (On-Board-unit) and RSU (Road-Side-Unit) share each other’s antennas, so that wireless cooperative communication can be employed, without increasing the number of antennas in a one-way tunnel. Therefore, this multipath fading internal electromagnetic wave propagation model can be used to improve performance. A deep reinforcement learning algorithm was used to solve the pairing problem to obtain a more accurate OBU and RSU pair, to form a V-MIMO system. Here, the RSU is regarded as an agent and interacts with the OBU in the tunnel. The optimal strategy was learned in a real-time changing simulation environment, and the experiment verified the convergence of the algorithm. The simulation results showed that, compared with the Q-learning based scheme, the optimal matching algorithm based on V-MIMO and a DQN (Deep Q-network) could effectively reduce the probability of transmission outages and improve the communication efficiency in tunnels.

Tidal Dissipation in Stratified and Semi-convective Regions of Giant Planets

We study how stably stratified or semi-convective layers alter the tidal dissipation rates associated with the generation of internal waves in planetary interiors. We consider if these layers could contribute to the high rates of tidal dissipation observed for Jupiter and Saturn in our solar system. We use an idealized global spherical Boussinesq model to study the influence of stable stratification and semi-convective layers on tidal dissipation rates. We carry out analytical and numerical calculations considering realistic tidal forcing and measure how the viscous and thermal dissipation rates depend on the parameters relating to the internal stratification profile. We find that the strongly frequency-dependent tidal dissipation rate is highly dependent on the parameters relating to the stable stratification, with strong resonant peaks that align with the internal modes of the system. The locations and sizes of these resonances depend on the form and parameters of the stratification, which we explore both analytically and numerically. Our results suggest that stable stratification can significantly enhance the tidal dissipation in particular frequency ranges. Analytical calculations in the low-frequency regime give us scaling laws for the key parameters, including the tidal quality factor due to internal gravity waves. Stably stratified layers can significantly contribute to tidal dissipation in solar and extrasolar giant planets, and we estimate substantial tidal evolution for hot Neptunes. Further investigation is needed to robustly quantify the significance of the contribution in realistic interior models, and to consider the contribution of inertial waves.

Breaking of Internal Waves Parametrically Excited by Ageostrophic Anticyclonic Instability

Abstract A gradient-wind balanced flow with an elliptic streamline parametrically excites internal inertia-gravity waves through ageostrophic anticyclonic instability (AAI). This study numerically investigates the breaking of internal waves and the following turbulence generation resulting from the AAI. In our simulation, we periodically distort the calculation domain following the streamlines of an elliptic vortex and integrate the equations of motion using a Fourier spectral method. This technique enables us to exclude the overall structure of the large-scale vortex from the computation and concentrate on resolving the small-scale waves and turbulence. From a series of experiments, we identify two different scenarios of wave breaking conditioned on the magnitude of the instability growth rate scaled by the buoyancy frequency λ/N. First, when , the primary wave amplitude excited by AAI quickly goes far beyond the overturning threshold and directly breaks. The resulting state is thus strongly nonlinear turbulence. Second, if , weak wave–wave interactions begin to redistribute energy across frequency space before the primary wave reaches a breaking limit. Then, after a sufficiently long time, the system approaches a Garrett–Munk-like stationary spectrum, in which wave breaking occurs at finer vertical scales. Throughout the experimental conditions, the growth and decay time scales of the primary wave energy are well correlated. However, since the primary wave amplitude reaches a prescribed limit in one scenario but not in the other, the energy dissipation rates exhibit two types of scaling properties. This scaling classification has similarities and differences with D’Asaro and Lien’s wave–turbulence transition model. Significance Statement Due to the gradients in buoyancy and pressure, density-stratified seawater supports oscillatory vertical motion called internal waves. When waves significantly skew a density isosurface, dense water lifts over lighter water resulting in gravitational instability and high energy dissipation. In this wave-breaking process, seawater is vertically mixed, transporting heat and nutrients essential to maintain Earth’s climate and ecosystems. This study investigates the generation and breaking of ocean internal waves in a novel numerical simulation setup; we temporally distort the model shape to emulate the wave excitation forced by a larger-size horizontal eddy, a ubiquitous situation at O(1–10) km scales in the upper ocean. The simulation results exhibit two unique wave-breaking scenarios with distinct scaling features in turbulence energy dissipation rates.

Monitoring Deep Sea Currents With Seafloor Distributed Acoustic Sensing

AbstractUnderwater fiber optic cables commonly traverse a variety of seafloor conditions, which leads to an uneven mechanical coupling between the cable and the ocean bottom. On rough seafloor bathymetry, some cable portions might be suspended and thus susceptible to vortex‐induced vibrations (VIV) driven by deep ocean currents. Here, we examine the potential of distributed acoustic sensing (DAS) to monitor deep‐sea currents along suspended sections of underwater telecom fiber optic cables undergoing VIV. Oscillations of a seafloor fiber optic cable located in southern France are recorded by DAS along cable sections presumably hanging. Their characteristic frequencies are lower than 1 Hz, at different ocean depths, and have an amplitude‐dependency consistent with the driving mechanism being VIV. Based on a theoretical proportionality between current speed and VIV frequencies, we derive ocean current speed time series at 2,390 m depth from the vortex shedding frequencies recorded by DAS. The DAS‐derived current speed time series is in agreement with recordings by a current meter located 3.75 km away from the hanging cable section (similar dominant period, high correlation after time shift). The DAS‐derived current speed time series displays features, such as characteristic periods and spectral decay, associated with the generation of internal gravity waves and weak oceanic turbulence in the Mediterranean Sea. The results demonstrate the potential of DAS along hanging segments of fiber optic cables to monitor a wide range of oceanography processes, at depths barely studied with current instrumentation.

The Impact of Internal Gravity Waves on the Spectra of Turbulent Fluctuations of Vertical Wind Velocity in the Stable Atmospheric Boundary Layer

The wave turbulence interactions in the stable boundary layer (SBL) of the atmosphere are studied based on data from lidar measurements of the vertical component of wind velocity during the propagation of internal gravity waves (IGWs). It is shown that as an IGW appears, the amplitude of the spectra of turbulent fluctuations of vertical wind velocity nearby the frequency of quasi-harmonic oscillations induced by an IGW increases significantly, sometimes by several orders of magnitude, compared to the spectra in the absence of an IGW. Since IGW energy is transferred to small-scale turbulence, the amplitude of spectra with the Kolmogorov–Obukhov −5/3 power-law frequency dependence in the inertial frequency range increases. The slope of the spectra in the low-frequency range between the frequency of IGW-induced oscillations and the frequency of the lower boundary of the inertial range exceeds the slope, corresponding to the −5/3 power-law dependence. In this frequency range, the spectra obey the power-law dependence on the frequency with the exponent ranging from −4.2 to −1.9. The average value of the exponent −3 is consistent with a low-frequency slope caused by IGWs in turbulent spectra in the lower SBL.

Numerical investigation on the generation and evolution of nonlinear internal waves in the southern Strait of Georgia

The generation and subsequent evolution of nonlinear internal waves (NLIWs) in the Strait of Georgia (British Columbia, Canada) is investigated with both remote sensing images and a three-dimensional regional non-hydrostatic numerical simulation. Many satellite images depict clear snapshots of two successive NLIWs propagating northward about 1 h or 4 km apart during the flood tides. In the model results, local energy budget analysis demonstrates that the generation processes of internal waves are dominated by the energy conversion from barotropic tides to internal tides, while propagation processes are dominated by high-frequency NLIWs after radiating away the Boundary Pass. To further investigate the generation mechanisms of local internal waves, sensitivity studies with different tidal forcing are carried out. In the standard spring tide experiment, the rank-order NLIW packets have relatively large leading waves (∼15 m amplitude) and small trailing waves radiating from the Boundary Pass, related to a complex evolution of an internal Froude number over the sill. The internal Froude number analysis also demonstrates that only when the diurnal (D1) and semidiurnal (D2) tides act in phase can paired NLIW packets be formed. However, either single D1 or D2 tides, or D1 and D2 tides not in phase, are not able to generate NLIWs, as condition of the flow remain subcritical at all times. Moreover, a series of sensitivity experiments demonstrate that the role of non-hydrostatic mode is crucial in the high-resolution model but less important in the coarse-resolution model, via comparing wave properties and wave energetics in non-hydrostatic and hydrostatic models.

A Vorticity‐Divergence View of Internal Wave Generation by a Fast‐Moving Tropical Cyclone: Insights From Super Typhoon Mangkhut

AbstractTropical cyclones (TCs) are powered by heat fluxes across the air‐sea interface, which are in turn influenced by subsurface physical processes that can modulate storm intensity. Here, we use data from 6 profiling floats to recreate 3D fields of temperature (T), salinity (S), and velocity around the fast‐moving Super Typhoon Mangkhut (western North Pacific, September 2018). Observational estimates of vorticity (ζ) and divergence (Γ) agree with output from a 3D coupled model, while their relation to vertical velocities is explained by a linear theoretical statement of inertial pumping. Under this framework, inertial pumping is described as a linear coupling between ζ and Γ, whose oscillations in quadrature cause periodic displacements in the ocean thermocline and generate near‐inertial waves (NIWs). Vertical profiles of T and S show gradual mixing of the upper ocean with diffusivities as high as κ ∼ 10−1 m2 s−1, which caused an asymmetric cold wake of sea surface temperature (SST). We estimate that ∼10% of the energy used by mixing was used to mix rainfall, therefore inhibiting SST cooling. Lastly, watermass transformation analyses suggest that κ > 3 × 10−3 m2 s−1 above ∼110 m depth and up to 600 km behind the TC. These analyses provide an observational summary of the ocean response to fast‐moving TCs, demonstrate some advantages of ζ and Γ for the study of internal wave fields, and provide conceptual clarity on the mechanisms that lead to NIW generation by winds.

Mechanical model and characteristics of deep-water drilling riser-wellhead system under internal solitary waves

Internal solitary waves with a huge amount of energy easily trigger the large dynamic responses of riser-wellhead system and threaten its structural safety. However, previous studies have only focused on the dynamic response of the riser under internal solitary waves. The riser may experience excessive traction from the platform, especially from the mooring platform, in response to the arrival of internal solitary waves. The bottom of the riser connects to the wellhead system, which in turn exerts a reaction force on the riser. To address this problem, a coupled dynamic model of deep-water drilling mooring platform-riser-wellhead system under internal solitary waves is developed in this paper. A dynamic response analysis method based on the fourth-order Runge-Kutta method and finite element method is also proposed for the mooring platform-riser-wellhead system. A dynamical solver for the coupled system is then developed using MATLAB. The dynamic response characteristics of the riser-wellhead system under internal solitary waves are calculated. Results show that the displacement and bending moment of the system initially increases and then decreases along with the propagation of internal solitary waves, and finally reach equilibrium position. The displacement and bending moment reach their peak before the trough of internal solitary waves passes through the riser-wellhead system. The dynamic responses of the riser-wellhead system under the influence of internal solitary wave loads are much larger than those without the effect of internal solitary wave loads. The riser system experiences shearing loads at the interface of internal solitary waves, which trigger a step-like bending moment variation. The bending moment of the conductor under the mudline is greatly increased by the internal solitary waves.

3D hydrodynamics simulations of internal gravity waves in red giant branch stars

ABSTRACT We present the first 3D hydrodynamics simulations of the excitation and propagation of internal gravity waves (IGWs) in the radiative interiors of low-mass stars on the red giant branch (RGB). We use the ppmstar explicit gas dynamics code to simulate a portion of the convective envelope and all the radiative zone down to the hydrogen-burning shell of a $1.2\, {\rm M}_{\odot }$ upper RGB star. We perform simulations for different grid resolutions (7683, 15363, and 28803), a range of driving luminosities, and two different stratifications (corresponding to the bump luminosity and the tip of the RGB). Our RGB tip simulations can be directly performed at the nominal luminosity, circumventing the need for extrapolations to lower luminosities. A rich, continuous spectrum of IGWs is observed, with a significant amount of total power contained at high wavenumbers. By following the time evolution of a passive dye in the stable layers, we find that IGW mixing in our simulations is weaker than predicted by a simple analytical prescription based on shear mixing and not efficient enough to explain the missing RGB extra mixing. However, we may be underestimating the efficiency of IGW mixing given that our simulations include a limited portion of the convective envelope. Quadrupling its radial extent compared to our fiducial set-up increases convective velocities by up to a factor 2 and IGW velocities by up to a factor 4. We also report the formation of a $\sim 0.2\, H_P$ penetration zone and evidence that IGWs are excited by plumes that overshoot into the stable layers.

Direct Simulation of the Surface Manifestation of Internal Gravity Waves with a Wave–Current Interaction Model

Abstract Internal solitary waves in the ocean are characterized by the surface roughness signature of smooth and rough bands that are observable in synthetic aperture radar satellite imagery, which is caused by the interaction between surface gravity waves and internal wave–induced surface currents. In this work, we study the surface signature of an internal wave packet in deep water over a large range of spatial scales using an improved wave–current interaction model that supports a moving surface current corresponding to a propagating internal gravity wave. After validating the model by comparison to previously published numerical results by Hao and Shen, we investigate a realistic case based on a recent comprehensive field campaign conducted by Lenain and Pizzo. Distinct surface manifestation caused by internal waves can be directly observed from the surface waves and the associated surface wave steepness. Consistent with observations, the surface is relatively rough where the internal wave–induced surface current is convergent (∂U/∂x < 0), while it is relatively smooth where the surface current is divergent (∂U/∂x > 0). The spatial modulation of the surface wave spectrum is rapid as a function of along-propagation distance, showing a remarkable redistribution of energy under the influence of the propagating internal wave packet. The directional wavenumber spectra computed in the smooth and rough regions show that the directional properties of the surface wave spectra are also rapidly modulated through strong wave–current interactions. Good agreement is found between the model results and the field observations, demonstrating the robustness of the present model in studying the impact of internal waves on surface gravity waves. Significance Statement The purpose of this study is to better understand the physical processes leading to the bands of rough and smooth surface waves arising from internal gravity waves. The surface manifestation of internal gravity waves allows them to be measured remotely via surface imagery, which can provide insight into their nonlinear behavior and sources and fate and which can ultimately inform the local stratification for assimilation into larger-scale models. Our results highlight the application of wave–current interaction models to the study of the interaction of surface waves with internal gravity waves and indicate strong modulation of the surface wave spectra over relatively short time scales despite the long time scales associated with the internal wave propagation.