Presence Of Stable Stratification Research Articles

Enhanced Core-Mantle Coupling Due to Stratification at the Top of the Core

Fluctuations in the length of day (LOD) over periods of several decades are commonly attributed to exchanges of angular momentum between the mantle and the core. However, the forces that enable this exchange are less certain. Suggestions include the influence of pressure on boundary topography, electromagnetic forces associated with conducting material in the boundary region and gravitational forces due to mass anomalies in the mantle and the core. Each of these suggestions has strengths and weaknesses. Here we propose a new coupling mechanism that relies on the presence of stable stratification at the top of the core. Steady flow of the core over boundary topography promotes radial motion, but buoyancy forces due to stratification oppose this motion. Steep vertical gradients develop in the resulting fluid velocity, causing horizontal electromagnetic forces in the presence of a radial magnetic field. The associated pressure field exerts a net horizontal force on the boundary. We quantify this hybrid mechanism using a local Cartesian approximation of the core-mantle boundary and show that the resulting stresses are sufficient to account for the observed changes in LOD. A representative solution has \SI{52}{\meter} of topography with a wavelength of \SI{100}{\kilo\meter}. We specify the fluid stratification using a buoyancy frequency that is comparable to the rotation rate and adopt a radial magnetic field based on geodetic constraints. The average tangential stress is \SI{0.027}{\newton\per\meter\squared} for a background flow of $\bar{V}=\SI{0.5}{\milli\meter\per\second}$. Weak variations in the stress with velocity (i.e. $\bar V^{1/2})$ introduce nonlinearities into the angular momentum balance, which may generate diagnostic features in LOD observations.

Outer Core Stratification From the High Latitude Structure of the Geomagnetic Field

The presence of stable stratification has broad implications for the thermal and compositional state of the outer core, the evolution of Earth's deep interior, and the energetics of the geodynamo. Yet the origin, strength, and depth extent of stratification in the region below the core-mantle boundary remain open questions. Here we compare magnetic fields produced by numerical dynamos that include heterogeneous stable thermal stratification below their outer boundary with models of the geomagnetic field on the core-mantle boundary, focusing on high latitude structures. We demonstrate that the combination of high magnetic field intensity regions and reversed magnetic flux spots, especially at high latitudes, constrains outer core stratification below the core-mantle boundary. In particular, we find that the negative contribution to the axial dipole from reversed flux spots is a strong inverse function of the stratification. Comparison of our numerical dynamo results to the structure of the historical geomagnetic field suggests up to 400 km of permeable, laterally heterogeneous thermal stratification below the core-mantle boundary.

Turbulent dispersion of pollutants in urban-type canopies under stable stratification conditions

Large eddy simulation is performed for the dispersion of a passive scalar in the turbulent boundary layer over an urban-like roughness surface under neutral and stable stratification. Square arrays of cubical obstacles are used to model the urban canopy with a ground level point source located in front of the obstacle. We design cases for varying building intervals to investigate the relationship between flow patterns and dispersion processes for different plan area densities λp. It has been found (Shen et al. 2015) that flow patterns in a three-dimensional urban canopy can be classified into five basic regimes in neutral stratification: isolated roughness, external wake interference, internal wake interference, skimming flow and streets network. This classification still holds in the presence of moderately stable stratification. In area with large λp, the material released from the point source tends to be trapped by the leeward recirculation and is well-mixed inside the canopy. The mean concentration level within roughness canopies is high due to the reduced advection velocity. In area with small λp, the great part of the material is entrained into the horseshoe vortex wrapping around the obstacle and carried downwind. The material is concentrated in the lower region of the canopy with a relatively higher temporal fluctuation. In the presence of stable stratification, the spread of the plume is reduced and the temporal fluctuation is suppressed as well. For area of large λp, the advective part of the scalar flux is responsible for carrying the material at ground level aloft into the urban canopy layer.

John Leask Lumley

John Leask Lumley

Large eddy simulation of turbulent horizontal buoyant jets

Large eddy simulations (LESs) of turbulent horizontal buoyant jets are carried out using a high-order numerical method and Sigma subgrid-scale (SGS) eddy-viscosity model, for a number of different Reynolds (Re) and Richardson (Ri) numbers. Simulations at previous experimental flow conditions (Re = 3200, 24, 000 and Ri = 0, 0.01) are carried out first, and the results are found to be qualitatively and quantitatively similar to the experimental results, thus validating the numerical methodology. The effect of varying Ri (values 2×10−4, 0.001, 0.005, and 0.01) and Re (3200 and 24, 000) is studied next. The presence of stable stratification on one side and unstable stratification on the other side of the jet centreline leads to an asymmetric development of horizontal buoyant jets. It is found that this asymmetry, the total radial spread and the vertical deflection are significantly affected by Ri, while Re affects only the radial asymmetry. The need for developing improved integral models, accounting for this asymmetry, is pointed out. Turbulent production and dissipation rates are investigated, and are found to be symmetric in the horizontal plane, but asymmetric in the mid-vertical plane. A previously proposed model, for correlation between the vertical component of the fluctuating scalar flux vector and the vertical cross-correlation component of the Reynolds tensor, is modified based on the current LES results. Instantaneous scalar and velocity fields are analysed to reveal the structure of horizontal buoyant jets. Similar to the developed turbulent jet, the flow close to the nozzle too is found to be markedly different in the stable and unstable stratification regions. Persistent coherent vortex rings are found in the stable stratification region, while intermittent breakdown of vortex rings into small-scale structures is observed in the unstable stratification region. Similarities and differences between the flow structures in the horizontal buoyant jet configuration and those in the jet in crossflow configuration are discussed. Finally, a dynamic mode decomposition analysis is carried out, which indicates that the flow in the unstable stratification region is more energetic and prone to instabilities, as compared to the flow in the stable stratification region.

Turbulent Diffusion of Magnetic Fields in Two-Dimensional Magnetohydrodynamic Turbulence with Stable Stratification

We calculate the correction, due to nonlinear wave-wave interactions, to the Zel'dovich estimate for the turbulent diffusivity of magnetic fields in a model of two-dimensional magnetohydrodynamic turbulence in the presence of stable stratification. Such a model has some relevance to hydromagnetic turbulence in stellar interiors. The significance of this correction is that, unlike the lowest-order Zel'dovich balance, it is independent of the molecular resistivity eta and so will not vanish in the limit of a large magnetic Reynolds number, although the correction is O(sigma;{4}), where sigma is the wave slope, which necessarily is small. Thus, we are led to the counterintuitive result that the presence of stable stratification can actually increase the vertical flux of magnetic fields relative to that in 2D MHD turbulence without stratification.

Langmuir circulations beneath growing or decaying surface waves

The instability to longitudinal vortices of two-dimensional density-stratified temporally evolving wavy shear flow is considered. The problem is posited in the context of Langmuir circulations, LCs, beneath wind-driven surface waves and the instability mechanism is generalized Craik–Leibovich, either CLg or CL2. Of interest is the influence of non-stationary base flows on the instability according to linear theory. It is found that the instability is described by a family of similarity solutions and that the growth rate of the instability, in non-stationary base flows, is doubly exponential in time, although the growth rate reduces to exponential when the base flow is stationary. An example is given for weakly sheared wind-driven flow evolving in the presence of growing irrotational surface waves. Waves aligned both with the wind and counter to it are considered, as is the role of stratification. Antecedent to the example is an initial value problem posed by Leibovich & Paolucci (1981) for neutral waves in slowly evolving shear. Here, however, the waves and shear may grow (or decay) at rates comparable with the LCs. Furthermore the current here has two components: a wind-driven portion due to the wind stress applied at the free surface and a second due to the diffusion of momentum due to the wave-amplitude-squared free-surface stress condition. Using the case for neutral waves in non-stratified uniform shear for reference, it is found, in general, that growing waves are stabilizing while decaying waves are destabilizing to the formation of LCs, although the latter applies only for sufficiently large spanwise spacings and is subject to a globally stable lower bound. Decaying waves in the absence of wind can also be destabilizing to LCs. When the wind is counter to the waves, however, only decaying waves are unstable to LCs. Furthermore, while growing waves are stable to the formation of LCs in the presence of stable stratification, decaying waves are unstable in both aligned and opposed wind-wave conditions. Unstable stratification on the other hand, is destabilizing to LCs for all temporal waves in both aligned and opposed wind-wave conditions.

Diffusion in stably stratified turbulence

We examine results of direct numerical simulations (DNS) of homogeneous turbulence in the presence of stable stratification. We focus on the effects of stratification on eddy diffusion, and the distribution of pairs of particles released in the flow. DNS results are presented over a range of stratification, and at Reynolds numbers compatible with aliased free spectral results for a resolution of 128 mesh points. We compare results for particle dispersion to simple analytic theories such as that proposed by Csanady (1964) and Pearson et al. (1983) by adapting the basic Langevin model to decaying turbulence at low Reynolds numbers. Stable stratification is found to arrest both single particle displacements and pair separation in the direction of stratification, but it leaves these quantities nearly unaltered in the transverse direction. With respect to the dynamics of stratified flows, we find that regions of strong viscous dissipation are intermittently spaced, and are associated with large horizontal vorticity, consistent with recent experimental results by Fincham et al. (1994).

The scaling of turbulence in the presence of stable stratification

The force of gravity singles out the vertical direction in a stably stratified fluid. Since buoyancy forces remove energy preferentially from the vertical component of velocity, there is a pervasive belief that turbulence in such systems may be significantly anisotropic, with horizontal length and velocity scales greatly exceeding their vertical counterparts. This paper examines the scaling of the equations of motion of a stratified fluid, assuming that the energy‐containing scales of the motion are significantly anisotropic and that nonlinear terms are important in the equations of motion (an assumption of the existence of “turbulence”). Relevant nondimensional parameters are found to be the vertical Reynolds number Rew ≡ wh/v, where w and h are vertical velocity and length scales respectively, and the turbulence Froude number Fr ≡ u/Nl, where u and l are the horizontal velocity and length scales, respectively, and N is the buoyancy frequency. Two determinate scalings are found. The first case, termed buoyancy‐affected high Rew turbulence and characterized by Rew ≫ 1 and Fr ∼ 1, is necessarily isotropic. This scaling has its roots in the work of Dougherty (1961); its use is widespread in recent literature. It is important to recognize this as the appropriate scaling for isotropic turbulence in which the importance of buoyancy forces is in limiting the vertical (hence through isotropy, also the horizontal) scale of the energy‐containing eddies which irreversibly transfer energy to smaller scales, while noting that in a stratified fluid there are other possible modes of motion which can transfer energy reversibly (linear waves) or to larger scales (vortical modes). The second, termed buoyancy‐affected low Rew turbulence and characterized by Rew ∼ 1 and Fr ∼ 1, is truly anisotropic, with the possibility of u ≫ w and h ≪ 1. The field observations of Gargett et al. (1984) and the laboratory observations of Stillinger et al. (1983) and Itsweire et al. (1986) are examined in the context of these scalings. It is concluded that the field observations are characteristic of the buoyancy‐affected high Rew regime, while the laboratory regime may be buoyancy‐affected low Rew throughout its reported evolution. A critical test for the existence of the latter regime is suggested.

On the Effect of Dissipation on Shear Instabilities in the Stable Atmospheric Boundary Layer

Abstract We are presenting the results of a stability analysis of a background wind shear in the presence of stable stratification and of height dependent coefficients of eddy viscosity and eddy thermal conduction. It is shown that the vertical gradients of the eddy coefficients substantially affect the phase velocities, growth rates and vertical structure of the gravity wave and are responsible for the appearance of some counter-gradient heat fluxes and Reynolds stresses. It is suggested that these gradients may explain the observed counter-gradient fluxes in the stable atmospheric boundary layer.

Instability of the Ekman Spiral Boundary-Layer Flow in the Presence of Stable Stratification

Instability of the Ekman Spiral Boundary-Layer Flow in the Presence of Stable Stratification