We construct the exact exchange-correlation potential of time-dependent density-functional theory and the approximation to it that is adiabatic but exact otherwise. For the strong-field double ionization of the Helium atom these two potentials are virtually identical. Thus, memory effects play a negligible role in this paradigm process of nonlinear, nonperturbative electron dynamics. We identify the regime of high-frequency excitations where the adiabatic approximation breaks down and explicitly calculate the nonadiabatic contribution to the exchange-correlation potential.

The inertial-range properties of quasi-stationary hydrodynamic turbulence under solid-body rotation are studied via high-resolution direct numerical simulations. For strong rotation the nonlinear energy cascade exhibits depletion and a pronounced anisotropy with the energy flux proceeding mainly perpendicularly to the rotation axis. This corresponds to a transition towards a quasi-twodimensional flow similar to a linear Taylor-Proudman state. In contrast to the energy spectrum along the rotation axis which does not scale self-similarly, the perpendicular spectrum displays an inertial range with k −2 ⊥ -behavior. A new phenomenology gives a rationale for the observations. The scaling exponents ζp of structure functions up to order p = 8 measured perpendicular to the rotation axis indicate reduced intermittency with increasing rotation rate. The proposed phenomenology is consistent with the inferred asymptotic non-intermittent behavior ζp = p/2.The inherent properties of turbulence in a rotating reference frame are important for, e.g., the dynamics of atmosphere and oceans, liquid planetary cores, and engineering problems. The nonlinear spectral transfer of energy by the direct turbulent cascade and the associated energy spectrum are particularly interesting due to their direct connection to the dynamical processes governing rotating turbulence. Most of the available experimental data [1,2,3,4,5] yields no conclusive information on the expected self-similar scaling of the energy spectrum in the inertial range of scales and its dependence on the rotation frequency Ω. Although recent experiments [6,7,8] have shed some light on these issues, the scaling of two-point statistics in rotating turbulence remains a controversial topic.Direct numerical simulations [9,10,11,12,13,14,15,16] and large-eddy simulations, see e.g. [17,18,19], have been carried out only at low and moderate Reynolds numbers precluding clear scaling observations. Nevertheless, most of the cited works agree in that the nonlinear spectral transfer of energy to smaller scales diminishes with growing Ω, accompanied by a transition of the flow towards a quasi-two-dimensional state perpendicular to the fixed rotation axis, Ω. The transition manifests itself in an increasing ratio of integral length scales parallel and perpendicular to Ω = Ωê 3 , defined as L i,j = L∞ 0dℓ v i (r)v i (r + ℓê j ) / v 2 i (r) , L ∞ representing the largest possible distance between two points in the simulation volume and ℓ denoting the respective space increment.This Letter presents high-resolution direct numerical simulations of incompressible rotating homogeneous turbulence driven at largest scales and proposes a phenomenology of the energy cascade which suggests a physical explanation for the observed attenuation of nonlinear spectral transfer under the influence of rotation. In addition, the model gives a rationale for the observed trend towards two-dimensionality in rapidly rotating turbulence which is corroborated by the simulations. The scaling of two-point structure fu...

Navier-Stokes turbulence subject to solid-body rotation is studied by high-resolution direct numerical simulations (DNS) of freely decaying and stationary flows. Setups characterized by different Rossby numbers are considered. In agreement with experimental results strong rotation is found to lead to anisotropy of the direct nonlinear energy flux, which is attenuated primarily in the direction of the rotation axis. In decaying turbulence the evolution of kinetic energy follows an approximate power law with a distinct dependence of the decay exponent on the rotation frequency. A simple phenomenological relation between exponent and rotation rate reproduces this observation. Stationary turbulence driven by large-scale forcing exhibits $k_\perp^{-2}$-scaling in the rotation-dominated inertial range of the one-dimensional energy spectrum taken perpendicularly to the rotation axis. The self-similar scaling is shown to be the cumulative result of individual spectral contributions which, for low rotation rate, display $k_\perp^{-3}$-scaling near the $k_\parallel=0$ plane. A phenomenology which incorporates the modification of the energy cascade by rotation is proposed. In the observed regime the nonlinear turbulent interactions are strongly influenced by rotation but not suppressed. {Longitudinal two-point velocity structure functions taken perpendicularly to the axis of rotation indicate weak intermittency of the $k_\parallel=0$ (2D) component of the flow while the intermittent scaling of $k_\parallel\neq 0$ (3D) fluctuations is well captured by a modified She-L\'ev\^eque intermittency model which yields the expression $\zeta_p=p/6 + 2(1-(2/3)^{p/2})$ for the structure function scaling exponents.Comment: accepted for publication in Journal of Fluid Mechanics, 2 figure in reduced quality (data reduction

Photoabsorption spectra for 2-electron singlet systems are obtained from the real-time propagation of the time-dependent Kohn-Sham equations in the adiabatically exact approximation. The latter is provided by the exact ground state exchange-correlation potential corresponding to the instantaneous density. The results are compared to exact data obtained from the solution of the interacting Schrödinger equation. We find that the adiabatically exact approximation provides very good results for transitions of genuinely single excitation character but yields incorrect results if double excitations contribute substantially. However, the extent of the error can vary: some double excitations are just shifted in energy whereas others are missed completely. These situations are analyzed with the help of transition densities.

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