Internal Wave Modes Research Articles

Mixing by internal waves quantified using combined PIV/PLIF technique

We present a novel characterization of mixing events associated with the propagation and overturning of internal waves, studied thanks to the simultaneous use of Particle Image Velocimetry (PIV) and Planar Laser Induced Fluorescence (PLIF) techniques. This combination of techniques had been developed earlier to provide an access to simultaneous velocity and density fields in two-layer stratified flows with interfacial gravity waves. Here, for the first time, we show how it is possible to implement it quantitatively in the case of a continuously stratified fluid where internal waves propagate in the bulk. We explain in details how the calibration of the PLIF data is performed by an iterative procedure, and we describe the precise spatial and temporal synchronizations of the PIV and PLIF measurements. We then validate the whole procedure by characterizing the Triadic Resonance Instability (TRI) of an internal wave mode. Very interestingly, the combined technique is then applied to a {precise} measurement of the turbulent diffusivity K_t associated with mixing events induced by an internal wave mode. Values up to K_t=15 mm^2\cdot s^{-1} are reached when TRI is present (well above the noise of our measurement, typically 1 mm^2\cdot s^{-1}), unambiguously confirming that TRI is a potential pathway to turbulent mixing in stratified flows. This work therefore provides a step on the path to new measurements for internal waves.

Internal tides in the coastal zone of the Sea of Japan in autumn

The results are presented of hydrological studies in the coastal zone of the Sea of Japan in autumn in different years. It is revealed that the typical density stratification of water is formed there in autumn. The amplitudes are estimated of regular (with the periodicity of tidal harmonic M2) vertical displacements of isotherms in the intermediate layer and maximum values of flow velocity in the surface and bottom layers. It is demonstrated that temperature perturbations are induced at the shelf edge and propagate to the coastal zone with the velocity that is close to the velocity of the first mode of internal gravity waves with the frequency of the tidal harmonic M2.

Toward the azimuthal characteristics of ionospheric and seismic effects of “Chelyabinsk” meteorite fall according to the data from coherent radar, GPS, and seismic networks

AbstractWe present the results of a study of the azimuthal characteristics of ionospheric and seismic effects of the meteorite ‘Chelyabinsk,’ based on the data from the network of GPS receivers, coherent decameter radar EKB, and network of seismic stations, located near the meteorite fall trajectory. It is shown that 6–14 min after the bolide explosion, GPS network observed the cone‐shaped wavefront of traveling ionospheric disturbances (TIDs) that is interpreted as a ballistic acoustic wave. The typical TIDs propagation velocity were observed 661 ± 256 m/s, which corresponds to the expected acoustic wave speed for 240 km height. Fourteen minutes after the bolide explosion, at distances of 200 km, we observed the emergence and propagation of a TID with annular wavefront that is interpreted as gravitational mode of internal atmospheric waves. The propagation velocity of this TID was 337 ± 89 m/s which corresponds to the propagation velocity of these waves in similar situations. At EKB radar, we observed TIDs in the sector of azimuthal angles close to the perpendicular to the meteorite trajectory. The observed TID velocity (400 m/s) and azimuthal properties correlate well with the model of ballistic wave propagating at 120–140 km altitude. It is shown that the azimuthal distribution of the amplitude of vertical seismic oscillations with periods 3–60 s can be described qualitatively by the model of vertical strike‐slip rupture, propagating at 1 km/s along the meteorite fall trajectory to distance of about 40 km. These parameters correspond to the direction and velocity of propagation of the ballistic wave peak by the ground. It is shown that the model of ballistic wave caused by supersonic motion and burning of the meteorite in the upper atmosphere can satisfactorily explain the various azimuthal ionospheric effects, observed by the coherent decameter radar EKB, GPS receivers network, and the azimuthal characteristics of seismic waves at large distances.

Dynamic response of a riser under excitation of internal waves

In this paper, the dynamic response of a marine riser under excitation of internal waves is studied. With the linear approximation, the governing equation of internal waves is given. Based on the rigid-lid boundary condition assumption, the equation is solved by Thompson-Haskell method. Thus the velocity field of internal waves is obtained by the continuity equation. Combined with the modified Morison formula, using finite element method, the motion equation of riser is solved in time domain with Newmark-β method. The computation programs are compiled to solve the differential equations in time domain. Then we get the numerical results, including riser displacement and transfiguration. It is observed that the internal wave will result in circular shear flow, and the first two modes have a dominant effect on dynamic response of the marine riser. In the high mode, the response diminishes rapidly. In different modes of internal waves, the deformation of riser has different shapes, and the location of maximum displacement shifts. Studies on wave parameters indicate that the wave amplitude plays a considerable role in response displacement of riser, while the wave frequency contributes little. Nevertheless, the internal waves of high wave frequency will lead to a high-frequency oscillation of riser; it possibly gives rise to fatigue crack extension and partial fatigue failure.

대형 성층 호수의 수온과 내부파의 3차원 수치 모델링

The momentum and kinetic turbulent energy carried by the wind to a stratified lake lead to basin-scale motions, which provide a major driving force for vertical and horizontal mixing. A three-dimensional (3D) hydrodynamic model was applied to Lake Tahoe, located between California and Nevada, USA, to simulate the dominant basin-scale internal waves in the deep lake. The results demonstrated that the model well represents the temporal and vertical variations of water temperature that allows the internal waves to be energized correctly at the basin scale. Both the model and thermistor chain (TC) data identified the presence of Kelvin modes and Poincare mode internal waves. The lake was weakly stratified during the study period, and produced large amplitude (up to 60 m) of internal oscillations after several wind events and partial upwelling near the southwestern lake. The partial upwelling and followed coastal jets could be an important feature of basin-scale internal waves because they can cause re-suspension and horizontal transport of fine particles from nearshore to offshore. The internal wave dynamics can be also associated with the distributions of water quality variables such as dissolved oxygen and nutrients in the lake. Thus, the basin-scale internal waves and horizontal circulation processes need to be accurately modeled for the correct simulation of the dissolved and particulate contaminants, and biogeochemical processes in the lake.

Internal tides near the Celtic Sea shelf break: A new look at a well known problem

Internal waves generated by tides in the Celtic Sea were investigated on the basis of in situ data collected at the continental slope in July 2012, and theoretically using a weakly nonlinear theory and the Massachusetts Institute of Technology general circulation model. It was found that internal solitary waves generated over the shelf break and propagated seaward did not survive in the course of their evolution. Due to the large bottom steepness they disintegrated locally over the continental slope radiating several wave systems seaward and transforming their energy to higher baroclinic modes. In the open part of the sea, i.e. 120km away from the shelf break, internal waves were generated by a baroclinic tidal beam which was radiated from the shelf break downward to the abyss. After reflection from the bottom it returned back to the surface where it hit the seasonal pycnocline and generated packets of high-mode internal solitary waves. Another effect that had strong implications for the wave dynamics was internal wave reflection from sharp changes of vertical fluid stratification in the main pycnocline. A large proportion of the tidal beam energy that propagated downward did not reach the bottom but reflected upward from the layered pycnocline and returned back to the surface seasonal pycnocline where it generated some extra higher mode internal wave systems, including internal wave breathers.

Propagation regimes of interfacial solitary waves in a three-layer fluid

Abstract. Long weakly nonlinear finite-amplitude internal waves in a fluid consisting of three inviscid layers of arbitrary thickness and constant densities (stable configuration, Boussinesq approximation) bounded by a horizontal rigid bottom from below and by a rigid lid at the surface are described up to the second order of perturbation theory in small parameters of nonlinearity and dispersion. First, a pair of alternatives of appropriate KdV-type equations with the coefficients depending on the parameters of the fluid (layer positions and thickness, density jumps) are derived for the displacements of both modes of internal waves and for each interface between the layers. These equations are integrable for a very limited set of coefficients and do not allow for proper description of several near-critical cases when certain coefficients vanish. A more specific equation allowing for a variety of solitonic solutions and capable of resolving most near-critical situations is derived by means of the introduction of another small parameter that describes the properties of the medium and rescaling of the ratio of small parameters. This procedure leads to a pair of implicitly interrelated alternatives of Gardner equations (KdV-type equations with combined nonlinearity) for the two interfaces. We present a detailed analysis of the relationships for the solutions for the disturbances at both interfaces and various regimes of the appearance and propagation properties of soliton solutions to these equations depending on the combinations of the parameters of the fluid. It is shown that both the quadratic and the cubic nonlinear terms vanish for several realistic configurations of such a fluid.

Multimodal Internal Waves Generated over a Subcritical Ridge: Impact of the Upper-Ocean Stratification

AbstractInteraction of barotropic tides with subsurface topography is vital to ocean mixing. Yet the behavior of large-amplitude, nonlinear, internal solitary waves (ISWs) that can cause strong mixing remains poorly understood, especially that of higher-mode and multimodal internal waves. Therefore, a 2.5-dimensional, nonhydrostatic model with adjustable vertical resolution was developed to investigate effects of upper-ocean stratification on tidally induced multimodal internal waves and to show how they are generated by the subcritical ridge where only upward-propagating internal wave beams (IWBs) are present. The effects of the stratification on properties and characteristics of the excited IWBs and on the energy partition of the radiated mode-1 and mode-2 internal waves were investigated based on the model results. Higher modes of internal waves can also be effectively generated in the IWBs by the subcritical topography, and the contribution to IWBs from higher modes increases with the upper-ocean stratification. Mode-2 ISWs can be excited from the IWBs if both the tidal Froude number and the contribution to IWBs from mode-2 waves are sufficiently high (U0 is the tidal current speed, and c2 is the phase speed of mode-2 waves). In a moderately stratified upper ocean, both mode-1 and mode-2 ISWs can be produced, but for weak (strong) stratification, only mode-1 (mode-2) ISWs are generated. Further, it is found that the distance between two successive mode-1 or mode-2 ISW trains increases linearly with the upper-ocean stratification. The ratio of the kinetic energy to the available potential energy for the mode-2 ISWs increases with the upper-ocean stratification in a strongly stratified ocean.

A composite vertical current spectrum for strongly and weakly stratified seas and oceans

An overall frequency (s) spectrum f w (s, N, fh ) is composed for vertical current (w) observations from ocean areas with different stratifications represented by large, 100 m scale buoyancy frequency N. The horizontal Coriolis parameter is denoted by fh . In the open Atlantic Ocean, the relatively strong horizontal layering in density supports the f w that is found in semiequilibrium under the degradation of the lowest internal wave mode. This f w is not constant with frequency; however, its variance increases between s = f and its peak near s = (0.5 – 0.7) N >> f, where f denotes the local inertial frequency. In contrast, the f w spectra from the weakly stratified deep Mediterranean and from the shallow North Sea peak at ~ 1.1 f, except for a tidal peak in North Sea data, and fall off at a rate of s–1 for 1.1 f 0, is contrary to the existing model of open-ocean equilibrium spectra that decrease with N (p < 0). A smooth transition between the two regimes is found to coincide with top-peak f w for N/fh =

Resonant excitation of island-trapped waves in a shallow, seasonally stratified sea

Analysis of oceanographic data collected during 2006 in the eastern Adriatic Sea indicated the presence of large internal waves (with a maximum range of about 30m) at the diurnal frequency around the island of Lastovo. The amplitude ratio and phase difference between diurnal surface tides and diurnal isotherm fluctuations changed considerably between pronounced internal wave episodes, depending on stratification properties, thus suggesting possible resonant excitation of internal oscillations. On the contrary, no significant diurnal thermocline fluctuations were observed at two other islands (Biševo and Sušac). Theoretical analysis presented here focused on the trapping of long-period internal waves around a circular island corresponding to Lastovo and confirmed that stratification properties during the summer of 2006 around the island were close to resonant ones. The analysis also showed that Biševo and Sušac are too small to support diurnal near-resonant excitation. Application of a numerical model for the current flow around equivalent circular and elliptical islands in the stratified sea provided more details on resonant excitation. Theoretical and numerical modeling results particularly emphasized the importance of island dimensions, stratification properties (pyconocline depth and density defect) and the periodicity of the forcing. Furthermore, idealized numerical simulations demonstrated that the waves trapped at Lastovo behave as the gravest azimuthal mode of internal Kelvin-like waves, revolving in a clockwise direction around the island, and that the eccentricity of the island has almost no effect on the resonant period.

A perspective of modeling internal wave/acoustic wave interactions at the Naval Research Laboratory 1992-2012

Interest in modeling internal gravity waves in littoral regions was stimulated by the discovery of anomalous transmission loss in the Yellow Sea, predicted by Zhou and Rogers in 1991 to be caused by solitary wave propagation along the acoustic transmission path. Over the past 20 years, we have been modeling acoustic wave/solitary internal wave interactions and an overview and perspective of some of this work, illustrated by examples, will be presented. The relationship between internal waves and the scintillation index, horizontal refraction of acoustic energy, oceanographic waveguide focusing, mode coupling between acoustic and internal wave modes, and the effect of internal waves on acoustic field uncertainty are discussed. Some thoughts on the future of 4-D simulation of acoustic/internal wave interactions and modeling in the context of incomplete environmental knowledge are considered. [Work supported by the Office of Naval Research.]

Observations of sound-speed fluctuations in the western Philippine Sea in the spring of 2009

As an aid to understanding long-range acoustic propagation in the Philippine Sea, statistical and phenomenological descriptions of sound-speed variations were developed. Two moorings of oceanographic sensors located in the western Philippine Sea in the spring of 2009 were used to track constant potential-density surfaces (isopycnals) and constant potential-temperature surfaces (isotherms) in the depth range 120-2000 m. The vertical displacements of these surfaces are used to estimate sound-speed fluctuations from internal waves, while temperature/salinity variability along isopycnals are used to estimate sound-speed fluctuations from intrusive structure often termed spice. Frequency spectra and vertical covariance functions are used to describe the space-time scales of the displacements and spiciness. Internal-wave contributions from diurnal and semi-diurnal internal tides and the diffuse internal-wave field [related to the Garrett-Munk (GM) spectrum] are found to dominate the sound-speed variability. Spice fluctuations are weak in comparison. The internal wave and spice frequency spectra have similar form in the upper ocean but are markedly different below 170-m depth. Diffuse internal-wave mode spectra show a form similar to the GM model, while internal-tide mode spectra scale as mode number to the minus two power. Spice decorrelates rapidly with depth, with a typical correlation scale of tens of meters.

태풍 에위니아 (0603) 통과 후 상층해양 변동 특성과 영향

Upper ocean response to typhoon Ewiniar (0603) and its impact on the following typhoon Bilis (0604) are investigated using observational data and numerical experiments. Data used in this study are obtained from the Ieodo Ocean Research Station (IORS), ARGO, and satellite. Numerical simulations are conducted using 3-dimensional Princeton Ocean Model. Results show that when Ewiniar passes over the western North Pacific, unique oceanic responses are found at two places, One is in East China Sea near Taiwan and another is in the vicinity of IORS. The latter are characterized by a strong sea surface cooling (SSC), and in simulation and observation, under the condition of typhoon with a fast translation speed (8m ) and lowering intensity (970 hPa). The record-breaking strong SSC is caused by the Yellow Sea Bottom Cold Water, which produces a strong vertical temperature gradient within a shallow depth of Yellow Sea. The former are also characterized by a strong SSC, in simulation, with a additional cooling of after a storm`s passage mainly due to enhanced and maintained upwelling process by the resonance coupling of storm translation speed and the gravest mode internal wave phase speed. The numerical simulation reveals that the Ewiniar produced a unfavorable upper-ocean thermal condition, which eventually inhibited the intensification of the following typhoon Bilis. Statistics show that 9% of the typhoons in western North Pacific are influenced by cold wakes produced by a proceeding typhoon. These overall results demonstrate that upper ocean response to a typhoon even after the passage is also important factor to be considered for an accurate intensity prediction of a following typhoon with similar track.

Mode-2 internal wave generation and propagation-impact on acoustic signal properties

Mode 2 internal wave spatial distributions, generation, propagation and dissipation in the vicinity of bathymetry variably on the continental shelf and near the shelf break of New Jersey, USA will be overviewed for early fall oceanographic conditions. The 3-D spatial and temporal evolution of the mode 2 waves, as simulated with the Naval Research Laboratory nonhydrostatic Model for Coastal Oceans, will be compared to tow-yo conductivity, temperature and depth (CTD) and high frequency acoustic flow visualization observations of mode -2 internal waves. Sound speed field perturbation and acoustic field spatial and temporal distributions in the presence of mode-2 internal waves will be summarized.

Autowave friction and nonequilibrium dynamic tribosystem self-regulation

The transition to the condition of autowave motion is illustrated on the example of a dynamic system consisting of weights linked to a pulley moving with friction in the pulley axis under the force of gravity. The coherent interaction between the external modes of nonstationary directed motion and the internal wave modes under the studied conditions induces the effects of negative dynamic friction. The tangential intensification of the counterbody friction in the intervals of positive feedback actuates both the tangential and normal component of the full contact response that has no counterparts in the equilibrium tribodynamics. This effect is explained by the resonance automodulation of contact friction by elastic waves of stresses. The qualitative parameters controlling the changes in external friction conditions are introduced, similar to the Reynolds number in hydroaeromechanics. The general problems of contact tribodynamics and hydroaerodymics of the boundary layer are analyzed in respect to the coherent interaction in the friction system and the wave impulse transfer.

Temporal variability of the standing internal tide in the Browse Basin, Western Australia

We have investigated the seasonal evolution of the internal tide using a yearlong mooring record in the Browse Basin on the Australian North‐West Shelf. Using a modal harmonic‐decomposition technique, we studied the modulation of the semi‐diurnal kinetic energy, potential energy, energy flux, group velocity and sea surface height anomaly for different internal wave modes. A very coherent and energetic, locally generated internal tide dominated the mooring record during spring‐tide periods. Relationships amongst the wave variables suggest that the interaction of multiple waves formed a standing wave pattern. To assist in explaining the seasonal variability of this standing wave pattern, we used an analytical model of internal wave generation and propagation in a double‐shelf system, representative of the area, to highlight the effects of changes in the stratification and barotropic forcing. A comparison of the low‐mode wave energy indicated that the analytical solution overestimated the observed wave energy by a factor of two and failed to detect an apparent seasonal shift in the conversion rate. We discuss potential mechanisms for this discrepancy.

Acoustical monitoring of the second mode internal solitary wave on oceanic shelf

The possibility of monitoring second gravitational mode internal solitons using interference pattern frequency shifts is discussed. The investigation is carried out for the shelf of the northern South China Sea near the Dongsha Atoll by means of numerical modeling. We used the data of the in-situ internal solitons measurements in this area. The “vertical modes and horizontal rays” approach is implemented to calculate the low frequency sound fields in the 3d environment. Stationary acoustic path is oriented at the right angle to the preferred internal wave propagation direction. A sound source and receivers are deployed at the sea bottom. Sound receivers are located at the different ranges where horizontal refraction is pronounced, and where it is insignificant. Numerical experiments demonstrate that some of acoustic waveguide modes are focused, and others are defocused in the horizontal plane when the second mode soliton propagates across the acoustic path. It is shown that the second mode internal solitary wave parameters can be successfully reconstructed from the frequency shifts in the spectrum of received signals only if horizontal refraction effects are weak. [Work supported by Russian Foundation for Basic Research and National Science Council of Taiwan # 10-02-92005]

On‐shelf transport of slope water lenses within the seasonal pycnocline

We show that discrete lenses of anomalously high‐salinity water, originating from the shelf edge and trapped within the seasonal pycnocline, are advected 100 km or more onto the Celtic Sea continental shelf. We propose that the lenses are created by increased diapycnal mixing at the shelf edge associated with breaking high‐frequency internal wave packets. Quasi‐synoptic hydrography sections show the lenses to be 3–5 km wide, their temporal persistence confirmed by moored instrumentation and a series of CTD casts. Estimates of the propagation speed of these features (∼0.020 m s−1) compare favorably with the magnitude of observed residual currents. Residual current variability within the pycnocline is dominated by vertical structures most consistent with the second baroclinic mode. The residual flow is therefore thought to be predominantly driven by non‐linear second mode internal tidal waves. These are observations of a shelf edge exchange process not previously identified.

A multi-layer model for nonlinear internal wave propagation in shallow water

AbstractIn this paper, a multi-layer model is developed for the purpose of studying nonlinear internal wave propagation in shallow water. The methodology employed in constructing the multi-layer model is similar to that used in deriving Boussinesq-type equations for surface gravity waves. It can also be viewed as an extension of the two-layer model developed by Choi &amp; Camassa. The multi-layer model approximates the continuous density stratification by an $N$-layer fluid system in which a constant density is assumed in each layer. This allows the model to investigate higher-mode internal waves. Furthermore, the model is capable of simulating large-amplitude internal waves up to the breaking point. However, the model is limited by the assumption that the total water depth is shallow in comparison with the wavelength of interest. Furthermore, the vertical vorticity must vanish, while the horizontal vorticity components are weak. Numerical examples for strongly nonlinear waves are compared with laboratory data and other numerical studies in a two-layer fluid system. Good agreement is observed. The generation and propagation of mode-1 and mode-2 internal waves and their interactions with bottom topography are also investigated.

Combination Mode of Internal Waves Generated by Surface Wave Propagating over Two Muddy Sea Beds

When surface wave propagating over the two layer system usually induces internal wave in three different modes: they are external, internal and combination. In the present study, the nonlinear response of an initially flat sea bed, with two muddy sections, to a monochromatic surface progressive wave was investigated. From this theoretical result, it shows that a surface water wave progressing over two different muddy sections, the surface wave will excite two opposite-traveling short interfacial waves, forming a nearly standing wave at the interface of the fresh water and the muddy layer. Meanwhile, two opposite-outgoing “mud” waves each with very long wavelength will be simultaneously induced at the interface of two muddy sections. As a result, the amplitudes of the two short internal waves are found to grow exponentially in time. Furthermore, it will be much difficult to excite the internal waves when surface water wave progressing over two muddy sections with the large density gap.