Xie Jinhan's research group and collaborators in the School of Engineering have confirmed that there is a two-way transfer of energy across scales in ocean turbulence

In cooperation with Dhruv Balwada of Columbia University and Raffaele Marino of the University of Lyon, the newly promoted turbulence structure function theory was applied to analyze the buoy data of the Gulf of Mexico by applying the newly promoted turbulence structure function theory to confirm the bidirectional transmission
of energy across scales in ocean turbulence 。 The study, titled "Direct observational evidence of an oceanic dual kineticenergy cascade and its seasonality," was published in Science Advances
.

There are multi-scale flow structures in ocean turbulence, and they interact to transmit
kinetic energy across scales.
There is a paradox of cross-scale energy transmission: due to the influence of georotation, large-scale eddies transmit energy from small scale to large scale through inverse series; The energy is eventually dissipated
at small scales due to viscosity.
Previous work has speculated that flow structures such as fronts and fluctuations can lead to positive strings
of energy transferred to small scales.
However , the simultaneous existence of this forward and reverse series unlike classical turbulence has not been previously
confirmed by observation.
This work uses the theory of turbulent third-order structural functions beyond the inertia region to analyze buoy data in the Gulf of Mexico
.

The classical theory of turbulent third-order structural functions considers the relationship between the scale of the third-order structural functions in the inertia region and the intensity and direction of energy transfer, and its application is related to the scale far away from energy injection and dissipation (cf.
Classical Kolmogorov third-order structural function theory of the inertial region[1]).

This work uses the tertiary structure functional number theory of turbulence beyond the inertial region, which describes the scale of energy injection and dissipation and the bidirectional transport of energy [2,3], which makes it possible to analyze ocean turbulence where energy transfer may be bidirectional, and the scale and intensity
of energy injection can be obtained while obtaining the direction of energy transfer.

The buoy data analyzed by this work is shown
in Figure 1.
The position of the buoy is monitored by satellites, so we can obtain the velocity of the buoy, which in turn can be statistically ordered by the third-order structural function, which can then be analyzed
using the structural function theory.
Figure 2 shows the main results
of this work.
We find that the kinetic energy is mainly injected at a scale of about 50km and 1km, which correspond to the deformation radius
of ocean depth and mixed layer depth, respectively.
Kinetic energy is transmitted in both directions to large and small scales at the same time, and energy transmission to small scales dominates
at scales below several kilometers.
And there is a seasonal effect on the intensity of energy transfer: the intensity of energy transfer to small scales increases in
winter.

Figure 1.
Spatial distribution of
buoys.
The black dot in the figure is the initial position of the buoy, and the colored line is the movement path of the buoy; The small graph is the corresponding Lagrangian frequency spectrum
.
A and B present two sets of observations, summer and winter, respectively

Figure 2.
Cross-scale transfer
of energy in the Gulf of Mexico in summer (top) and winter (bottom) based on third-order structural functions.
A and D are third-order structural functions; B and E are the scale and intensity of energy injection; C and F are the intensity of energy transfer across scales, where the transfer of energy to large and small scales corresponds to negative and positive signs, respectively

On the one hand, this work answers the question of whether bidirectional energy transmission exists in ocean turbulence, and also provides some inspiration for the parameterization of ocean models.
On the other hand, the information we obtain through the theory of turbulent structural functions raises some questions of fluid dynamics and physical oceanography, for example, what causes seasonal changes in energy transfer across scales? What is the mechanism of bidirectional energy transfer and which flow structures are it related to? What physical processes correspond to the characteristic energy injection scale?

This work was supported
by the National Natural Science Foundation of China Major Research Program No.
92052102 and the Shandong Province Support Qingdao Marine Science and Technology Pilot National Laboratory Major Science and Technology Special No.
2022QNLM010201.

References

[1] Kolmogorov, A.
N.
1941 Dissipation of energy in locally isotropic turbulence.
Dokl.
Akad.
Nauk SSSR 32, 16–18.

[2] Xie J.
-H.
& Bühler O.
2019 Third-order structure functions for isotropic turbulence with bidirectional energy transfer,J.
Fluid Mech.
877, R3.

[3] Xie J.
-H.
2020 Quantifying the linear damping in two-dimensional turbulence, Phys.
Rev.
Fluids.
5, 094605.