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David M. Farmer

Abstract

This paper describes observations of large-amplitude, long internal waves in Babine Lake. A unique feature of the observations is that they were taken simultaneously at several different points along the major axis. This permits study of the formation and subsequent development of individual waves as they travel along the lake. The waves typically begin as depressions on the thermocline at the south end following strong westerly winds directed along the lake's major axis. A bend in the southern part of the lake, together with the influence of surrounding mountains, can introduce a divergence in the longitudinal component of the wind stress which in turn produces a thermocline elevation. These two effects then combine to form a northward traveling surge. Subsequent modification of the waveform is interpreted in terms of nonlinear steepening and dispersion.

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David Farmer and Ming Li

Abstract

A commonly observed property of near-surface bubble distributions is their collective organization into long rows aligned with the wind under the influence of Langmuir circulation. Time series observations with sonars having fixed orientation reveal the temporal evolution of bubble distributions as they drift through the sonar measurement path, Here this concept is extended to provide a time sequence, at 37-s intervals, of two-dimensional images generated by horizontally rotating sonars. Observations obtained during a storm in the Strait of Georgia show individual Langmuir convergence zones as they evolve above the freely drifting sonar. The resulting images are processed to generate a binary representation of the convergence zone patterns from which their orientation, length, spacing, and other properties can be extracted. Although there is some angular spreading, most convergence lines are aligned within 20° of the wind. The spacing between convergence lines reveals a wide range of scales, but the mean spacing increases slightly with wind speed. Measurement of downwind length reveals the presence of numerous short bubble clouds, possibly associated directly with wave breaking; however, there is a general trend toward a length that increases with wind speed.

A dominant characteristic at higher wind speeds is the formation of Y junctions in which three linear bubble clouds are joined together. Each branch of a Y junction was observed to be approximately 50 m. The junctions preferentially point downwind with the angle between the two side branches being approximately 30°. Although the junctions deform with time, they can be readily tracked through successive images The existence of convergence zone junctions suggests the reconnection of counterrotating longitudinal vortices and the formation of U-shaped vortex tubes.

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Burkard Baschek and David M. Farmer

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Air bubbles can be used as oceanographic tracers that indicate the strength of a downwelling current by which they are subducted. In a tidal front in the Fraser Estuary, British Columbia, Canada, vertical currents of up to 0.70 m s−1 subduct bubbles to depths of more than 160 m. Echo sounder measurements are compared with simultaneous ADCP current measurements and are interpreted with a bubble model by S. A. Thorpe, yielding an estimate of the vertical current that carries the bubbles to the depth of measurement.

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Dimitris Menemenlis and David M. Farmer

Abstract

An acoustical instrument has been developed to measure path-averaged horizontal current and vorticity in the subice boundary layer of the eastern Arctic during the spring of 1989. A triangular acoustic array of side 200 m was used to obtain reciprocal transmission measurements at 132 kHz, at 8, 10, and 20 m beneath an ice floe. Pseudorandom coding and real-time signal processing provided precise acoustic travel time and amplitude for each reciprocal path.

Mean current along each acoustic path is proportional to travel-time difference between reciprocal transmissions. Horizontal velocity normal to the acoustic paths is measured using scintillation drift. The instrument measures horizontal circulation and average vorticity relative to the ice, at length scales characteristic of high-frequency internal waves in the region. The rms noise level of the measurements is less than 0.1 mm s−1 for velocity measurements and 0.01 f for vorticity, averaged over 1 min. Except near the mechanical resonance frequency of the moorings, the measurement accuracy is limited by multipath interference.

Path-averaged horizontal velocity is compared to point measurements, and marked differences are observed due to local anomalies of the flow field. The integral measurement of current is particularly sensitive to the passage of internal waves that have wavelengths longer than the horizontal separation of the transducers. A comparison of horizontal velocity at two depths in the boundary layer shows good coherence at internal-wave frequencies, and some attenuation as the ice is approached. Relative vorticity at internal-wave length scales is dominated by horizontal shear caused by flow interaction with ice topography, and not by planetary vorticity.

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Svein Vagle and David M. Farmer

Abstract

A multifrequency acoustical-backscatter technique is described for determining the size distribution of bubbles with radii between 8 and 130 µm. The method makes use of the resonance in the microbubbles and operates at six frequencies ranging from 28 to 400 kHz. It has the advantage that vertical profiles of the bubble-size distribution can be obtained for extended periods without need for in situ instrumentation. Algorithms have been developed for real-time calculation, including correction for wave orbital displacement, bubble attenuation of the transmitted pulse, and other effects.

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Li Ding and David M. Farmer

Abstract

An acoustical system is described with emphasis on its signal-processing scheme. The system consists of a small broadband hydrophone array of span 8.5 m and 5-kHz bandwidth, which is able to track individual breaking surface waves by passive detection of the naturally generated sound of wave breaking. The generalized cross-correlation technique is used to determine time differences of acoustical signals from breaking waves arriving at the array. Breaking events are identified in correlation time sequences, and the identification is aided by image enhancement and pattern recognition. Determination of source positions from the estimated time delays is also discussed. The instrument was first employed during the Surface Wave Program (SWAPP), and preliminary results clearly demonstrate the ability to track individual breaking events. This system can be used to measure some spatial and temporal characteristics of breaking waves, such as frequency of breaking, lifetime, velocity, and spatial distributions.

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Li Ding and David M. Farmer

Abstract

Breaking surface waves were observed during the Surface Wave Process Program with a novel acoustical instrument that makes use of underwater ambient sound to track individual breaking events. The spatial and temporal statistics of braking waves such as duration, velocity, spacing and breaking probability were determined under various wind and wave conditions. Statistical models are developed to assess and when appropriate, correct for any bias resulting from limitations of the measurement approach. Empirical relations of these statistics with wind speed are obtained. Comparison of the observed distributions with simultaneously measured directional wave spectra suggests that wave breaking occurs at multiple scales and that the mean scale of breaking is substantially smaller than the associated with the dominant wind wave component. Preliminary analysis indicates that the dependence of breaking probability on the fourth moment of the wave spectrum is consistent with a linear statistical model.

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David M. Farmer and Eddy Carmack

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The cooling of a freshwater take provides an opportunity for studying wind mixing and restratification under the peculiar conditions associated with a density maximum. The concepts are explored using a mixing-layer model that incorporates both nonlinearity and pressure dependence in the equation of state; the results provide a basis for interpreting temperature structure in Babine Lake and for making some more general observations on mixing and restratification. Following destruction of summer stratification by wind mixing and convection in autumn, the lake is essentially isothermal as it cools through 4°C. Near this temperature, the coefficient of expansion becomes so small that pressure effects, which play little part in the dynamics at higher temperatures, can dominate the stability. In effect, the depth at which the local temperature equals the temperature of maximum density at constant pressure marks the transition between forced and free convection. Above this transition depth, the wind must work against buoyancy forces during cooling, below it the water is gravitationally unstable. The existence of a transition depth allows conditional instabilities to occur in which a downward movement of initially stable water can lead to gravitational instability.

As the lake cools the stability becomes less sensitive to pressure and a given heat flux produces a progressively greater buoyancy flux leading to the process of restratification. The essential physics are contained in the specification of a Monin-Obukhov mixing length, for a cooling lake near the temperature of maximum density this length can assume complex values, both real and imaginary components having distinct physical interpretations. The theory predicts that if the boat flux and the work done by the wind remain relatively constant the mixing layer properties will change exponentially with time, a prediction that is supported by the observations. Since the temperature profile that evolves beneath a retreating mixed layer retains information on the conditions that led to its formation, the theory also provides a consistent basis for interpreting winter profiles in terms of the relative strength of wind mixing and buoyancy flux during the cooling period. It is shown that, in general, lakes subjected to relatively more intense wind mixing during winter restratification will have lower interior temperatures. The observations lead to a calculation of the fraction of energy that is used to redistribute buoyancy. Estimates based on 33 days of data yield a value of 0.26r0 u * 3, with standard deviation 0.04, where u * is the friction velocity of the water. Measurable temperature gradients exist within the mixing layer and these gradients increase as the mixing layer retreats,

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Qiang Li and David M. Farmer

Abstract

Time series observations of nonlinear internal waves in the deep basin of the South China Sea are used to evaluate mechanisms for their generation and evolution. Internal tides are generated by tidal currents over ridges in Luzon Strait and steepen as they travel west, subsequently generating high-frequency nonlinear waves. Although nonlinear internal waves appear repeatedly on the western slopes of the South China Sea, their appearance in the deep basin is intermittent and more closely related to the amplitude of the semidiurnal than the predominant diurnal tidal current in Luzon Strait. As the internal tide propagates westward, it evolves under the influence of nonlinearity, rotation, and nonhydrostatic dispersion. The interaction between nonlinearity and rotation transforms the internal tide into a parabolic or corner shape. A fully nonlinear two-layer internal wave model explains the observed characteristics of internal tide evolution in the deep basin for different representative forcing conditions and allows assessment of differences between the fully and weakly nonlinear descriptions. Matching this model to a wave generation solution for representative topography in Luzon Strait leads to predictions in the deep basin consistent with observations. Separation of the eastern and western ridges is close to the internal semidiurnal tidal wavelength, contributing to intensification of the westward propagating semidiurnal component. Doppler effects of internal tide generation, when combined with a steady background flow, suggest an explanation for the apparent suppression of nonlinear wave generation during periods of westward intrusion of the Kuroshio.

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Kevin G. Lamb and David Farmer

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Observations of internal solitary-like waves (ISWs) on the Oregon Shelf suggest the presence of Kelvin–Helmholtz billows in the pycnocline and larger-scale overturns at the back of the wave above the pycnocline. Numerical simulations designed to explore the mechanisms responsible for these features in one particular wave reveal that shear instabilities occur when (i) the minimum Richardson number Ri in the pycnocline is less than about 0.1; (ii) Lx/λ > 0.8, where Lx is the length of the unstable region with Ri < 0.25 and λ is a half wavelength of the wave; and (iii) a linear spatial stability analysis predicts that ln(af/ai) >≈ 4, where ai and af are the amplitudes of perturbations entering and leaving the unstable region. The maximum energy loss rate in our simulations is 50 W m−1, occurring at a frequency 8% below that with the maximum spatial growth rate.

The observations revealed the presence of anomalously light fluid in the center of the wave above the pycnocline. Simulations of a wave encountering a patch of light surface water were used to model this effect. In the presence of a background current with near-surface shear, the simulated ISW has a trapped surface core. As this wave encounters a patch of lighter surface water, the light surface water at first passes beneath the core. Convective instabilities set in and the light fluid is entrained into the core. This results in the formation of overturning features, which exhibit some similarities with the observed overturns.

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