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Using filter-space techniques, we study the scale-to-scale transport of energy in a quasi-two-dimensional, weakly turbulent fluid flow averaged along the trajectories of fluid elements. We find that although the spatial mean of this Lagrangian-averaged flux is nearly unchanged from its Eulerian counterpart, the spatial structure of the scale-to-scale energy flux changes significantly. In particular, its features appear to correlate with the positions of Lagrangian coherent structures (LCS's). We show that the LCS's tend to lie at zeros of the scale-to-scale flux, and therefore that the LCS's separate regions that have qualitatively different dynamics. Since LCS's are also known to be impenetrable barriers to advection and mixing, we therefore find that the fluid on either side of an LCS is both kinematically and dynamically distinct. Our results extend the utility of LCS's by making clear the role they play in the flow dynamics in addition to the kinematics. [ABSTRACT FROM AUTHOR]

Using a recently developed filtering technique, we study the spatiotemporal properties of the scale-to-scale fluxes of energy and enstrophy in a weakly turbulent experimental quasi-two-dimensional flow. Although these spectral properties vary in time and space, we show that they persist along the Lagrangian trajectories of fluid elements for times that can be nearly as long as the correlation time of the velocity field itself. Additionally, we show that at small scales, the spectral energy flux persists longest for fluid elements in strongly hyperbolic regions of the flow, whereas at large scales it persists in strongly elliptic regions. [ABSTRACT FROM AUTHOR]

Dynamics occurring in the Earth's outer core involve convection, dynamo action, geomagnetic reversals, and the effects of rapid rotation, among other processes. Inertial waves are known to arise in rotating fluids, and their presence in the core has been previously argued using seismological data (Aldridge and Lumb 1987). They may also be involved in flows affecting the geodynamo. We report experimental observations of inertial wave modes in an Earth-like geometry: laboratory spherical Couette flow with an aspect ratio 0.33, using liquid sodium as the working fluid. Inertial modes are detected via magnetic induction and show good agreement with theoretical predictions in frequency, wavenumber, and magnetic induction structure. Our findings imply that linear wave behavior can dominate the dynamics even in turbulent flows with large Reynolds number Re, where nonlinear behaviors might be expected (here Re ∼ 107). We present evidence that strong differential rotation excites the modes via over-reflection. Earth's inner core may also super-rotate and thereby excite inertial modes in the same way. Zonal flows in the core, likely to have higher speeds than the super-rotation, may be a stronger source for exciting inertial modes in the Earth. [ABSTRACT FROM AUTHOR]

A novel approach for studying the spatial relationship between the production and dissipation rates of turbulent kinetic energy and vortical structures is presented. Two turbulent flows were investigated: the zero pressure gradient boundary layer and the two-stream mixing layer. In both flows, a multisensor hot-wire probe was used to measure the velocity components in all three coordinate directions, as well as six components of the velocity gradient tensor. The remaining three velocity gradients were determined using Taylor’s hypothesis. With these data, the “instantaneous” production and dissipation rates, defined by [formula] and D=-ν[(∂ui/∂xj)2+(∂ui/∂xj)(∂uj/∂xi)], respectively, were determined. Cross-correlating the fluctuations of these two signals reveals that they are not randomly distributed in time with respect to each other; rather they display significant levels of correlation. Plotting the cross-correlation coefficients versus a dimensionless length scale, defined as L′=sgn(τ)|τ|/νU, reveals an asymmetric pattern that persists at several cross-stream locations for both flows. Furthermore, correlating both the dissipation and production rates with a vortex identifier, ωxy=[(ωx)2+(ωy)2]1/2, also reveals consistent cross-stream patterns. The magnitude of these correlations and their persistent shapes across the flows suggest that the spatial separation between regions of concentrated dissipation and production rates is associated with the presence of quasistreamwise vortices in both of these flows. More specifically, they imply that regions of concentrated rates of dissipation are primarily in the cores of the vortices, whereas regions of rates of production are more concentrated on their periphery. [ABSTRACT FROM AUTHOR]