Dynamics Of Internal Waves Research Articles

Fate of Internal Waves on a Shallow Shelf

AbstractInternal waves strongly influence the physical and chemical environment of coastal ecosystems worldwide. We report novel observations from a distributed temperature sensing (DTS) system that tracked the transformation of internal waves from the shelf break to the surf zone over a narrow shelf slope region in the South China Sea. The spatially continuous view of temperature fields provides a perspective of physical processes commonly available only in laboratory settings or numerical models, including internal wave reflection off a natural slope, shoreward transport of dense fluid within trapped cores, and observations of internal rundown (near‐bed, offshore‐directed jets of water preceding a breaking internal wave). Analysis shows that the fate of internal waves on this shelf—whether transmitted into shallow waters or reflected back offshore—is mediated by local water column density structure and background currents set by the previous shoaling internal waves, highlighting the importance of wave‐wave interactions in nearshore internal wave dynamics.

Direct simulation of surface roughness signature of internal wave with deterministic energy-conservative model

In this simulation-based study, we investigate the surface roughness signature induced by internal solitary waves in oceans. We present the first-ever effort to directly capture the surface roughness signature with a deterministic two-layer model to avoid the singularity encountered in the traditional wave–current interaction theory. By capturing over four million wave components, the simulation resolves the surface wave and internal wave dynamics simultaneously. The surface signature characterized by a rough region followed by a smooth region travelling with an internal wave is quantified by the local wave geometry variation and the wave energy change. The surface wave dynamics are analysed in the wavenumber–frequency slope spectrum calculated in the frame moving with the internal wave. The asymmetric behaviours of right-moving and left-moving surface waves are found to contribute to the surface signature formation. Our results show that the formation of the surface signature is essentially an energy-conservative process and justify the use of the wave-phase-resolved two-layer model.

Internal waves pump waters in and out of a deep coastal embayment of a large lake

AbstractLarge internal waves are a ubiquitous feature of many thermally stratified lakes, and result in oscillating baroclinic flows that pump water into and out of deep coastal embayments. In the long, narrow, and deep Kempenfelt Bay of Lake Simcoe, we show that stratification and circulation were coupled, so that movements of the thermocline can effectively flush the embayment much faster than hydraulic residence time from river input alone. Internal currents were driven by long‐period internal waves and resulted in large horizontal excursion lengths of several kilometers, which could drive exchange of embayment waters with the main basin. If the embayments are long, wide, and deep, Coriolis forces also deflect the internal wave to follow the coastline on the right‐hand side in the direction of travel as a Kelvin‐type wave, resulting in a net cyclonic circulation in the embayment. This residual counterclockwise flow further facilitated flushing of Kempenfelt Bay. For the summer of 2015, we estimate that forced and free internal wave dynamics alone resulted in a seasonally averaged flushing timescale as short as 17 ± 6 d for the surface mixed layer, and of 13.5 ± 5 d for the hypolimnetic waters of Kempenfelt Bay. Kempenfelt Bay is representative of many long, deep, and narrow embayments found in the Laurentian Great Lakes and arctic fjords. The exchange processes investigated here are relevant for determining the dynamics of water quality parameters used as indicators to evaluate lake health and fish habitat.

Numerical Simulation of Marine Internal Wave Dynamics Based on Functional Analysis

Liu, H., 2018. Numerical simulation of marine internal wave dynamics based on functional analysis. In: Liu, Z.L. and Mi, C. (eds.), Advances in Sustainable Port and Ocean Engineering. Journal of Coastal Research, Special Issue No. 83, pp. 12–16. Coconut Creek (Florida), ISSN 0749-0208.For the low utilization rate of marine resources and little understanding of the dynamics of some marine resources, it is necessary to study the dynamic numerical simulation of ocean waves. The current method has a problem of low utilization rate. In this paper, a numerical simulation of marine internal wave power based on functional analysis is presented. The method firstly combines the solving method of N-S equation to establish the theoretical problem of water wave power numerical tank and the interaction between water particles is expressed through the nucleon function. The concept of particle density is introduced to realize the incompressibility of the fluid and the numerical simulation analysis of the wave power in the ocean is carried out by using functional analysis.The experimental results show that this method can be used effectively in marine resources.

Seasonal dynamics of internal waves governed by stratification stability and wind: Analysis of high‐resolution observations from the Dead Sea

AbstractInternal waves in stratified lakes are affected by the seasonally varying stratification and the wind forcing. We studied the seasonal dynamics of internal waves by means of high‐resolution observations and model simulations for the Dead Sea. A two‐layer hydrostatic model provided high correlations between measured thermocline depth and the lake level oscillations. Seasonally, the amplitude of the thermocline fluctuations were anticorrelated with the density difference between the water layers; the largest fluctuations were observed when stratification was weak in spring/fall and moderate to weak fluctuations in mid‐summer when stratification was fully developed. The surface and the internal waves propagated counterclockwise along the coasts at a speed of ~0.5 m s−1. Power spectra of the observed wind as well as the measured and simulated lake level and thermocline depth show a pronounced diurnal period during summer, suggesting forcing by the diurnally varying wind. During spring and fall, when the water column stability diminishes, a hint of longer wind periods appear in addition to the diurnal mode. Accordingly, the lake level and thermocline depth fluctuations respond at lower frequencies. In the fall, the longer wind periods are close to the lake's first vertical normal mode, suggesting that resonant amplification of the internal waves may explain the observed lower frequency response of the level and thermocline oscillations. Reduction of the stratification stability originating from anthropogenic water diversion over the past four decades, associated with lake level decline and salinity increase, have led to increases of internal waves amplitude and periods.

Fine scale depth regulation of invertebrate larvae around coastal fronts

AbstractVertical migrations of zooplankters have been widely described, but their active movements through shallow, highly dynamic water columns within the inner shelf may be more complex and difficult to characterize. In this study, invertebrate larvae, currents, and hydrographic variables were sampled at different depths during and after the presence of fronts on three different cruises off the southern coast of South Africa. Internal wave dynamics were observed in the hydrographic data set but also through satellite imagery, although strong surface convergent currents were absent and thermal stratification was weak. During the first two cruises, fronts were more conspicuous and they preceded strong onshore currents at depth which developed with the rising tide. Vertical distributions of larvae changed accordingly, with higher abundances at these deep layers once the front disappeared. The third cruise was carried out during slack tides, the front was not conspicuous, deep strong onshore currents did not occur afterward and larval distributions did not change consistently through time. Overall, the vertical distributions of many larval taxa matched the vertical profiles of shoreward currents and multivariate analyses revealed that these flows structured the larval community, which was neither influenced by temperature nor chlorophyll. Thus, the ability to regulate active vertical positioning may enhance shoreward advection and determine nearshore larval distributions.

Numerical investigation of internal solitary waves of elevation type propagating on a uniform slope

Numerous laboratory-scale physical experiments and numerical simulations have been carried out to explore the shoaling dynamics of internal solitary waves (ISWs) on slope topographies. Detailed features during wave breaking have been investigated under relatively low Reynolds numbers, but for real ocean-scale or lake-scale scenarios with a much higher Reynolds number, laboratory-scale modeling is inadequate to capture the three-dimensional turbulent characteristics in the wave shoaling process. As a result, a three-dimensional large-eddy simulation (LES) is performed in the present study to investigate the shoaling process of the elevation-typed ISWs traveling on uniform slopes in a two-layer fluid system. Scale effects due to the Reynolds numbers (varied from 103 to 105) and three-dimensional characteristics during wave shoaling are also explored and discussed. Detailed ISW-slope interaction dynamics, including the typical shoaling features, the characteristics of internal boluses, and both the velocity field and the energy transformation, are systematically obtained and analyzed. It is found that, while reaching the maximum vertical displacement (i.e., maximum run-up height), the frontal part of the heavier lower-layer fluid can evolve into the internal bolus if the internal Iribarren number, Ir, defined as the ratio of the topographic slope and the square root of the incident wave steepness, is less than 0.65. The maximum wave-induced velocities and energy loss are also well related to Ir. Empirical regressed equations for seven important physical parameters during the shoaling process are also proposed. The extreme velocities, wave energy loss, and three-dimensionality of the flow field are all identified to be very sensitive to Reynolds numbers, indicating that traditional two-dimensional laboratory-scale modeling tools may be insufficient to accurately capture the shoaling mechanisms of the ISWs of elevation type.

Dynamics of surface and internal long waves generated by atmospheric pressure disturbances

Different from non-dispersive wave models such as the shallow water equations, MCC (Miyata, Choi, and Camassa) type strongly nonlinear dispersive wave model can describe not only the dynamics of surface waves, but also those of internal waves. The MCC model for a two-layer fluid system is applied to study dynamics of both surface waves and internal waves. The resonance mechanisms with atmospheric pressure disturbances are numerically studied not only for surface waves, so-called Proudman resonance, but also for internal waves. Baroclinic internal waves are generated when the speed of the atmospheric pressure disturbance is comparable to the critical linear internal wave speed. We compare the amplitudes of generated internal waves to the resonance theory for surface waves. Although most baroclinic internal wave phenomena can be explained by this linear theory, the relative magnitudes of amplitudes for forced and free waves do not agree with the theory. In addition, sequentially generated surface waves with resonance are observed when the radius of the atmospheric pressure disturbance is small. Finally, the dynamics of both surface and internal waves over non-uniform bottom topography are discussed in terms of Froude numbers to understand how they propagate and interact with each other when the Proudman resonance condition is satisfied while they travel.

Spectral-analysis for Internal Wave Dynamics in a Small Lake and the Example of the Analysis

Spectral-analysis for Internal Wave Dynamics in a Small Lake and the Example of the Analysis

Resolving high-frequency internal waves generated at an isolated coral atoll using an unstructured grid ocean model

We apply the unstructured grid hydrodynamic model SUNTANS to investigate the internal wave dynamics around Scott Reef, Western Australia, an isolated coral reef atoll located on the edge of the continental shelf in water depths of 500,m and more. The atoll is subject to strong semi-diurnal tidal forcing and consists of two relatively shallow lagoons separated by a 500 m deep, 2 km wide and 15 km long channel. We focus on the dynamics in this channel as the internal tide-driven flow and resulting mixing is thought to be a key mechanism controlling heat and nutrient fluxes into the reef lagoons. We use an unstructured grid to discretise the domain and capture both the complex topography and the range of internal wave length scales in the channel flow. The model internal wave field shows super-tidal frequency lee waves generated by the combination of the steep channel topography and strong tidal flow. We evaluate the model performance using observations of velocity and temperature from two through water-column moorings in the channel separating the two reefs. Three different global ocean state estimate datasets (global HYCOM, CSIRO Bluelink, CSIRO climatology atlas) were used to provide the model initial and boundary conditions, and the model outputs from each were evaluated against the field observations. The scenario incorporating the CSIRO Bluelink data performed best in terms of through-water column Murphy skill scores of water temperature and eastward velocity variability in the channel. The model captures the observed vertical structure of the tidal (M2) and super-tidal (M4) frequency temperature and velocity oscillations. The model also predicts the direction and magnitude of the M2 internal tide energy flux. An energy analysis reveals a net convergence of the M2 energy flux and a divergence of the M4 energy flux in the channel, indicating the channel is a region of either energy transfer to higher frequencies or energy loss to dissipation. This conclusion is supported by the mooring observations that reveal high frequency lee waves breaking on the turning phase of the tide.

Mixing and Formation of Layers by Internal Wave Forcing

AbstractThe energy pathways from propagating internal waves to the scales of irreversible mixing in the ocean are not fully described. In the ocean interior, the triadic resonant instability is an intrinsic destabilization process that may enhance the energy cascade away from topographies. The present study focuses on the integrated impact of mixing processes induced by a propagative normal mode‐1 over long‐term experiments in an idealized setup. The internal wave dynamics and the evolution of the density profile are followed using the light attenuation technique. Diagnostics of the turbulent diffusivity KT and background potential energy BPE are provided. Mixing effects result in a partially mixed layer colocated with the region of maximum shear induced by the forcing normal mode. The maximum measured turbulent diffusivity is 250 times larger than the molecular value, showing that diapycnal mixing is largely enhanced by small‐scale turbulent processes. Intermittency and reversible energy transfers are discussed to bridge the gap between the present diagnostic and the larger values measured in Dossmann et al. (). The mixing efficiency η is assessed by relating the BPE growth to the linearized KE input. One finds a value of , larger than the mixing efficiency in the case of breaking interfacial wave. After several hours of forcing, the development of staircases in the density profile is observed. This mechanism has been previously observed in experiments with weak homogeneous turbulence and explained by Phillips (1972) argument. The present experiments suggest that internal wave forcing could also induce the formation of density interfaces in the ocean.

Internal wave scattering in continental slope canyons, Part 2: A comparison of ray tracing and numerical simulations

When internal waves interact with topography, such as continental slopes, they can transfer wave energy to local dissipation and diapycnal mixing. Submarine canyons comprise approximately ten percent of global continental slopes, and can enhance the local dissipation of internal wave energy, yet parameterizations of canyon mixing processes are currently missing from large-scale ocean models. As a first step in the development of such parameterizations, we conduct a parameter space study of M2 tidal-frequency, low-mode internal waves interacting with idealized V-shaped canyon topographies. Specifically, we examine the effect of varying the canyon mouth width, shape and slope of the thalweg (line of lowest elevation) (i.e. flat bottom or near-critical slope). In Part 1 of this study (Nazarian and Legg, 2017a), we developed a ray tracing algorithm and used it to estimate how canyons can increase the wave Froude number, by increasing energy density and increasing vertical wavenumber. Here in Part 2 we examine the internal wave scattering in continental slope canyons using numerical simulations, and compare the results with the linear ray tracing predictions. We find that at intermediate canyon widths, a large fraction of incoming wave energy can be dissipated, which can be explained as a consequence of the increase in ray density and, for near-critical slope canyons, increase in vertical wave number, which leads to lower Richardson number followed by instability. Relative to a steep continental slope without a canyon, we find that V-shaped flat bottom canyons always dissipate more energy and are an effective geometry for wave trapping and subsequent energy loss. When both flat bottom canyons and near-critical slope canyons are made narrower, less wave energy enters the canyon, but a larger fraction of that energy is lost to dissipation due to subsequent reflections and wave trapping. There is agreement between the diagnostics calculated from the numerical model and the linear ray tracing, lending support for the use of linear theory to understand the fundamental dynamics of internal wave scattering in canyons.

A reflecting, steepening, and breaking internal tide in a submarine canyon

AbstractSubmarine canyons are common features of the coastal ocean. Although they are known to be hotspots of turbulence that enhance diapycnal transport in their stratified waters, the dynamics of canyon mixing processes are poorly understood. Most studies of internal wave dynamics within canyons have focused on a handful of canyons with along‐axis slopes less steep than semidiurnal (D2) internal wave characteristics (subcritical). Here, we present the first tidally resolving observations within a canyon with a steeply sloping axis (supercritical). A process study consisting of two 24 h shipboard stations and a profiling mooring was conducted in the La Jolla Canyon off the coast of La Jolla, CA. Baroclinic energy flux is oriented up‐canyon and decreases from 182 ±18 W m−1 at the canyon mouth to W m−1 near the head. The ratio of horizontal kinetic energy to available potential energy and the observed group speed of each mode are lower than expected for freely propagating D2 internal waves at each station, indicating partial reflection. Harmonic analysis reveals that variance is dominated by the D2 tide. Moving up‐canyon, the relative importance of D2 decreases and its higher harmonics are needed to account for a majority of the observed variance, indicating steepening. Steep internal tides cause large isopycnal displacements (∼50 m in 100 m water depth) and high strain events. These events coincide with enhanced O( m2 s−3) dissipation of turbulent kinetic energy at mid‐depths.

The viscous lee wave problem and its implications for ocean modelling

Ocean circulation models employ ‘turbulent’ viscosity and diffusivity to represent unresolved sub-gridscale processes such as breaking internal waves. Computational power has now advanced sufficiently to permit regional ocean circulation models to be run at sufficiently high (100 m–1 km) horizontal resolution to resolve a significant part of the internal wave spectrum. Here we develop theory for boundary generated internal waves in such models, and in particular, where the waves dissipate their energy. We focus specifically on the steady lee wave problem where stationary waves are generated by a large-scale flow acting across ocean bottom topography. We generalise the energy flux expressions of [Bell, T., 1975. Topographically generated internal waves in the open ocean. J. Geophys. Res. 80, 320–327] to include the effect of arbitrary viscosity and diffusivity. Applying these results for realistic parameter choices we show that in the present generation of models with O(1) m2s−1 horizontal viscosity/diffusivity boundary-generated waves will inevitably dissipate the majority of their energy within a few hundred metres of the boundary. This dissipation is a direct consequence of the artificially high viscosity/diffusivity, which is not always physically justified in numerical models. Hence, caution is necessary in comparing model results to ocean observations. Our theory further predicts that O(10−2) m2s−1 horizontal and O(10−4) m2s−1 vertical viscosity/diffusivity is required to achieve a qualitatively inviscid representation of internal wave dynamics in ocean models.

A method of accounting for tidal changes in regional climates of a water basin under conditions of an ice-free Barents Sea

To account for tidal variations in the regional climate of a water basin, we propose adding up the vertical eddy diffusivity, determined by wind and thermohaline forcings, and the diapycnal diffusivity, determined from the solution to the problem of the internal tidal wave (ITW) dynamics. This approach agrees with the approximation of “weak interaction” between turbulence of various origins. Then, the hydrothermodynamics equations are integrated with and without regard for ITW-induced diapycnal diffusion until a quasistationary solution is reached. Next we compare these solutions, found by using the 3D finite-element hydrostatic model QUODDY-4. This comparison shows that the contribution of tides to the formation of the Barents Sea climate in summer is not negligible with respect to certain hydrological characteristics. We present the fields of the dynamic topography of a free surface, surface current velocities, and seawater temperature and salinity at the depth of the pycnocline in the sea to illustrate the occurrence of tidal effects.

Three‐dimensional simulation of high‐frequency nonlinear internal wave dynamics in Cayuga Lake

AbstractThree‐dimensional (3‐D) hydrostatic and nonhydrostatic versions of the MITgcm were applied to simulate the dynamics of the internal wave field (basin‐scale seiches, nonlinear surges, and high‐frequency nonlinear internal waves, NLIWs) in Cayuga Lake, NY. The simulations were performed using up to 226 million computational cells with several horizontal grid resolutions, varying from 450 × 450 m to 22 × 22 m. Vertical grid spacing was not varied and ranged from 0.5 to 2.95 m. The 22 × 22 m nonhydrostatic grid reproduced qualitatively the formation, propagation, and shoaling of observed NLIWs using >10 grid points along the wavelength and a grid lepticity λ of O(1). This ensured, respectively, that the waves were not aliased and physical dispersion predominated over numerical dispersion. Using a sensitivity analysis, we generalize that correctly simulating NLIWs in real domains, using second‐order discretization, requires grid resolutions that are an order of magnitude smaller than the wavelength and amplitude with λ ∼ 2; consistent with published work on idealized domains. Local gyre‐like circulation was simulated, near midbasin headlands, and transverse shoaling of NLIW packets on lateral boundaries was associated with topographic reflection and refraction, in agreement with published field observations from estuaries, which show NLIW propagation in long narrow quasi‐2‐D systems (e.g., Finger Lakes, lochs, fjords, estuaries, and straits) is fundamentally 3‐D. These results, therefore, help fill the gap in understanding and correctly modeling the multiscale 3‐D dynamics of NLIWs in complex natural systems.

The impact of seasonal changes in stratification on the dynamics of internal waves in the Sea of Okhotsk

The impact of seasonal changes in stratification on the dynamics of internal waves in the Sea of Okhotsk

Oscillatory stratified flow over supercritical topography: Wave energetics and turbulence

Topographic features with steep, supercritical slope on the ocean bottom are sites of large energy conversion from the oscillating tide to internal waves according to linear theory. At the same time, they are also sites with potentially large local energy loss as is suggested by nonlinear waves and overturns found in field observations and two-dimensional simulations. Here, we investigate the internal wave dynamics and turbulence at an isolated supercritical obstacle using three-dimensional, high resolution large-eddy simulations (LES) conducted with a body conforming grid. An obstacle with a smoothed triangular shape having supercritical slope is considered as a laboratory-scale model for a two-dimensional ocean ridge. Three simulations are performed with constant Reynolds number and an excursion number (Ex) that varies from 0.066 to unity, corresponding to a large obstacle and a small obstacle, respectively. The dominant nonlinear flow feature is a downslope jet with intensified velocity whose length and thickness increase with increasing Ex. During the flow reversal phase, the downward jet encounters upward flow along the slope and the interaction creates a rebounding jet which distorts the density resulting in convective instability. Turbulence is generated predominantly by shear in the jet, convective instabilities from the rebounding jet, and breaking of transient lee waves. The active region of turbulence grows as Ex increases although the local normalized turbulent kinetic energy becomes smaller. Analysis of the baroclinic energy budget shows that, with increasing Ex, there is a substantial decrease of energy conversion (C) to the wave field as well as a substantial increase in local energy loss (q).

The effects of remote SST forcings on ENSO dynamics, variability and diversity

Air-sea interactions with remote regions in the tropical Indian and Atlantic, and extra-tropical oceans can influence ENSO features in the tropical Pacific. In this study these effects are explored by using an AGCM coupled with a Slab Ocean and a simple recharge oscillator ENSO model through switched on/off air-sea interaction in respective ocean area. It is shown that the decoupling in different remote regions has different impacts on ENSO dynamics, variability and diversity. The most interesting result is that the air-sea interactions with remote tropical oceans provide a delayed negative feedback to ENSO similar to that of the tropical Pacific Ocean internal wave dynamics. This is caused by the ENSO teleconnections: they lead to a delayed remote warming and cooling, which in turn feedbacks to ENSO effectively giving a delayed negative feedback. The model simulations suggest that this remote delayed feedback may contribute about 40% to the total delayed negative feedback of ENSO. Thus a central element of ENSO dynamics is partly due to interactions with other tropical ocean basins by atmospheric teleconnections. Furthermore, all remote regions effectively provide stochastic forcings for the ENSO variability and therefore increase the ENSO variability. The influence from the remote regions also causes different patterns of sea surface temperature (SST) variability in the tropical Pacific, contributing to the diversity of the ENSO mode. In particular the extra-tropical Pacific regions force SST variability that is different from the equatorial ENSO mode of variability. The influence that the remote regions have on the ENSO dynamics and variability is significantly altered by the interaction between the equatorial recharge oscillator dynamics and the simple thermodynamic slab ocean processes.

The Dynamics of Flat Surface Internal Geophysical Waves with Currents

A two-dimensional water wave system is examined consisting of two discrete incompressible fluid domains separated by a free common interface. In a geophysical context this is a model of an internal wave, formed at a pycnocline or thermocline in the ocean. The system is considered as being bounded at the bottom and top by a flatbed and wave-free surface respectively. A current profile with depth-dependent currents in each domain is considered. The Hamiltonian of the system is determined and expressed in terms of canonical wave-related variables. Limiting behaviour is examined and compared to that of other known models. The linearised equations as well as long-wave approximations are presented.