Interaction Of Internal Waves Research Articles

What is the “Near-Inertial” Band and Why Is It Different from the Rest of the Internal Wave Spectrum?

Abstract The “near-inertial” part of the internal wave continuum is dominant and also different from the rest of the spectrum. A simple possible reason for the difference is that waves generated at the surface are not reflected or scattered from the seafloor until they have propagated equatorward to a latitude where their frequency exceeds the local inertial frequency. This excess is easily estimated and is of the order of 10% of f at midlatitudes. The estimate is in reasonable agreement with data on the depth dependence of the peak frequency over smooth topography and on the frequency band within which there is little upward propagating energy. Internal wave propagation and interactions with bottom topography may thus be just as important as wave–wave interactions in controlling the energetic parts of the internal wave spectrum and, hence, in determining mixing rates in the ocean.

Sound fluctuations caused by internal waves in a shallow sea

Estimates are presented for the fluctuations of the parameters of low-frequency sound fields in shallow-water regions of the Barents Sea, in the presence of seasonal internal gravity waves. The objective of the experiments is to reveal the main mechanisms that govern the sound fluctuations and their statistical parameters on paths of moderate lengths (50–60 to 100–120 km). Another objective is to determine the features of the sound interaction with internal waves for the sound speed profile of the summer—autumn type for which the water stratification is most pronounced. As the probing signals, continuous tonal ones produced by bottommoored sources at the frequencies about 100 and 300 Hz are used along with the 1/3-octave noise signals with the central frequency 1000 Hz, which are generated by a source deployed from a vessel. For the signal reception, both fixed bottom-moored hydrophones and a vertical chain of hydrophones are used, the chain also being deployed from the vessel. The water temperature, the salinity, and the thermocline displacements are monitored with standard hydrographic sensors. The following main results are presented: the estimate of the degree of correlation between the sound fluctuations and the parameters of the water layer, the comparison of the fluctuations in the signal amplitude envelope with the data obtained in other regions, and the estimate of the statistical parameters of the signal amplitude fluctuations, including their dependence on the path length. One more result consists in the proof of the wave nature of the interaction of sound and internal waves, which manifests itself in a strong dependence of the sound interaction with internal waves of discrete frequencies on the frequency of the probing signal and on the angle at which these wave beams intersect. An attempt is made to explain the observed phenomena by the synchronism in the interacting sound and gravity waves. The data obtained can be used to analyze and compare the fluctuations of the sound fields in the ocean, especially in shallow-water regions.

Internal Wave Interactions with Equatorial Deep Jets. Part II: Acceleration of the Jets

Abstract What drives the equatorial deep jets is a puzzle because of their isolation from surface forcing by the intervening main pycnocline and the Equatorial Undercurrent, and from lateral boundaries by distances of tens of thousands of kilometers. It would take decades for energy to propagate to the jets’ midbasin location from boundary sources. Their persistence points to some mechanism maintaining them in situ. The authors hypothesize that the ambient internal wave field deposits momentum fluxes at critical layers within the deep jets and, using calculated momentum- and energy-flux divergences as forcing, estimate acceleration of the mean zonal flow in the deep jets. Internal wave momentum-flux divergences are more than sufficient to sustain the jets, acting to sharpen the shear between the jets on timescales of months to years. Predicted energy-flux divergences produce turbulent dissipation rates compatible with those observed.

Numerical study of internal wave–wave interactions in a stratified fluid

A finite volume method is used to study the generation, propagation and interaction of internal waves in a linearly stratified fluid. The internal waves were generated using single and multiple momentum sources. The full unsteady equations of motion were solved using a SIMPLE scheme on a non-staggered grid. An open boundary, based on the Sommerfield radiation condition, allowed waves to propagate through the computational boundaries with minimum reflection and distortion. For the case of a single momentum source, the effects of viscosity and nonlinearity on the generation and propagation of internal waves were investigated.Internal wave–wave interactions between two wave rays were studied using two momentum sources. The rays generated travelled out from the sources and intersected in interaction regions where nonlinear interactions caused the waves to break. When two rays had identical properties but opposite horizontal phase velocities (symmetric interaction), the interactions were not described by a triad interaction mechanism. Instead, energy was transferred to smaller wavelengths and, a few periods later, to standing evanescent modes in multiples of the primary frequency (greater than the ambient buoyancy frequencies) in the interaction region. The accumulation of the energy caused by these trapped modes within the interaction region resulted in the overturning of the density field. When the two rays had different properties (apart from the multiples of the forcing frequencies) the divisions of the forcing frequencies as well as the combination of the different frequencies were observed within the interaction region.The model was validated by comparing the results with those from experimental studies. Further, the energy balance was conserved and the dissipation of energy was shown to be related to the degree of nonlinear interaction.

Analysis of internal wave interactions with broadband acoustic signals propagating along the shelf during the SWARM’95 experiment

A multi-institution experiment was conducted in 1995 on the New Jersey continental shelf to assess the Shallow Water Acoustic propagation in Random Media (SWARM’95). Two major source/receiver geometries were established. One was parallel to the continental shelf edge and the other was perpendicular. The orthogonal propagation consisted of two broadband sources transmitting signals perpendicular to the direction of internal wave field. The first signal was a transient airgun source (0.1-s duration), while the second was a linear frequency modulated sweep (30-s duration). Placed above and below the thermocline, these sources were transmitting signals every minute for a few hours at one location. Here we present a 2-h segment of these observations during 4 August 1995 when nonlinear internal waves were present. The transmissions were received by two vertical line arrays at different ranges and angles from the source. The dependence on the azimuth between the internal waves and the acoustic transmissions was examined. It is found that sound speed fluctuations induced by internal waves cause a 10–12-min temporal variations in the intensity of received signals. These temporal variations are azimuthally dependent since the environment is anisotropic due to internal solitary waves. [Work supported by ONR.]

On a model system for the oblique interaction of internal gravity waves

We give local and global well-posedness results for a system of two Kadomtsev-Petviashvili (KP) equations derived by R. Grimshaw and Y. Zhu to model the oblique interaction of weakly nonlinear, two dimensional, long internal waves in shallow fluids. We also prove a smoothing effect for the amplitudes of the interacting waves. We use the Fourier transform restriction norms introduced by J. Bourgain and the Strichartz estimates for the linear KP group. Finally we extend the result of [3] for lower order perturbation of the system in the absence of transverse effects.

Internal Wave Interactions with Equatorial Deep Jets. Part I: Momentum-Flux Divergences

Abstract Equatorial deep jets are an unsolved mystery of the equatorial oceans. These alternating zonal currents appear steady over time spans of years, but no postulated energy source has proven plausible, and elevated turbulent dissipation in the jets does not appear to erode them. Transfer of energy between the internal wave field and mean flow can occur through momentum-flux divergences, which could act to maintain the jets. Using a Garrett–Munk spectrum adjusted to the equator, the authors estimate the momentum-flux divergence from internal waves encountering critical layers in deep jets. The net momentum-flux divergences are sensitive to the rate at which wave–wave interactions replenish the internal wave spectrum depleted by critical-layer interactions with adjacent jets. Order-of-magnitude arguments indicate that even modest momentum-flux divergences could dramatically impact the mean flow.

Mixing caused by internal waves and turbulence: a comparative analysis

Physical definitions of currents, internal waves and turbulence, and estimates of criteria for discriminating between them are given. It is shown that internal gravity waves can be taken as effective and universal mechanisms to cause such phenomena as fine-structure and large global vertical fluxes of energy and buoyancy in the ocean. Formation of vertical fine-structure (FS) is a natural result of interaction of internal waves (IW) with initially monotonous density profiles. In the process of the interaction, IW and FS are mutually adjusting and expanding their spectra to high frequencies and wave-numbers. In regions with large horizontal gradients of density, IW can induce vertical diffusion with effective coefficients of order 10 −4–10 −3 m 2 s −1. In most parts of the ocean, where horizontal gradients are small, «slow» IW form background shears and density gradients for «fast» IW, and their interaction can lead to vertical fluxes with effective diffusion coefficients of order 10 −5–10 −3 m 2 s −1. The interaction of quasihorizontal turbulence with long wavelength IW leads to vertical diffusion of the same order. Parametric interactions of IW and their interaction with quasihorizontal turbulence in the ocean interior can meet the requirements of global energy and mass vertical transport, and compensate for turbulent fluxes in the upper homogeneous layer of the ocean.

Lithosphere–ionosphere coupling mechanism and its application to the earthquake in Iran on June 20, 1990. A review of ionospheric measurements and basic assumptions

Analysis of the reliable ionospheric data that have been obtained by different research groups near a seismically active region in western Iran has enabled us to infer that: (1) Disturbances in the lower ionosphere ( h∼90 km, radio wave phase anomalies), F region ( h∼270 km, airglow anomaly), and upper ionosphere ( h∼2400 km, VLF noise anomalies measured by the satellite) were recorded at distances of 250 km, 1000 km, and 2000 km, respectively, from the epicentral zone. These might be considered as precursors (h/days before the event) and/or as after-effects of seismical activity. (2) Disturbances in the lower ionosphere correspond to density enhancement in this part of the ionosphere. (3) Decreasing the 630-nm emission intensity in the F region may be interpreted as a formation of the region with plasma depletion. (4) Anomalous impulse VLF-emissions in the upper ionosphere, apparently, may be related with whistler trapping into the ducts, formed in the ionosphere above the seismically active region. (5) LH-noise frequency rising corresponds to increasing the plasma density in the upper ionosphere. To interpret these anomalies, we exploit a new lithosphere–ionosphere coupling mechanism related to internal gravity wave generation in seismically active regions. Under favourable conditions, these waves can reach the ionosphere. The quantitative analysis of ionospheric disturbances caused by internal gravity wave interaction with ionospheric plasma will be published elsewhere.

A dynamic model for laminated plates with delaminations

A generalized theory for laminated plates, including delamination, is developed. The laminate model is based on a generalized displacement formulation implemented at the layer level. The equations of motion for a layer, which are explicitly coupled with both the interfacial traction continuity and the interfacial displacement jump conditions between layers, are used to develop the governing equations for a laminated composite plate. The delamination behavior can be modeled using any general constitutive fracture law. The interfacial displacement jumps are expressed in an internally consistent fashion in terms of the fundamental unknown interfacial tractions. The current theory imposes no restrictions on the size, location, distribution, or direction of growth of the delaminations. Therefore, the theory can predict the initiation and growth of delaminations at any location as well as interactive effects between delaminations at different locations within the laminate.The proposed theory is used to consider the dynamic response of laminated plates in cylindrical bending. First it is shown that the dynamic implementation agrees well with the exact predictions of a plate under static loading conditions. Static, cylindrical bending is considered to validate the numerical implementation. Next, different dynamic loading cases are considered. First, the required level of discretization through the thickness of the laminate necessary to accurately capture the wave propagation characteristics for monotonic tensile loading transverse to the plate is determined. Next, the influence of the delamination on the free vibration behavior of a plate is considered. It is shown that the presence of delaminations can result in significant deviations from the perfectly bonded free vibration behavior. Finally, the plate is subjected to dynamic loading conditions that demonstrate the influence of internal wave interactions on the overall behavior of the plate.

On the Interactions of Internal Waves Reflecting from Slopes

Abstract Incident internal waves and those reflected from a uniform slope interact at second order. These interactions are considered for incident waves traveling obliquely to the slope in a uniformly stratified rotating fluid. It is found that (i) resonant interactions cannot occur unless the inclination of the slope to the horizontal, α, is less than the inclination of the wave group velocity vector to the horizontal, β; (ii) interactions generate a nonzero Eulerian upslope flow, which is exactly balanced by a Stokes drift, so leading to zero Lagrangian upslope flow; (iii) a Stokes drift parallel to the isobaths is generated by the reflecting waves, provided the incident waves are not in a plane normal to the slope. This drift is in addition to the possible Eulerian flows along the slope, which are in geostrophic balance with a correspondingly perturbed density field and are zero in a nonrotating flow. The order of magnitude of the drift is typically 0.01 m s−1. These secondary flows do not depend on di...

Near‐inertial internal wave interactions with mesoscale fronts: Observations and models

Moored observations of near‐inertial currents and buoyancy fluctuations from the Frontal Air Sea Interaction Experiment (FASINEX) may be understood as nearinertial internal waves reflecting off sheared background currents. The FASINEX moored array measured upper ocean currents, temperature, and conductivity between January and June 1986 in a region of the Sargasso Sea heavily populated by strong upper ocean fronts. The background jets associated with these features have typical cross‐front scales of 20km, maximum currents of 0.5 m s−1, and relative vorticities of ±0.3ƒ. In the vicinity of fronts, observed near‐inertial currents have short horizontal scales, show no clear horizontal phase structure, and trace out elongated current ellipses with elevated across‐front over along‐front variance. During these periods, inertial band‐pass buoyancy fluctuations often correlate with major‐axis currents. WKB ray‐tracing models of propagating, monochromatic plane waves exhibit horizontal phase propagation and correlations between minor‐axis currents and buoyancy and thus cannot explain these results. Models of near‐inertial internal waves reflected or trapped by a barotropic frontal jet produce mode‐like structures with short horizontal scales, little horizontal phase propagation, and anisotropic current ellipses aligned primarily cross front. Model buoyancy may correlate with one or both current ellipse components, depending on the incidence angle of the wave and the degree to which it reflects. Completely reflected waves with horizontal scales similar to those of the front and near‐normal incidence angle produce current ellipses and correlation patterns consistent with the observations.

Propagation and interaction of non-linear surface and internal waves in a two-layer fluid

This paper focuses on the study of linear and non-linear surface and internal waves, in a complete setting, using a two-layer model of a stratified fluid. The respective Korteweg-de Vries evolutionary equations have been obtained, analysed, and compared with the ‘rigid lid’ model data. Boussinesq-type equations have been derived for the interacting modes pertaining to one type and to different types. It is shown that in addition to the known mechanisms of interaction between internal and surface waves, interaction between long non-linear baroclinic modes and barotropic modes, propagating in the same direction, is likely in such a system.

Acoustic wave–internal wave interaction experiment in the Yellow Sea

Simultaneous observations of internal wave activity and acoustic wave propagation in 70 m water in the Yellow Sea were made in the late summer of 1996. The objective of the experiment was to validate the predicated modal coupling and resulting fluctuations and alterations in propagation loss induced by shallow-water internal waves. Propagation over distances up to 50 km (using narrow- and broadband sources over the frequency range of 50 Hz to 6 kHz) was measured with moored and suspended arrays which spanned the water column. Internal wave activity was monitored using several thermistor chains. Details of the experiment and preliminary data will be presented. [Work supported by ONR and the Chinese Academy of Sciences.]

Interaction of Internal Waves with a Topographic Sill in a Two-Layered Fluid

Abstract Sills and seamounts may alter or even disrupt internal waves that approach them. The authors study by one-dimensional laboratory experiment: (i) the fission of an internal solitary wave of a two-layered fluid by a triangular obstruction, (ii) the form preservation of the transmitted wave, and (iii) the energy dissipated by the vortex induced by the obstruction. The potential energy stored in the wave signal is taken as a measure to quantify the above notions. Results are presented for upper to lower depth ratio rH = 3 and rH = ⅓. The results show in general a pronounced dependence on the degree of blocking (B ≡ depth of obstruction/lower layer depth), but experiments are less conclusive for dependence on particle speeds and slope angles of the triangle. The authors determine for a given degree of blocking how much energy of an approaching wave is fed into the reflected and transmitted wave. For B ≤ 0.6 the obstruction is virtually ineffective; for B ≥ 0.8 a compact solitary wave hump transforms i...

Modal sensitivity of acoustic interactions with internal waves in shallow water

Analyses of individual acoustic mode interactions with internal waves should permit both qualitative and quantitative understanding of the influences of internal waves on multimode signals in shallow water. In this report, some experimental results taken in the Yellow Sea during the summer with strong thermoclines, will be reported. Numerical simulations will be used to analyze the potential internal wave interactions suggested by these data. (a) A multimode signal obtained at a single hydrophone and the first acoustic mode obtained by a mode filter array, both from a fixed 442-Hz cw source, exhibit very different fluctuation characteristics. (b) The transmission loss (TL) measured with explosive sources indicates a strong source/receiver depth dependence. (c) TL is, generally, anisotropic and can be abnormally large over some frequency range. It has been shown that the acoustic mode-coupling induced by internal waves can be an important loss mechanism for sound propagation during the summer [Zhou etal., J. Acoust. Soc. Am. 90, 2042–2054 (1991)]. The observed fluctuations can be explained in terms of the propagation characteristics of individual modes to the presence of internal waves. In so far as the mode-coupling and both the intensity and arrival time fluctuations are concerned, certain acoustic modes are more sensitive to internal waves than others. The characteristics of acoustic-internal wave interaction strongly depend on signal frequency, thermocline profile, seabottom properties, source/receiver depths and distance. [Work supported by ONR.]

Propagation and interaction of non-linear surface and internal waves in a two-layer fluid

This paper focuses on the study of linear and non-linear surface and internal waves, in a complete setting, using a two-layer model of a stratified fluid. The respective Korteweg-de Vries evolutionary equations have been obtained, analysed, and compared with the ‘rigid lid’ model data. Boussinesq-type equations have been derived for the interacting modes pertaining to one type and to different types. It is shown that in addition to the known mechanisms of interaction between internal and surface waves, interaction between long non-linear baroclinic modes and barotropic modes, propagating in the same direction, is likely in such a system.

A mechanism of atmospheric ozone disturbance by internal gravity wave in a stratified shear flow

In a number of experiments on ozone layer investigations, short-term ozone variations with periods of an hour or several hours at heights of 20–50 km were observed. We suppose that this phenomenon may originate due to the interaction of internal gravity waves with stratified shear flows in the vicinity of a critical layer, where the phase velocity of the wave is equal to the flow velocity. The amplitude and period of the ozone density oscillations are found in a gravity wave of constant amplitude, when the flow pattern near the critical layer is determined by nonlinearity, and viscosity effects are small. We have found that the density variation of the passive admixture of air can be comparable with the unperturbed density.

Intermodal interaction of internal solitary waves

Intermodal interaction of internal solitary waves

Intermodal interaction of internal solitary waves

Interaction of internal solitary waves of different modes in an incompressible fluid with an exponential stratification in density is considered. Two such waves are considered. These waves may be going in the same direction or in opposite directions. The analysis shows that the interaction produces two pairs of waves, whose mode indices are the difference and the sum of those of the original waves, respectively. Each pair consists of a right-going wave and a left-going one, and a part that vanishes eventually everywhere. Higher-order terms affecting interaction are briefly discussed. The interaction of more than two waves can be dealt with pair by pair.