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On the Connection between Intermittency and Dissipation in Ocean Turbulence: A Multifractal Approach

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  • 1 a Institut de Ciències del Mar, ICM-CSIC, Barcelona, Spain
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Abstract

The multifractal theory of turbulence is used to investigate the energy cascade in the northwestern Atlantic Ocean. The statistics of singularity exponents of horizontal velocity gradients computed from in situ measurements at 2-km resolution are used to characterize the anomalous scaling of the velocity structure functions at depths between 50 and 500 m. Here, we show that the degree of anomalous scaling can be quantified using singularity exponents. Observations reveal, on one side, that the anomalous scaling has a linear dependence on the exponent characterizing the strongest velocity gradient and, on the other side, that the slope of this linear dependence decreases with depth. Since the observed distribution of exponents is asymmetric about the mode at all depths, we use an infinitely divisible asymmetric model of the energy cascade, the log–Poisson model, to derive the functional dependence of the anomalous scaling with the exponent of the strongest velocity gradient, as well as the dependence with dissipation. Using this model we can interpret the vertical change of the linear slope between the anomalous scaling and the exponents of the strongest velocity gradients as a change in the energy cascade. This interpretation assumes the validity of the multifractal theory of turbulence, which has been assessed in previous studies.

© 2021 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: Jordi Isern-Fontanet, jisern@icm.csic.es

Abstract

The multifractal theory of turbulence is used to investigate the energy cascade in the northwestern Atlantic Ocean. The statistics of singularity exponents of horizontal velocity gradients computed from in situ measurements at 2-km resolution are used to characterize the anomalous scaling of the velocity structure functions at depths between 50 and 500 m. Here, we show that the degree of anomalous scaling can be quantified using singularity exponents. Observations reveal, on one side, that the anomalous scaling has a linear dependence on the exponent characterizing the strongest velocity gradient and, on the other side, that the slope of this linear dependence decreases with depth. Since the observed distribution of exponents is asymmetric about the mode at all depths, we use an infinitely divisible asymmetric model of the energy cascade, the log–Poisson model, to derive the functional dependence of the anomalous scaling with the exponent of the strongest velocity gradient, as well as the dependence with dissipation. Using this model we can interpret the vertical change of the linear slope between the anomalous scaling and the exponents of the strongest velocity gradients as a change in the energy cascade. This interpretation assumes the validity of the multifractal theory of turbulence, which has been assessed in previous studies.

© 2021 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: Jordi Isern-Fontanet, jisern@icm.csic.es
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