Internal Wave Modes Research Articles

Observation and interpretation of a high-frequency internal wave packet and surface slick pattern

A packet of high-frequency (period ∼8 min) internal gravity waves was observed on a precision-depth recorder (PDR) chart while an anchor station was being conducted during the Cue 1 experiment off Oregon. The anchor station was located over the continental shelf and in the frontal zone associated with coastal upwelling. The packet appeared as a set of three oscillations (maximum peak-to-peak amplitude of 11 m) of a scattering layer located at a depth of about 20 m, which was immediately below the center of the permanent pycnocline (25.5–26.0 sigma t) at that time and location (water depth 80 m, 10-km offshore). The scattering layer occurred at the depth of a chlorophyll A maximum; strong temperature, salinity, and sound speed gradients; and strong vertical shear of the horizontal velocity. Simultaneously, a series of surface slicks, oriented parallel to the isobaths and propagating onshore, was observed under conditions of light winds. From the spacing of the slicks a horizontal scale of 100 m was estimated; this scale corresponded most nearly to the wavelength of the first internal wave mode for the observed wave period. From time series of nearby moored current and temperature sensors, bursts of high-frequency oscillations were noted to occur on semidiurnal tidal cycles. Such bursts had occurred a few hours before the internal wave packet was observed on the PDR. It is concluded that the semidiurnal baroclinic tide breaks down in the frontal zone off Oregon, forming large-amplitude high-frequency internal gravity waves. These waves can induce detectable surface slicks under light wind conditions and major perturbations of a shallow scattering layer when it is present.

A description of short period temperature fluctuations in the upper ocean

Dynamical properties of short-period temperature fluctuations are studied. Water temperature was measured continuously at several depths at the following stations: at 38°29.5′N, 141°35.8′E (100 m depth) on the continental shelf off Miyagi Prefecture in the summer of 1967, at 35°01.8′N, 139°0.8.5′E (100 m depth) in Sagami Bay in the summer of 1968, and at 32°32.2′N, 129°53.7′E (74 m depth) in Tachibana Bay in the summer of 1970. These measurements were made with a thermistor array laid down from the R. V.Tanseimaru (Ocean Research Institute, University of Tokyo) which was fixed with bow and stern anchors. Significant temperature fluctuations found at the first and the third stations are thought to be due to first mode internal waves having amplitude 3 to 5 m and period 5 to 20 minutes. The wave length of the waves is estimated to be 25 m to 400 m from the observed density structure. At the second station, we found second-mode internal waves. The period, amplitude and wave length of the waves are about 30 minutes, 1.3 m and 600 m, respectively. In all cases, the spectral density of the temperature fluctuations decreases with increase in frequency. However, the decrease obey neither the −3 power law nor the −5/3 power law. Coherences in the temperature fluctuations between two depths of measurement in the seasonal thermocline are significantly high in the range of frequencies lower than the local Brunt-Vaisala frequency, but are low in the higher frequency range. At the first and the third stations, the difference in the level of coherences between the lower frequencies and the higher frequencies are large. Phase differences between two depths in the thermocline are small in the lower frequency range. This suggests that the first-mode internal waves are predominant over higher-mode internal waves and over other disturbances.

Effects of shear on the properties of internal gravity wave modes

Effects of shear on the properties of internal gravity wave modes

M2 tidal currents in the western North Atlantic

A number of current meter records collected by the Woods Hole Oceanographic Institution have been examined to determine the structure of M 2 tides in the western North Atlantic. Though the signal to noise ratio is low, a simple picture emerges when sufficiently many records are averaged. At a site north of the Gulf Stream, the tidal current is baroclinic, and concentrated near the surface. The result is consistent with generation of internal tides along the continental slope just to the north. At positions south of the Gulf Stream, the records are too few to conclude more than that the tidal velocities are consistent with high mode internal waves.

Occurrence and features of ducted modes of internal gravity waves over western Europe and their influence on microwave propagation

Several years of intense investigation of internal gravity waves propagating in low-level ducts in the atmosphere over a rather flat region not influenced by land-sea circulation or mountains are reported. This study gives a rather complete picture of the occurrence, features, and of some of the excitation conditions of these waves. Simultaneous direct measurements made on a meteorological tower, 250 m high, using temperature, vector wind, and sonic anemometer sensors at different altitudes are reported along with indirect measurements using an array of microbarographs with separations over a range of more than 100 km. The study also included microwave propagation links crossing over the meteorological site. Individual wave crests some tens of kilometers long could be followed over a path of more than 100 km. Because of the variability and non-stationary conditions of the lower atmosphere, a direct correlation between a propagating internal wave group and the fading pattern of EM propagation could be found in only a few cases.

Trapped gravity waves and the five-minute oscillations of the solar atmosphere

The various modes of hydrodynamic waves are considered for a model of the solar atmosphere which is based on the Bilderberg model and includes the effects of ionization. The atmosphere forms a ‘potential well’ for internal gravity waves, since the stability is low at the base (near the convection) and low again in the region of partial ionization in the chromosphere. Calculations show that there are two resonant (trapped) modes of internal gravity waves for horizontal wavelengths based on the scale of the granulation. The properties of these modes are in close agreement with the two modes of oscillation observed by Frazier (1968). Trapped acoustic modes are found to have periods too short to account for the observations.

The decay of internal wave modes in a multi-layered system

The frictional decay of internal wave modes is considered in a system consisting of super-posed layers of immiscible fluid. A scheme is given for the determination of the attenuation with time in the case of an arbitrary number of such layers. This is evaluated explicitly for three layers and then investigated numerically. The results are interpreted in the context of internal waves on a double thermocline structure. It is shown that internal waves may be heavily damped in comparison with the surface mode.

A note on the interaction between internal gravity waves and currents

Experiments are described on the propagation of lowest mode internal waves and their amplification by a local adverse current, generated by a moving contraction in a labortory tank. In the absence of any current, the wavelength, frequency relation was found to agree well with the theoretical form. In an adverse current, the wavelength reduces and the amplitude increases, but rather less rapidly than is predicted. The difference is apparently the result of the observed partial breakdown of the waves to less regular (turbulent) motion. When the adverse current speed exceeds approximately one quarter of the initial phase speed of the waves, a kinematic limit is attained and it was observed that the waves no longer propagated.

The stability of oscillatory internal waves

The stability of a periodic internal wave has been investigated experimentally and theoretically. From the analysis it is found that if a primary wave, with wave-number k0 and frequency ω0, is perturbed by two infinitesimal wave-like disturbances with wave-numbers k1 and k1 + k0 and frequencies ω1 and ω1 + ω0, exponential growth of these disturbances will take place under certain conditions. The analysis also indicates which resonantly interacting disturbances can induce an instability and, when viscous dissipation is accounted for, predicts the minimum amplitude for which a wave is unstable. Experimental results demonstrate that this type of instability can cause the breakdown of a first mode internal wave propagating in a fluid composed of two layers of uniform density separated by a thin region in which the density varies continuously.

Theoretical and experimental studies of gravity wave interactions

This paper is concerned with various aspects of the resonant interactions among waves. An experiment was suggested by Longuet-Higgins (1962) to detect this type of interaction among surface waves. This was subsequently performed by Longuet-Higgins & Smith (1966) and by McGoldrick, Phillips, Huang & Hodgson (1966). The results of the two sets of experiments are compared. Together they demonstrate very clearly the principal characteristics of the interaction; the maximum response at resonance and the linear growth with interaction distance, the decrease in band width with interaction distance and the shift of the resonance point that results from the amplitude dispersion. It is shown further that the instability of the Stokes wave, discovered and analysed by Benjamin & Feir, can be described in terms of these interactions and that it is not restricted to purely two dimensional motion. A Stokes wave is unstable to a disturbance containing a pair of wavenumbers defined by any point in the zone just inside the figure-of-eight loop shown in figure 12. Another example of resonant wave interactions is provided by short, internal gravity waves in a stratified fluid with constant Brunt-Väisälä frequency. The interactions among Fourier modes are considered, and it is shown that there arise both free and forced modes. In the latter, the dispersion relation for internal waves is not satisfied; there is no particular relation between wavenumber and frequency. The amplitudes of these are small compared with those of the internal wave modes provided the harmonic mean of the vorticity in the two interacting waves is small compared with the Brunt-Väisälä frequency. The motion then consists of interacting internal gravity waves, whose interaction sets are closed. On the other hand, if the forced components are comparable in magnitude with the wave modes, these interact strongly and indiscriminately; a ‘cascade’, characteristic of turbulence, develops.

Effect of density variation on fluid flow

The effect of density variation on the flow of an incompressible and inviscid fluid is twofold. On the one hand, the inertia of the fluid changes in direct proportion to the density. On the other hand, the body force acting on a fluid element also changes in direct proportion to the density. Since body force is not the only force acting on the fluid, the inertia effect and the gravity effect of density variation do not cancel each other, and many interesting phenomena occur in the flow of a heterogeneous fluid that do not occur in the flow of a homogeneous fluid. In this paper it is shown that the inertia effect can be simply evaluated for steady flows. If the velocity in the steady flow of a heterogeneous fluid in the absence of gravity is multiplied by the square root of the density, the result represents a dynamically possible flow of a homogeneous fluid. At the other extreme, when the gravitational effect dominates the flow, it has been shown both analytically and experimentally that the motion of a fluid is confined to the layer at which it originates. As usual, it is when the inertia effect and the gravity effect are comparable that the solutions of stratified flows become difficult, even if the flow is assumed to be steady and the fluid inviscid. From one series of such solutions and the supporting experiments one sees that, on the one hand, infinitely many modes of stationary internal waves of finite amplitude are dynamically possible (apart from the consideration of generation), and, on the other hand, physically significant solutions of stratified flows may involve velocity discontinuities.