## Final Report Summary - 3DZZI (Three-dimensional structure of stratified turbulence)

A new flow instability, known as 'zig-zag' instability (ZZI), has been revealed to be at the origin of the spontaneous formation of decoupled horizontal layers in stably stratified fluids. Recent results show that strongly stratified turbulence has a three-dimensional dynamic but is strongly anisotropic. A direct cascade associated with a -5/3 horizontal kinetic energy spectrum has been predicted when the buoyancy Reynolds number is sufficiently large. In order to check this hypothesis, we have investigated experimentally forced stratified turbulence. The flow has been generated by 12 vortex generators (flaps) placed on the side of a large stably and linearly stratified tank. The interaction of the randomly produced vortex pairs is able to create a statistically stationary turbulent flow with a low Froude number and a buoyancy Reynolds number of order unity. Velocity measurements in vertical cross-sections show that the flow organises itself into horizontal layers via the ZZI. The ZZI can lead to the formation of thin 'pancake' vortices, characterised by a very small aspect ratio. Many examples of such vortices exist in the ocean (Meddies) and the atmosphere (high / low pressure cells). One peculiar feature of pancake vortices is a high vertical shear and an anomaly of pressure due to their characteristic shape. These features may induce the formation of secondary instabilities, like the shear and the gravitational instabilities. These motions, still not well understood, could play a relevant role in the physical mechanisms underlying the direct cascade of energy to small dissipative scales in stratified turbulence. In order to better characterise the conditions of onset and evolution of secondary instabilities, the stability of a pancake vortex has been investigated numerically as a function of its vertical thickness. Numerical results have revealed that reducing the vertical aspect ratio has a destabilising effect on the vortex stability. Applying the general criteria for each of possible instabilities, we have shown that the dominant mechanism is related to an anomaly in the density structure. This procedure permitted to obtain the stability boundaries in the relevant parameter space and so to calculate the critical aspect ratios for each instability: surprisingly, the shear instability appears for much lower aspect ratios as compared to the gravitational instability. The comparison of the numerical results with the classical gravitational stability theory reveals an excellent agreement. To better explain the properties of the gravitational instability in the pancake vortex, we have considered analytically the stability of a linearly and unstably stratified fluid in solid body rotation. We have obtained a general dispersion relation in terms of the Bessel functions and two types of solutions were found: neutral wave solutions for large vertical wavenumbers and unstable solutions for small vertical wavenumbers. This is a new interesting result since in the stably stratified case only neutral wave solutions are possible. We generalised the results to any vertical and radial velocity profile. Herein we obtained a condition on the radial distribution of velocity which is able to predict the dominant instability. This stability criterion represent a new important result because of its simplicity and wide applications opportunities for geophysical flows.