Lagrangian dispersion in experimental stratified turbulence

Abstract

Lagrangian measurements of tracer particle dispersion in stratified turbulence are presented from a large-scale experiment achieving both high buoyancy Reynolds numbers and low Froude numbers -- a regime characteristic of oceanic conditions. Stratification has a pronounced effect on the vertical particle dispersion, which is observed to be constrained to distances on the order of $w_{\mathrm{std}}/N$, where $w_{\mathrm{std}}$ is the standard deviation of the vertical velocity and $N$ is the Brunt-Väisälä frequency. As expected in strongly nonlinear, stratified turbulence, the frequency spectrum of the Lagrangian velocity becomes isotropic at frequencies higher than $N$. The spectral decay follows a $1/f^3$ scaling, which contrasts with the $1/f^2$ behavior typical of homogeneous isotropic turbulence. At time scales corresponding to internal waves, the statistics of velocity increments remain Gaussian, consistent with the weakly nonlinear regime of wave turbulence. At smaller scales, however, the flow exhibits strongly non-Gaussian statistics, indicative of fully nonlinear turbulent dynamics driven by wave breaking.

Figures (3)

• Figure 1: Lagrangian velocity power spectra. Fourier transforms are computed only on trajectories longer than 1024 frames. Main figure: EXP4. The dashed blue line shows the raw velocity $u$ spectrum, while the solid lines spectra are computed from the low-pass filtered velocity components, removing the noise-dominated high-frequency part. The vertical dashed line highlights $f=N/2\pi$. The red dahsed line is a $f^{-3}$ decay. Insert: Spectra of $u$ for all experiments.
• Figure 2: Dispersion of single particles. (a) EXP4. The black dashed line is the ballistic regime for the $x$ component $\Delta_u(t)=u_{std}t$. The magenta dashed line is an empirical fit of the data in the diffusive regime with an exponent $0.4$.(b) Rescaled vertical dispersion for the four experiments. (c) Autocovariance of the velocity components for EXP4. The purple curve is the covariance of the vertical velocity after applying a notch filter in the frequency band $[0.67,0.73]N$ (forcing frequencies).
• Figure 3: Main figure: evolution of the kurtosis $K$ of the velocity increments as a function of the scale $\tau$ for EXP4. The horizontal dashed line highlights the Gaussian value $K=3$. Right insert: Evolution of the kurtosis of the horizontal increments $\delta_\tau u$ as a function of $\tau$ and $Re_b$. Left insert: PDF of the normalized acceleration components $\hat{a}_i=a_i/{a_i}_{std}$ for EXP4 (numerical values of ${a_i}_{std}$ are given in SM). The color for the components are similar to that of the main figure. The black dashed line is a Gaussian distribution.