Subjects: Geosciences >> Marine Sciences submitted time 2023-05-31
Abstract： Quantifying eddy mixing in the ocean is a hot and tough problem in the area of physical oceanography. Based on the theory of effective diffusivity, the present study investigated the stirring effects of geostrophic turbulence that lead to stretching, distorting, deforming, and folding of tracer contours. These changes are then related to the efficiency of turbulent mixing. Results show that under the stirring effect of geostrophic turbulence, the length of tracer contour can be quickly elongated and fine-scale tracer filaments and fronts are also generated. This fractal elongation of tracer contour, about 10-20 times longer than the original length, is the dominant contributor to the mixing efficiency, whereas the gradient enhancement associated with filament and front generations only plays a secondary role. On the other hand, fine-scale features are smoothed out by small-scale diffusivity which eventually suppresses the increase of contour length and the generation of tracer filaments. This imposes an upper bound of the mixing efficiency when the stirring and smoothing effects are in a dynamical balance. Through a ‘box-counting’ method, the fractal dimension of tracer contour is also found between 1.4~1.6, indicating a geometric dimension lies somewhere between 1D and 2D. Due to the limitation of data resolution, contour length and thus mixing efficiency may be underestimated. Finally, the present study made an empirical relation between the fractal dimension and mixing efficiency, providing an opportunity for estimating mixing efficiency through a well-developed pattern recognition technique in remote sensing, and a new way of diagnosing ocean mixing and its parameterization.
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