Fractal Analysis of Deep Ocean Current Speed Time Series

Abstract

Fractal properties of deep ocean current speed time series, measured at a single-point mooring on the Madeira Abyssal Plain at 1000-and 3000-m depth, are explored over the range between one week and 5 years, by using the detrended fluctuation analysis and multifractal detrended fluctuation analysis methodologies. The detrended fluctuation analysis reveals the existence of two subranges with different scaling behaviors. Long-range temporal correlations following a power law are found in the time-scale range between approximately 50 days and 5 years, while a Brownian motion-type behavior is observed for shorter time scales. The multifractal analysis approach underlines a multifractal structure whose intensity decreases with depth. The analysis of the shuffled and surrogate versions of the original time series shows that multifractality is mainly due to long-range correlations, although there is a weak nonlinear contribution at 1000-m depth, which is confirmed by the detrended fluctuation analysis of volatility time series.

A Multifractal Cascade Model for Energy Evolution and Dissipation in Ocean Turbulence

“…Many researchers use multifractal phenomenological models to characterize the energy transfer of eddies at different scales. Nowadays, the effectiveness of multifractal theory in turbulence has been validated [23][24][25]. The multifractal spectrum is a method based on the multifractal theory to describe the fractal structure in a system.…”

“…The generalized Hurst exponent H (q) was utilized to describe the scaling behavior of the moment of order q. Because H (q) was related to the scaling exponent (τ(q) = qH (q) − 1) [25], the generalized Hurst exponent H (q) could be derived with Equation ( 6):…”