Direct numerical simulations of three-dimensional (3D) homogeneous turbulence under rapid rigid rotation are conducted to examine the predictions of resonant wave theory for both small Rossby number and large Reynolds number. The theory predicts that "slow modes" of the velocity, with zero wavenumber parallel to the rotation axis (k z = 0), will decouple from the remaining "fast modes" and solve an autonomous system of twodimensional (2D) Navier-Stokes equations for the horizontal velocity components, normal to the rotation axis, and a 2D passive scalar equation for the vertical velocity component, parallel to the rotation axis. The Navier-Stokes equation for three-dimensional rotating turbulence is solved in a 128 3 mesh after being diagonalized via "helical decomposition" into normal modes of the Coriolis term. A force supplies constant energy input at intermediate scales. To verify the theory, we set up parallel simulations for the 2D Navier-Stokes equation and 2D passive scalar equation to compare them with the slowmode dynamics of the 3D rotating turbulence. The simulation results reveal that there is a clear inverse energy cascade to the large scales, as predicted by 2D Navier-Stokes equations for resonant interactions of slow modes. As the rotation rate increases, the vertically-averaged horizontal velocity field from 3D Navier-Stokes converges to the velocity field from 2D Navier-Stokes, as measured by the energy in their difference field. Likewise, the vertically-averaged vertical velocity from 3D Navier-Stokes converges to a solution of the 2D passive scalar equation. The slow-mode energy spectrum approaches k, where k h is the horizontal wavenumber, and energy flux becomes closer to constant, as in 2D, the greater the rotation rate. Furthermore, the energy flux directly into small wave numbers in the k z = 0 plane from non-resonant interactions decreases, while fast-mode energy concentrates closer to that plane. The simulations are consistent with an increasingly dominant role of resonant triads for more rapid rotation.

We report on the measurement of new low-lying states in the neutron-rich 81,82,83,84Zn nuclei via in-beam γ -ray spectroscopy. These include the View the MathML source41+→21+ transition in 82Zn, the View the MathML source21+→0g.s.+ and View the MathML source41+→21+ transitions in 84Zn, and low-lying states in 81,83Zn were observed for the first time. The reduced View the MathML sourceE(21+) energies and increased View the MathML sourceE(41+)/E(2+1) ratios at N=52N=52, 54 compared to those in 80Zn attest that the magicity is confined to the neutron number N=50N=50 only. The deduced level schemes are compared to three state-of-the-art shell model calculations and a good agreement is observed with all three calculations. The newly observed 2+2+ and 4+4+ levels in 84Zn suggest the onset of deformation towards heavier Zn isotopes, which has been incorporated by taking into account the upper sdg orbitals in the Ni78-II and the PFSDG-U models