Analytical theory of forced rotating sheared turbulence: The parallel case

Forced turbulence combined with the effect of rotation and shear flow is studied. In a previous paper [N. Leprovost and E. J. Kim, Phys. Rev. E 78, 016301 (2008)], we considered the case where the shear and the rotation are perpendicular. Here, we consider the complementary case of parallel rotation and shear, elucidating how rotation and flow shear influence the generation of shear flow (e.g., the direction of energy cascade), turbulence level, transport of particles, and momentum. We show that turbulence amplitude and transport are always quenched due to strong shear (ξ=νky2∕A⪡1, where A is the shearing rate, ν is the molecular viscosity, and ky is a characteristic wave number of small-scale turbulence), with stronger reduction in the direction of the shear than those in the perpendicular directions. In contrast with the case where rotation and shear are perpendicular, we found that rotation affects turbulence amplitude only for very rapid rotation (Ω⪢A) where it reduces slightly the anisotropy due to shear flow. Also, concerning the transport properties of turbulence, we find that rotation affects only the transport of particle and only for rapid rotation, leading to an almost isotropic transport (whereas, in the case of perpendicular rotation and shear, rotation favors isotropic transport even for slow rotation). Furthermore, the interaction between the shear and the rotation is shown to give rise to nondiffusive flux of angular momentum (Λ effect), even in the absence of external sources of anisotropy, which can provide a mechanism for the creation of shearing structures in astrophysical and geophysical systems

Analytical theory of forced rotating sheared turbulence: The perpendicular case

Rotation and shear flows are ubiquitous features of many astrophysical and geophysical bodies. To understand their origin and effect on turbulent transport in these systems, we consider a forced turbulence and investigate the combined effect of rotation and shear flow on the turbulence properties. Specifically, we study how rotation and flow shear influence the generation of shear flow (e.g., the direction of energy cascade), turbulence level, transport of particles and momentum, and the anisotropy in these quantities. In all the cases considered, turbulence amplitude is always quenched due to strong shear (ξ=νky2/A⪡1, where A is the shearing rate, ν is the molecular viscosity, and ky is a characteristic wave number of small-scale turbulence), with stronger reduction in the direction of the shear than those in the perpendicular directions. Specifically, in the large rotation limit (Ω⪢A), they scale as A−1 and A−1|ln ξ|, respectively, while in the weak rotation limit (Ω⪡A), they scale as A−1 and A−2/3, respectively. Thus, flow shear always leads to weak turbulence with an effectively stronger turbulence in the plane perpendicular to shear than in the shear direction, regardless of rotation rate. The anisotropy in turbulence amplitude is, however, weaker by a factor of ξ1/3|ln ξ| (∝A−1/3|ln ξ|) in the rapid rotation limit (Ω⪢A) than that in the weak rotation limit (Ω⪡A) since rotation favors almost-isotropic turbulence. Compared to turbulence amplitude, particle transport is found to crucially depend on whether rotation is stronger or weaker than flow shear. When rotation is stronger than flow shear (Ω⪢A), the transport is inhibited by inertial waves, being quenched inversely proportional to the rotation rate (i.e., ∝Ω−1) while in the opposite case, it is reduced by shearing as A−1. Furthermore, the anisotropy is found to be very weak in the strong rotation limit (by a factor of 2) while significant in the strong shear limit. The turbulent viscosity is found to be negative with inverse cascade of energy as long as rotation is sufficiently strong compared to flow shear (Ω⪢A) while positive in the opposite limit of weak rotation (Ω⪡A). Even if the eddy viscosity is negative for strong rotation (Ω⪢A), flow shear, which transfers energy to small scales, has an interesting effect by slowing down the rate of inverse cascade with the value of negative eddy viscosity decreasing as |νT|∝A−2 for strong shear. Furthermore, the interaction between the shear and the rotation is shown to give rise to a nondiffusive flux of angular momentum (Λ effect), even in the absence of external sources of anisotropy. This effect provides a mechanism for the existence of shearing structures in astrophysical and geophysical systems

Visco-magnetic torque at the core mantle boundary

A magneto-hydrodynamic model of boundary layers at the Core-Mantle Boundary (CMB) is derived and used to compute the viscous and electromagnetic torques generated by the Earth's nutation forcing. The predicted electromagnetic torque alone cannot account for the dissipation estimated from the observations of the free core nutation. The presence of a viscous boundary layer in the electromagnetic skin layer at the CMB, with its additional dissipative torques, may explain the geodetic data. An apparent Ekman number at the top of the core between 3 and $5 10^{-11}$ is inferred depending on the electrical conductivity of the mantle

Field observations of shear waves in the surf zone

Author Posting. © American Geophysical Union, 2004. This article is posted here by permission of American Geophysical Union for personal use, not for redistribution. The definitive version was published in Journal of Geophysical Research 109 (2004): C01031, doi:10.1029/2002JC001761.Alongshore propagating meanders of the mean alongshore current in the surf zone called shear waves have periods of a few minutes and wavelengths of a few hundred meters. Here shear wave properties are estimated with arrays of current meters deployed for 4 months within 300 m of the shoreline of a sandy beach. Shear wave velocity fluctuations are approximately horizontally isotropic, with root mean square values between 10 and 40% of the mean (3-hour-averaged) alongshore current V. Cross-shore variations of the time-averaged shear wave momentum flux are consistent with shear wave energy generation close to shore where the breaking wave-driven mean alongshore current V and current shear Vx are strong and with shear wave energy dissipation and transfer back to the mean flow farther offshore where V and Vx are weak. In case studies where V is a narrow jet near the shoreline the observed strong decay of shear wave energy levels seaward of the jet, and the cross-shore and alongshore structure of shear waves within the jet, are similar to predictions based on the linearly unstable modes of the observed V. Shear wave energy levels also are high in a marginally unstable case with a strong, but weakly sheared, V.This research was supported by the Office of Naval Research, the National Ocean Partnership Program and the National Science Foundation

Turbulent spectrum of the Earth's ozone field

The Total Ozone Mapping Spectrometer (TOMS) database is subjected to an analysis in terms of the Karhunen-Loeve (KL) empirical eigenfunctions. The concentration variance spectrum is transformed into a wavenumber spectrum, $E_c(k)$. In terms of wavenumber $E_c(k)$ is shown to be $O(k^{-2/3})$ in the inverse cascade regime, $O(k^{-2})$ in the enstrophy cascade regime with the spectral {\it knee} at the wavenumber of barotropic instability.The spectrum is related to known geophysical phenomena and shown to be consistent with physical dimensional reasoning for the problem. The appropriate Reynolds number for the phenomena is $Re\approx 10^{10}$.Comment: RevTeX file, 4 pages, 4 postscript figures available upon request from Richard Everson <[email protected]