Periodic Internal Waves Research Articles

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

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

The boundary layer instability beneath internal solitary waves and its sensitivity to vortex wakes

We investigated the stability of the bottom boundary layer (BBL) beneath periodic internal solitary waves (ISWs) of depression over a flat bottom through two-dimensional direct numerical simulations. We explored the convective versus absolute/global nature of the BBL instability in response to changes in Reynolds number, and the sensitivity of the instability to seeding noise in the front of the ISW – spanning laboratory to geophysical scales. The BBL was laminar at $Re_{ISW}=90$ and convectively unstable at $Re_{ISW}=300$ . At laboratory-scale $Re_{ISW}=300$ , the convective wave packet was periodically amplified by each successive ISW, until vortex shedding occurred. The associated noise-amplification behaviour potentially explains the discrepancies of the critical $Re_{ISW}$ between the lock–release laboratory experiments and our Dubreil–Jacotin–Long-initialized numerical simulations as the result of the difference in background noise. Instability energy decreased under the front shoulder of the ISW, analogous to flow relaminarization under a favourable pressure gradient. At geophysical-scale $Re_{ISW}=900$ , the BBL was initially convectively unstable, and then the instability tracked with the ISW, appearing phenomenologically similar to a global instability. The simulated initial convective instability at both $Re_{ISW}=300$ and $Re_{ISW}=900$ is in agreement with local linear stability analysis which predicts that the instability group speed is always lower than the ISW celerity. Increased free stream perturbations in front of the ISW and larger $Re_{ISW}$ shift the location of vortex shedding (and enhanced bed shear stress) beneath the wave, closer to the ISW trough, thereby potentially changing the location of maximum sediment resuspension, in agreement with field observations at higher $Re_{ISW}$ .

Transient internal wave excitation of resonant modes in a density staircase

The density of the ocean generally increases continuously with depth as a consequence of variations in salinity and temperature. In some regions, however, the density profile of the ocean adopts a (double diffusive) staircase structure in which successive layers of uniform density fluid are separated by rapid density jumps. Previous work has theoretically examined the transmission and reflection of periodic internal (gravity) waves incident upon a density staircase. This predicted the existence of transmission spikes (global modes) for certain combinations of frequency and horizontal wave number in which the incident waves transmit perfectly across a density staircase. It was hypothesized that the transmission spikes occur when the incident waves resonate with natural modes of disturbances in the staircase. Here we derive theory to investigate the interactions between incident internal waves and modes. We demonstrate a close correspondence between the frequency for incident waves at a transmission spike and the real part of the frequency of modes at the same horizontal wave number. However, the frequency of the corresponding modes has a negative imaginary part corresponding to exponential decay of the modes in time. We perform numerical simulations to examine the impact of this near-resonant coupling when a vertically localized, quasimonochromatic internal wave packet interacts with a density staircase. In a range of simulations with fixed incident wave frequency and varying horizontal wave number, the measured transmission coefficient does not exhibit transmission spikes, but decreases monotonically with increasing horizontal wave number about the critical wave number separating strong and weak transmission. We show this occurs because the incident wave excites modes that then slowly transmit energy above and below the staircase at a rate consistent with the predicted decay rate of the modes. This rate is slower for staircases with more steps with the decay time increasing as the cube of the number of steps. Published by the American Physical Society 2024

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.

The global bifurcation and geometric properties of steady periodic equatorial internal waves with fixed-depth

In this paper, we mainly consider steady periodic equatorial internal waves with a fixed mean depth d>0. By extending the local bifurcation curve obtained in [1], we prove the existence of equatorial internal waves of large amplitude, where the analytic bifurcation theorem and analysis of nodal patterns play a key role. Furthermore, we also obtain some important geometric properties on equatorial internal waves, including the concavity and convexity and symmetry of wave profile.

Vertical oscillations of the thermocline caused by internal waves modify coldwater pelagic fish distribution: Results from a large stratified lake

Fishes typically occupy a species-specific temperature range, with their occupied depth being related to the lake’s temperature profile. When a fish’s preferred temperature range coincides with the thermocline, the location of their preferred thermal habitat is influenced by the rise and fall of internal waves, leading to possible changes in fish depth. These internal waves are common in large, stratified lakes, yet we do not know how they affect the spatial distribution and behavior of freshwater fishes. We conducted nighttime hydroacoustic surveys in a large, deep embayment of a large thermally stratified lake to observe whether pelagic fish respond to vertical oscillations of the thermocline caused by internal waves. The coldwater pelagic fish in our study (primarily cisco, Coregonus artedi) typically occupied a narrow vertical band approximately 5–8 m thick and temperatures between 10.8 ± 0.8–13.6 ± 1.6 °C (fishes sized 106–500 mm), just below the thermocline (centered around 15–17 °C). Importantly, the upper bound of fish depth varied in response to vertical thermocline movements associated with internal waves, suggesting fish respond to changes in their physical environment on timescales commensurate with basin-scale internal wave periods (hours to days), to remain within their preferred thermal habitat. Dissolved-oxygen levels were typically above avoidance thresholds of these fish, thus not likely exerting a strong influence on fish location. Our findings emphasize the need to account for internal waves when designing hydroacoustic and netting surveys, as thermocline movements can influence where fish are located.

Conventional Partial and Complete Solutions of the Fundamental Equations of Fluid Mechanics in the Problem of Periodic Internal Waves with Accompanying Ligaments Generation

The problem of generating beams of periodic internal waves in a viscous, exponentially stratified fluid by a band oscillating along an inclined plane is considered by the methods of the theory of singular perturbations in the linear and weakly nonlinear approximations. The complete solution to the linear problem, which satisfies the boundary conditions on the emitting surface, is constructed taking into account the previously proposed classification of flow structural components described by complete solutions of the linearized system of fundamental equations without involving additional force or mass sources. Analyses includes all components satisfying the dispersion relation that are periodic waves and thin accompanying ligaments, the transverse scale of which is determined by the kinematic viscosity and the buoyancy frequency. Ligaments are located both near the emitting surface and in the bulk of the liquid in the form of wave beam envelopes. Calculations show that in a nonlinear description of all components, both waves and ligaments interact directly with each other in all combinations: waves-waves, waves-ligaments, and ligaments-ligaments. Direct interactions of the components that generate new harmonics of internal waves occur despite the differences in their scales. Additionally, the problem of generating internal waves by a rapidly bi-harmonically oscillating vertical band is considered. If the difference in the frequencies of the spectral components of the band movement is less than the buoyancy frequency, the nonlinear interacting ligaments generate periodic waves as well. The estimates made show that the amplitudes of such waves are large enough to be observed under laboratory conditions.

Internal wave analyzer for thermally stratified lakes

Interwave Analyzer is an open source software that provides detailed characterization of the dynamics of internal waves in lakes and reservoirs. It is based on well-established theories and empirical knowledge on internal waves and lake mixing and facilitates a general physical classification of lakes and reservoirs. As input data, the program requires time series of water temperature from various depths and meteorological data, which can be obtained from measurements or numerical models. Interwave Analyzer performs an in-depth analysis of periodic motion by spectral analysis to identify predominant internal wave periods. To facilitate the identification of wave modes, the software is coupled with a multi-layer model. Interwave Analyzer is a powerful, easily accessible, and universal tool, which can be used for obtaining detailed understanding lake hydrodynamics not only in physical sciences, but also in the context of water quality, ecological interactions and biogeochemical fluxes in aquatic ecosystems.

Computation of Density Perturbation and Energy Flux of Internal Waves from Experimental Data

We hereby present two different spectral methods for calculating the density anomaly and the vertical energy flux from synthetic Schlieren data, for a periodic field of linear internal waves (IW) in a density-stratified fluid with a uniform buoyancy frequency. The two approaches operate under different assumptions. The first method (hereafter Mxzt) relies on the assumption of a perfectly periodic IW field in the three dimensions (x, z, t), whereas the second method (hereafter MxtUp) assumes that the IW field is periodic in x and t and composed solely of wave components with downward phase velocity. The two methods have been applied to synthetic Schlieren data collected in the CNRM large stratified water flume. Both methods succeed in reconstructing the density anomaly field. We identify and quantify the source of errors of both methods. A new method mixing the two approaches and combining their respective advantages is then proposed for the upward energy flux. The work presented in this article opens new perspectives for density and energy flux estimates from laboratory experiments data.

Internal lee waves and baroclinic bores over a tropical seamount shark ‘hot-spot’

Oceanographic observations were made with a subsurface oceanographic mooring over the summit and flanks of two neighbouring seamounts in the tropical Indian Ocean to identify processes that may be responsible for the aggregation of silvertip sharks (Carcharhinus albimarginatus) in the deep water drop-off surrounding the summits. The seamounts, which are in the Chagos Archipelago in the British Indian Ocean Territories, are narrow in horizontal extent (<10 km), have steeply sloping (>15°) sides that rise from depths of > 600 m, and flat summits at a depth of 70 m. They are subjected to forcing at subinertial, basin-scales and local scales that include a mixed tidal regime and storm-generated near inertial waves. At the drop-off, at a depth of between 70 and 100 m, isotherms oscillate at both diurnal and semidiurnal frequencies with amplitudes of ∼ 20–30 m. The waves of tidal origin are accompanied by short period (∼5 min) internal waves with amplitudes O(10 m) and frequencies close to the local buoyancy frequency, N, within the thermocline which is the maximum frequency possible for freely propagating internal waves. The tidal oscillations result from internal lee waves with 30 m vertical wavelength generated by the prevailing currents over the supercritical seamount flanks, whereby the bottom slope is greater than the internal tide wave slope. The ‘near-N’ waves are due to enhanced shear associated with the hydraulic jumps that form from the lee waves due to the abrupt transition from steeply sloping sides to a relatively flat summit. The jumps manifest themselves as bottom-trapped bores that propagate up the slope towards the summit. Further observations over the summit reveal that the bores subsequently flush the summits with cold water with tidal periodicity. The bores, which have long wave phase speeds more than double that of the bore particle velocities, are characterised by intense vertical velocities (>0.1 m s−1) and inferred local resuspension but relatively little turbulence based on temperature overturns. Our results strongly implicate lee waves as the dynamic mechanism of leading order importance to the previously observed accumulation of biomass adjacent to the supercritical slopes that are commonplace throughout the archipelago. We propose that further investigation should identify the spatiotemporal correlation between internal wave activity and fish schooling around the summit, and whether such schooling attracts predators.

Turbulent convection and high‐frequency internal wave details in 1‐m shallow waters

AbstractVertically 0.042‐m‐spaced moored high‐resolution temperature sensors are used for detailed internal wave‐turbulence monitoring near Texel North Sea and Wadden Sea beaches on calm summer days. In the maximum 2‐m deep waters, irregular internal waves are observed supported by the density stratification during day‐times’ warming in early summer, outside the breaking zone of &lt; 0.2 m surface wind waves. Internal‐wave–induced convective overturning near the surface and shear‐driven turbulence near the bottom are observed in addition to near‐bottom convective overturning due to heating from below. Small turbulent overturns have durations of 5–20 s, close to the surface wave period and about one third to one tenth of the shortest internal wave period. The largest turbulence dissipation rates are estimated to be of the same order of magnitude as found above deep‐ocean seamounts, whereas overturning scales are observed 100 times smaller. The turbulence inertial subrange is observed to link between the internal and surface wave spectral bands.

Wind-induced internal seiches in Vossoroca reservoir, PR, Brazil

ABSTRACT The vertical movements caused by internal waves in lakes and reservoirs have chemical and biological consequences for these ecosystems. The vast majority of studies that investigate internal waves are conducted on large lakes. There are just few researches that investigate this phenomenon on dendritic reservoirs. The purpose of this research was to identify internal waves (baroclinic mode) in the Vossoroca reservoir by using temperature time series recorded between May to November 2012. A two-layer method was used which considered rigid upper and lower boundaries. Moreover, the potential flow theory was used for both layers since the flow within each layer was considered irrotational. From the dispersion relation, we obtained the theoretical shallow internal wave period. The power spectral density (PSD) of temperature series of thermocline depth, provided by fast Fourier transform, helped in the identification on the frequency peak. Subsequently, the theoretical period was compared with the frequency spectra. Using a careful analysis (excluding the interference of solar radiation and intensity of wind), we observed a clear peak in November due to an internal wave with period around 8 hours, which matched the theoretical calculation from the dispersion relation equation for V1H1 mode. Weak winds from southwest excited a V1H1 baroclinic mode. According to spectral analysis, after the passage of this long-basin internal seiches, we identified the formation of higher vertical internal seiche modes. In addition, we observe indications of V1H1 mode degeneration.

SAR Mode Altimetry Observations of Internal Solitary Waves in the Tropical Ocean Part 1: Case Studies

It is well known that internal waves (IWs) of tidal frequency (i.e., internal tides) are successfully detected in sea surface height (SSH) by satellite altimetry. Shorter period internal solitary waves (ISWs), whose periods (and spatial scales) are an order of magnitude smaller than tidal internal waves, have been generally assumed too small to be detected with conventional altimeters. This is because conventional (pulse-limited) radar altimeter footprints are somewhat larger than or of similar size, at best, as the typical wavelengths of the ISWs. Here we demonstrate that the synthetic aperture radar altimeter (SRAL) on board the Sentinel-3A can detect short-period ISWs. A variety of signatures owing to the surface manifestations of the ISWs are apparent in the SRAL Level-2 products over the ocean. These signatures are identified in several geophysical parameters, such as radar backscatter (sigma0), sea level anomaly (SLA), and significant wave height (SWH). Radar backscatter is the primary parameter in which ISWs can be identified owing to the measurable sea surface roughness perturbations in the along-track sharpened SRAL footprint. The SRAL footprint is sufficiently small to capture radar power fluctuations over successive wave crests and troughs, which produce rough and slick surface patterns arrayed in parallel bands with scales of a few kilometers. The ISW signatures are unambiguously identified in the SRAL because of the exact synergy with OLCI (Ocean Land Colour Imager) images, which in cloud-free conditions allow clear identification of the ISWs in the sunglint OLCI images. We show that both sigma0 and SLA yield realistic estimates for routine observation of ISWs with the SRAL, which is a significant improvement from previous observations recently reported for conventional pulse-limited altimeters (Jason-2). Several case studies of ISW signatures are interpreted in light of our knowledge of radar backscatter in the internal wave field. An analysis is presented for the tropical Atlantic Ocean off the Amazon shelf to infer the frequency of the phenomena, being consistent with previous satellite observations in the study region.

Long wave approximation using conformal mapping for large-amplitude internal waves in a two-fluid system

This paper describes a new type of long wave model for periodic internal waves propagating in permanent form at the interface between two immiscible inviscid fluids. This model for irrotational plane motion of these waves is derived in the complex velocity potential planes where the flow domains are conformally mapped. Since no smallness assumption of wave amplitude is made and the wave elevation at the interface is represented by a single-valued function of the velocity potential, this model is applicable to large-amplitude motions of which wave profile may overhang. Numerical examples demonstrate that the proposed model can produce overhanging solutions, and variations of solutions with wavelength or wave amplitude are qualitatively similar to those of the full Euler system. It is also pointed out that the kinematic condition at the interface is exactly satisfied in the proposed model for all wave amplitudes, but not in an existing long wave model derived in the physical plane.

Singular perturbed components of flows – linear precursors of shock waves

A comparative analysis of the infinitesimal symmetries of various well-known systems of governing equations used for mathematical descriptions of flows and waves in fluids has shown that only the basic system of equations, including the empirical equation of state and the partial differential equations of mass, momentum, energy and matter transport, is characterized by a ten-parameter Galilean transformation group. An analysis of the complete solutions of the linearized system of fundamental equations for weakly dissipating media reveals a wide class of previously unknown singularly perturbed solutions supplementing well investigated regular solutions describing propagating waves. Fine flow components, whose geometry is typical for internal boundary layers that supplement the wave fields exist both at the boundaries and inside the volume of the liquid, are classified as linear precursors of shock waves. The calculated pattern of periodic internal waves beams covered with high-gradient envelopes agrees with data from independently performed experiments on measurements and visualization of the fine structure of linear and nonlinear waves in continuously stratified media.

Characteristics of bolus formation and propagation from breaking internal waves on shelf slopes

A series of laboratory experiments was conducted to study the formation of internal boluses through the run up of periodic internal wave trains on a uniform slope/shelf topography in a two-layer stratified fluid system. In the experiments, the forcing parameters of the incident waves (wave amplitude and frequency) are varied for constant slope angle and layer depths. Simultaneous particle image velocimetry (PIV) and planar laser-induced fluorescence (PLIF) measurements are used to calculate high resolution, two-dimensional velocity and density fields. Over the range of wave forcing conditions, four bolus formation types were observed: backward overturning into a coherent bolus, top breaking into a turbulent bolus, top breaking into a turbulent surge and forward breaking into a turbulent surge. Wave forcing parameters, including a wave Froude number $Fr$, a wave Reynolds number $Re$ and a wave steepness parameter $ka_{0}$, are used to relate initial wave forcing to a dominant bolus formation mechanism. Bolus characteristics, including the bolus propagation speed and turbulent components, are also related to wave forcing. Results indicate that for $Fr&gt;0.20$ and $ka_{0}&gt;0.40$, the generated boluses become more turbulent in nature. As wave forcing continues to increase further, boluses are no longer able to form.

The mean flow and long waves induced by two-dimensional internal gravity wavepackets

Through theory supported by numerical simulations, we examine the induced local and long range response flows resulting from the momentum flux divergence associated with with a two-dimensional Boussinesq internal gravity wavepacket in a uniformly stratified ambient. Our theoretical approach performs a perturbation analysis that takes advantage of the separation of scales between waves and the amplitude envelope of a quasi-monochromatic wavepacket. We first illustrate our approach by applying it to the well-studied case of deep water surface gravity waves, showing that the induced flow, UDF, resulting from the divergence of the horizontal momentum flux is equal to the Stokes drift. For a localized surface wavepacket, UDF is itself a divergent flow and so there is the well-known non-local response manifest in the form of a deep return flow beneath the wavepacket. For horizontally periodic and vertically localized internal wavepackets, the divergent-flux induced flow, uDF, is found from consideration of the vertical gradient of the vertical flux of horizontal momentum associated with the waves. Because uDF is itself a non-divergent flow field, this accounts entirely for the wave-induced flow; there is no response flow. Our focus is upon internal wavepackets that are localized in the horizontal and vertical. We derive a formula for the divergent-flux induced flow that, as in this case of surface wavepackets, is itself a divergent flow. We show that the response is a horizontally long internal wave that translates vertically with the wavepacket at its group velocity. Scaling relationships are used to estimate the wavenumber, horizontal extent, and amplitude of this induced long wave. At higher order in perturbation theory we derive an explicit integral formula for the induced long wave. Thus, we provide validation of Bretherton's analysis of flows induced by two-dimensional internal wavepackets [F. P. Bretherton, “On the mean motion induced by gravity waves,” J. Fluid Mech. 36, 785–803 (1969)] and we provide further analyses that give intuitive insights into the physics governing the properties of the induced long wave. In particular, consistent with momentum conservation, we show that the horizontally-integrated horizontal flow associated with the long wave is given exactly by the horizontal integral of uDF. However, qualitatively different from horizontally periodic internal waves, the vertical profile of the induced horizontal flow across the horizontally localized wavepacket is positive at the leading edge and negative at the trailing edge. These results are validated by the results of numerical simulations of a Gaussian wavepacket initialized in an otherwise stationary ambient.

Transformation of internal solitary waves at the &amp;quot;deep&amp;quot; and &amp;quot;shallow&amp;quot; shelf: satellite observations and laboratory experiment

Abstract. An interaction of internal solitary waves with the shelf edge in the time periods related to the presence of a pronounced seasonal pycnocline in the Red Sea and in the Alboran Sea is analysed via satellite photos and SAR images. Laboratory data on transformation of a solitary wave of depression while passing along the transverse bottom step were obtained in a tank with a two-layer stratified fluid. The certain difference between two characteristic types of hydrophysical phenomena was revealed both in the field observations and in experiments. The hydrological conditions for these two processes were named the "deep" and the "shallow" shelf respectively. The first one provides the generation of the secondary periodic short internal waves – "runaway" edge waves – due to change in the polarity of a part of a soliton approaching the shelf normally. Another one causes a periodic shear flow in the upper quasi-homogeneous water layer with the period of incident solitary wave. The strength of the revealed mechanisms depends on the thickness of the water layer between the pycnocline and the shelf bottom as well as on the amplitude of the incident solitary wave.

Generation of mountain wave‐induced mean flows and turbulence near the tropopause

AbstractGravity waves interacting with the tropopause are investigated using linear and nonlinear numerical simulations. The tropopause is modelled as the interface between two layers of constant Brunt–Väisälä frequency. The simulations are two‐dimensional with uniform horizontal flow, the background rotation is ignored, and the gravity waves are generated by flow over an idealized isolated obstacle shape at the surface. The nonlinear simulation results show a horizontal wave‐induced mean flow at the tropopause similar to previous results treating horizontally periodic internal waves impinging on a density‐gradient interface. The mean flow created by the impinging gravity waves is increased over the background wind below the tropopause and decreased above the tropopause. This effect is not present in the linear simulations. The nonlinear effect is felt more strongly for cases with higher mountain heights and larger values of the stability in the upper layer. The final steady mountain‐wave flow appears to permanently retain this mean‐flow change. The deceleration region above the tropopause results in a patch of slow‐moving fluid near the interface which induces local regions of reduced Richardson number and may help explain some observational results of higher turbulence intensities near the tropopause over mountainous regions.

Internal wave-mediated shading causes frequent vertical migrations in fishes

We provide evidence that internal waves cause frequent vertical migrations (FVM) in fishes. Acoustic data from the Benguela Current revealed that pelagic scattering layers of fish below ~140 m moved in opposite phases to internal waves, ascending ~20 m towards the wave trough and descending from the wave crest. At the trough, the downward displacement of upper waters and the upward migration of fish created an overlapping zone. Near-bottom fish correspond- ingly left the benthic boundary zone at the wave trough, ascending into an acoustic scattering layer likely consisting of zooplankton and then descend- ing to the benthic boundary zone at the wave crest. We suggest that this vertical fish migration is a response to fluctuations in light intensity of 3 to 4 orders of magnitude caused by shading from a turbid surface layer that had chlorophyll a values of 3 to 4 mg m −3 and varied in thickness from ~15 to 50 m at a temporal scale corresponding to the internal wave period (30 min). This migration fre- quency thus is much higher than that of the com- mon and widespread light-associated diel vertical migration. Vertical movements affect prey en - counters, growth, and survival. We hypothesize that FVM increase the likelihood of prey encoun- ters and the time for safe visual foraging among planktivorous fish, thereby contributing to efficient trophic transfer in major upwelling areas.