Lagrangian statistics of mesoscale turbulence in a natural environment: The Agulhas return current

The properties of mesoscale geophysical turbulence in an oceanic environment have been investigated through the Lagrangian statistics of sea surface temperature measured by a drifting buoy within the Agulhas return current, where strong temperature mixing produces locally sharp temperature gradients. By disentangling the large-scale forcing which affects the small-scale statistics, we found that the statistical properties of intermittency are identical to those obtained from the multifractal prediction in the Lagrangian frame for the velocity trajectory. The results suggest a possible universality of turbulence scaling.

Figure 1

A snapshot of the SST taken on 12 March 2013. The black dots represent the 24 h averaged position of the buoy during the period 30 November 2010 through 09 March 2011. The buoy was deployed at $38.5^{\circ }\mathrm{S}, 30.0^{\circ }\mathrm{E}$ (first black dot).

Figure 2

Solid line: sea surface temperature measured in the period 30 November 2010 through 09 March 2011 with a sampling time $\mathrm{\Delta }t=600$ s. Dashed line: residual $r_n\left(t\right)$ obtained through the EMD decomposition related to the annual temperature cycle in the Agulhas current [23].

Figure 3

Second-order structure functions $S_2\left(\tau \right)$ (open circles) and $S_q^{\prime }\left(\tau \right)$ (solid circles), as a function of the scale $\tau$. The scalings ${\tau }^{3/2}$ (dashed line) and $\tau$ (dash-dotted line) are reported for reference.

Figure 4

Compensated power spectrum $R_j\left(\omega \right)={\mathrm{\Theta }}_j\left(\omega \right){\omega }^2$ as a function of the frequency $\omega$, for $j=2,3,\cdots ,7$. The horizontal dashed line, reported for reference, indicates the range where ${\widehat{\mathrm{\Theta }}}_j\left(\omega \right)\sim {\omega }^{-2}$.

Figure 5

The Hilbert spectra ${\mathcal{L}}_q\left(\omega \right)$ for $q=1,2,3$. The curves have been shifted for clarity. Dashed lines represent the least squares fit.

Figure 6

Comparison of the scaling exponent obtained for velocity and temperature data: ${\zeta }_L^{HS}$ multifractal scaling exponents for single particle velocity trajectories [44]. Exp. 1, Exp. 2, Exp. 3, Exp. 4: scaling exponent for multiple particle dispersion from [55], at different Reynolds number $\text{Re}=510,570,810,1000$, respectively. DNS 1 and DNS 2: scaling exponent from numerical simulation of multiple particle dispersion from [55], at $\text{Re}=75,140$, with 5000 and 10 000 particles, respectively. ${\xi }_{\mathrm{\Theta }}\left(q\right)$: scaling exponent for ARC-SST obtained through the HSA. ${\alpha }_{\mathrm{\Theta }}\left(q\right)$: scaling exponent evaluated from renormalized structure function for ARC-SST. Dashed line ($K41,q/2$): Lagrangian scaling exponents as estimated from dimensional analysis [24]. Solid line: multifractal theory [56].