Shannon entropy as an indicator of age for turbulent overturns in the oceanic thermocline

The Shannon entropy is a measure of the degree of intricacy contained in any graphable n ‐dimensional realization of an observable quantity. We use the Shannon entropy to measure the intricacy of density overturns in the oceanic thermocline and find that the Shannon entropy is related to the Thorpe scale L T [ Thorpe , 1977] and the Ozmidov scale L O [ Ozmidov , 1965]. We find that (1) small Shannon entropy corresponds to small values of R OT (≡ L O / L T ), while large Shannon entropy is associated with large values of R OT ; (2) density spectra are typically more steep than inertial subrange spectra when both Shannon entropy and R OT are small, whereas the spectral slope tends to be flatter than inertial subrange spectra when both Shannon entropy and R OT are large; (3) the Grashof number is very large ( O (10 10 )) when Shannon entropy is small, indicating that these patches are extremely density unstable; (4) spectral bandwidth is much larger for patches with small Shannon entropy than for those with large entropy, indicating that large‐scale, or “bulk” Reynolds number is large when entropy is small. We discuss the hypothesis that the degree of intricacy, and hence the Shannon entropy, increases with increasing time in a turbulent overturn and is observed to decrease only when the resolution limits of the measuring system are exceeded. On the basis of these arguments we suggest that some classes of overturns are created with Thorpe scale larger than the Ozmidov scale. In these overturns the kinetic energy dissipation rate (ε) is small during the initial growth of the overturn. Later, a small‐scale structure develops, and a more complex, higher‐order flow evolves. This behavior is discussed and compared with gridgenerated laboratory turbulence, in which initially small, energetic, rapidly growing boundary layers detached from the grid and advect downstream, forcing R OT to be largest adjacent to the grid and thereafter decrease as a result of entrainment.