Deposits of clastic carbonate-dominated (calciclastic) sedimentary slope systems in the rock record have been identified mostly as linearly-consistent carbonate apron deposits, even though most ancient clastic carbonate slope deposits fit the submarine fan systems better. Calciclastic submarine fans are consequently rarely described and are poorly understood. Subsequently, very little is known especially in mud-dominated calciclastic submarine fan systems. Presented in this study are a sedimentological core and petrographic characterisation of samples from eleven boreholes from the Lower Carboniferous of Bowland Basin (Northwest England) that reveals a >250 m thick calciturbidite complex deposited in a calciclastic submarine fan setting. Seven facies are recognised from core and thin section characterisation and are grouped into three carbonate turbidite sequences. They include: 1) Calciturbidites, comprising mostly of highto low-density, wavy-laminated bioclast-rich facies; 2) low-density densite mudstones which are characterised by planar laminated and unlaminated muddominated facies; and 3) Calcidebrites which are muddy or hyper-concentrated debrisflow deposits occurring as poorly-sorted, chaotic, mud-supported floatstones. These

Phd by thesis

▪ Abstract We review the direct numerical simulation (DNS) of turbulent flows. We stress that DNS is a research tool, and not a brute-force solution to the Navier-Stokes equations for engineering problems. The wide range of scales in turbulent flows requires that care be taken in their numerical solution. We discuss related numerical issues such as boundary conditions and spatial and temporal discretization. Significant insight into turbulence physics has been gained from DNS of certain idealized flows that cannot be easily attained in the laboratory. We discuss some examples. Further, we illustrate the complementary nature of experiments and computations in turbulence research. Examples are provided where DNS data has been used to evaluate measurement accuracy. Finally, we consider how DNS has impacted turbulence modeling and provided further insight into the structure of turbulent boundary layers.

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DIRECT NUMERICAL SIMULATION: A Tool in Turbulence Research

The potential for sea ice-albedo feedback to give rise to nonlinear climate change in the Arctic Ocean – defined as a nonlinear relationship between polar and global temperature change or, equivalently, a time-varying polar amplification – is explored in IPCC AR4 climate models. Five models supplying SRES A1B ensembles for the 21 st century are examined and very linear relationships are found between polar and global temperatures (indicating linear Arctic Ocean climate change), and between polar temperature and albedo (the potential source of nonlinearity). Two of the climate models have Arctic Ocean simulations that become annually sea ice-free under the stronger CO 2 increase to quadrupling forcing. Both of these runs show increases in polar amplification at polar temperatures above-5 o C and one exhibits heat budget changes that are consistent with the small ice cap instability of simple energy balance models. Both models show linear warming up to a polar temperature of-5 o C, well above the disappearance of their September ice covers at about-9 o C. Below-5 o C, surface albedo decreases smoothly as reductions move, progressively, to earlier parts of the sunlit period. Atmospheric heat transport exerts a strong cooling effect during the transition to annually ice-free conditions. Specialized experiments with atmosphere and coupled models show that the main damping mechanism for sea ice region surface temperature is reduced upward heat flux through the adjacent ice-free oceans resulting in reduced atmospheric heat transport into the region.

Geophysical fluid dynamics.

The Structure of Turbulent Shear Flow By Dr. A. A. Townsend. Pp. xii + 315. 8¾ in. × 5½ in. (Cambridge: At the University Press.) 40s.

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The Structure of Turbulent Shear Flow

An Introduction to Magnetohydrodynamics

The influence or rotation on the spectral energy transfer of homogeneous turbulence is investigated in this paper. Given the fact that linear dynamics, e.g. the inertial waves regime tackled in an RDT (Rapid Distortion Theory) fashion, cannot Affect st homogeneous isotropic turbulent flow, the study of nonlinear dynamics is of prime importance in the case of rotating flows. Previous theoretical (including both weakly nonlinear and EDQNM theories), experimental and DNS (Direct Numerical Simulation) results are gathered here and compared in order to give a self-consistent picture of the nonlinear effects of rotation on tile turbulence. The inhibition of the energy cascade, which is linked to a reduction of the dissipation rate, is shown to be related to a damping due to rotation of the energy transfer. A model for this effect is quantified by a model equation for the derivative-skewness factor, which only involves a micro-Rossby number Ro(sup omega) = omega'/(2(OMEGA))-ratio of rms vorticity and background vorticity as the relevant rotation parameter, in accordance with DNS and EDQNM results fit addition, anisotropy is shown also to develop through nonlinear interactions modified by rotation, in an intermediate range of Rossby numbers (Ro(omega) = (omega)' and Ro(omega)w greater than 1), which is characterized by a marco-Rossby number Ro(sup L) less than 1 and Ro(omega) greater than 1 which is characterized by a macro-Rossby number based on an integral lengthscale L and the micro-Rossby number previously defined. This anisotropy is mainly an angular drain of spectral energy which tends to concentrate energy in tile wave-plane normal to the rotation axis, which is exactly both the slow and the two-dimensional manifold. In Addition, a polarization of the energy distribution in this slow 2D manifold enhances horizontal (normal to the rotation axis) velocity components, and underlies the anisotropic structure of the integral lengthscales. Finally is demonstrated the ability of a generalized EDQNM (Eddy Damped Quasi-Normal Markovian) model to predict the underlying spectral transfer structure and all the subsequent developments of classic anisotropy indicators in physical space, when compared to recent LES results. Even if the applications mainly concern developed strong turbulence, a particular emphasis is given to the strong formal analogy of this EDQNM2 model with recent weakly nonlinear approaches to wave-turbulence.

Energy transfer in rotating turbulence

This paper investigates some irreversible mechanisms occurring in homogeneous stably stratified turbulent flows. In terms of the eigenmodes of the linear regime, the velocity‐temperature field is decomposed into a vortex and two wavy components. Using an eddy‐damped quasinormal Markovian (EDQNM) closure with the axisymmetry hypothesis, an analysis of the anisotropic energy transfers between the vortex kinetic energy, the wave kinetic and potential energy is made. Within the light of triadic exchanges, and by analogy of the resonance condition for three linearly interacting gravity waves, the closure model allows one to compute the detailed transfers for eight types of interactions. Results of the calculations include time evolution plots, for the isotropic closure model as well as two different types of the anisotropic closure. The pure vortical interactions are shown to be responsible for the irreversible anisotropic structure created by stable stratification, and this structure prevents the inverse casc...

Detailed investigation of energy transfers in homogeneous stratified turbulence

An asymptotic quasi-normal Markovian (AQNM) model is developed in the limit of small Rossby number Ro and high Reynolds number, i.e. for rapidly rotating turbulent flow. Based on the 'slow' amplitudes of inertial waves, the kinetic equations are close to those that would be derived from Eulerian wave-turbulence theory. However, for their derivation we start from an EDQNM statistical closure model in which the velocity field is expanded in terms of the eigenmodes of the linear wave regime. Unlike most wave-turbulence studies, our model accounts for the detailed anisotropy as the angular dependence in Fourier space. Nonlinear equations at small Rossby number are derived for the set e, Z, h - energy, polarization anisotropy, helicity - of spectral quantities which characterize second-order two-point statistics in anisotropic turbulence, and which generate every quadratic moment of inertial wave amplitudes. In the simplest symmetry consistent with the background equations, i.e. axisymmetry without mirror symmetry, e, Z and h depend on both the wavevector modulus k and its orientation θ to the rotation axis. We put the emphasis on obtaining accurate numerical simulations of a generalized Lin equation for the angular-dependent energy spectrum e(k, θ , t ), in which the energy transfer reduces to integrals over surfaces given by the triadic resonant conditions of inertial waves. Starting from a pure three-dimensional isotropic state in which e depends only on k and Z = h = 0, the spectrum develops an inertial range in the usual fashion as well as angular anisotropy. After the development phase, we observe the following features: (a) A k^−3 power law for the spherically averaged energy spectrum. However, this is the average of power laws whose exponents vary with the direction of the wavevector from k^−2 for wavevectors near the plane perpendicular to the rotation axis, to k^−4 for parallel wavevectors. (b) The spectral evolution is self-similar. This excludes the possibility of a purely two-dimensional large-time limit. (c) The energy density is very large near the perpendicular wavevector plane, but this singularity is integrable. As a result, the total energy has contributions from all directions and is not dominated by this singular contribution. (d ) The kinetic energy decays as t^−0.8 , an exponent which is about half that one without rotation.

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Wave turbulence in rapidly rotating flows

At asymptotically high rotation rates, rotating turbulence can be described as a field of interacting dispersive waves by the general theory of weak wave turbulence. However, rotating turbulence has some complicating features, including the anisotropy of the wave dispersion relation and the vanishing of the wave frequency on a non-vanishing set of 'slow' modes. These features prevent straightforward application of existing theories and lead to some interesting properties, including the transfer of energy towards the slow modes. This transfer competes with, and might even replace, the transfer to small scales envisioned in standard turbulence theories.In this paper, anisotropic spectra for rotating turbulence are proposed based on weak turbulence theory; some evidence for their existence is given based on numerical calculations of the wave turbulence equations. Previous arguments based on the properties of resonant wave interactions suggest that the slow modes decouple from the others. Here, an extended wave turbulence theory with non-resonant interactions is proposed in which all modes are coupled; these interactions are possible only because of the anisotropy of the dispersion relation. Finally, the vanishing of the wave frequency on the slow modes implies that these modes cannot be described by weak turbulence theory. A more comprehensive approach to rotating turbulence is proposed to overcome this limitation.

Advances in wave turbulence: rapidly rotating flows

The goal of this work is to analyse how solid body rotation affects forced turbulence enclosed within solid boundaries, and to compare it to results of the experiment performed by Hopfinger et al. (1982). In order to identify various mechanisms associated with rotation, confinement, and forcing, a numerical pseudo-spectral code is used for performing direct numerical simulations. The geometry is simplified with respect to the experimental one. First, we are able to reproduce the linear regime, as propagating inertial waves that undergo reflections at the walls. Second, the Ekman pumping phenomenon, proportional to the rotation rate, is identified in freely decaying turbulence, for which the evolution of the flow bounded by walls is compared to the evolution of unbounded homogeneous turbulence. Finally we introduce a local forcing on a plane in physical space, for simulating the effect of an oscillating grid, so that diffusive turbulence is created, and we examine the structuring of the flow under the combination of the linear and nonlinear mechanisms. A transition to an almost two-dimensional state is shown to occur between the region close to the forcing and an outer region in which vortices appear, the number of which depends on the Reynolds and Rossby numbers. In this region, the anisotropy of turbulence is examined, and the numerical predictions are shown to reproduce many of the most important features present in the experimental flow.

Fabien S. Godeferd

Papers

Energy transfer in rotating turbulence

Detailed investigation of energy transfers in homogeneous stratified turbulence

Wave turbulence in rapidly rotating flows

Advances in wave turbulence: rapidly rotating flows

Direct numerical simulations of turbulence with confinement and rotation