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Roman Stocker and Jörg Imberger

Abstract

The response of a stratified rotating basin to the release of a linearly tilted interface is derived. This case is compared with a uniformly forced basin in the two limits when the duration of the forcing is much greater than the period of the dominant internal waves and when it is much smaller. Energy partitioning is studied as a function of the Burger number S (relative importance of stratification versus rotation), showing the dominance of a geostrophic component over the wave field for low S. Trajectories are integrated numerically, revealing the Stokes drift of the waves to be always cyclonic. Transport properties are classified in terms of S and the Wedderburn number W (relative importance of the disturbance versus stratification). The geostrophic flow is the main source of advection, but only the waves allow particles to break the barrier to transport between the two geostrophic gyres, ultimately leading to stretching and folding. For low values of W, advection can become chaotic. Conservation of potential vorticity explains the difference in transport properties between the forced cases and the initial tilt release. A transition time between spreading dominated by turbulence and that dominated by large-scale motions is derived as a function of the initial size of a cloud. The results show that spreading is mainly due to turbulence for weak forcing, small time, and small clouds; for stronger forcing, larger time, or larger clouds the effect of large-scale motions can be dominant.

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Jörg Imberger and Boualem Boashash

Abstract

The Wigner–Ville distribution, a new tool in the time–frequency analysis of signals, is applied to temperature gradient microstructure records. In particular, the Wigner–Ville distribution is used to compute the local instantaneous and maximum frequencies of the signal as a function of depth, and these frequencies are then related to the dissipation of turbulent kinetic energy. The method is applied to two temperature gradient microstructure records from the Wellington Reservoir. It is shown that a high resolution estimate of the dissipation is obtained that provides insight into the patchiness, the wavenumber content, and the Reynolds–Froude number variability of the integral scales of motion in a strongly stratified water column.

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David A. Luketina and Jörg Imberger

Abstract

An algorithm is presented for obtaining the rate of turbulent kinetic energy dissipation by fitting the theoretical Batchelor spectrum to the temperature gradient spectrum at high wavenumbers. The algorithm is relatively robust in selecting the turbulent Batchelor component from temperature gradient spectra, which have finestructure, internal wave, and noise contributions. The theoretical curve is fitted using an error function that takes into account many of the characteristics of the Batchelor spectrum. Overall, the use of the algorithm to determine dissipation of the turbulent kinetic energy is considerably more time efficient than manual methods. Some limits on the accuracy of the method are also discussed.

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Robert Hays Spigel and Jörg Imberger

Abstract

An analysis of the time scales of processes relevant to wind mixing in lakes indicates that the response of a lake to wind may be classified into four regimes with respect to thermocline deepening behavior, depending on the relative sizes of the parameters describing wind strength, basin size and stratification. The dependence is described in terms of a mixed layer Richardson number and the aspect ratio of the mixed layer thickness to length. The classification is used to explain the diversity of phenomena reported in the literature for wind events in a number of different lakes and laboratory tanks which are either short enough or narrow enough for rotational effects to be unimportant. The classification is derived with reference to a two-layer, rectangular basin in the absence of Coriolis forces and surface heating. The classification is exended in a simple way to more realistic stratifications and basin shapes to predict the overall mixing features of a wind event. Response to wind varies from one in which entrainment proceeds very slowly and has negligible effect on baroclinic motions to one in which any stratification is rapidly destroyed by wind before baroclinic motions can occur. Between these two extremes entrainment and mean motions interact through the production of turbulent kinetic energy by velocity shear at the base of the mixed layer. The nature of this interaction is investigated, and scales for velocity shear, stable interface thickness, and times for internal seiching, internal wave decay and vertical and longitudinal mixing are developed. A computer algorithm parameterizing the effects of shear production on mixed layer deepening is described, based on the analysis presented. By incorporating this algorithm in a more comprehensive reservoir simulation model, DYRESM, effects of surface heating, realistic stratification, and complicated basin shape may be accounted for. Interaction between these effects and the wind deepening mechanism is described explicitly by the program logic. Results of a successful simulation by DYRESM for a season in the Wellington Reservoir, Western Australia, are discussed.

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Farhad M. Fozdar, Geoffrey J. Parkar, and Jörg Imberger

Abstract

A method to match the response of the SBE-3 temperature sensor and the SBE-4 conductivity cell is described. The technique uses a recursive filter in the time domain, which allows direct calculation of salinity and density, and thus offers a significant computational advantage over other methods. The response of any sensor may be matched or sharpened using this method provided that the sensor can be modeled appropriately.

Using this method the useful bandwidth of the SBE-3 temperature sensor may be improved by a factor of between 3 and 7, depending on the permissible signal-to-noise ratio degradation. It is also possible to match the SBE-3 and SBE-4 responses closely and thus remove spikes in the profiles of calculated salinity and density.

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