Uniform Horizontal Shear Research Articles

Effect of the Froude number on a stratified turbulence under two shear orientations using coupled SSG and SL models

In the present investigation, the evolution of homogeneous and stratified turbulence under a horizontal and a vertical shear is deliberate by coupled second-order model SSG-SL. This model is a result of a combination between the Speziale, Sarkar and Gatski model (SSG) and the Shih and Lumley model (SL). Horizontal shear and vertical shear are related to the angle between the shear and the vertical gradient of stratification; θ = π/2 and θ = 0, respectively. This study is performed for different values of Froude number Fr ranging from 0.35–1.11. The SSG-SL model confirms the asymptotic equilibrium states for various physical parameters governing the problem (b12, b11, ε/KS, , K/E and Kρ/E) for two shear orientations (θ = π/2 and θ = 0). A comparison between findings using the present coupled model of SSG-SL and those by Direct Numerical Simulation of Jacobitz (DNSJ) [Jacobitz F, Sarkar S. A direct numerical study of transport and anisotropy in a stably stratified turbulent flow with uniform horizontal shear. Flow Turbul Combust. 2000;63:343–360.; Jacobitz F. A comparison of the turbulence evolution in a stratified fluid with vertical or horizontal shear. J Turbul. 2002;3:1–18.] is carried out. For the horizontal shear related to θ = π/2, an excellent agreement between predictions by the SSG-SL model and the results of DNSJ [Jacobitz, Sarkar;Jacobitz] is detected for turbulent thermal and dynamic fields.

Deep heterogeneity of the stress state in the horizontal shear zones

The formation structures of brittle destruction in a rock layer above an active strike-slip fault in the crystalline basement is studied. The problem is analyzed from the standpoint of loading history, when after the stage of pure gravitational loading, an additional strain state of uniform horizontal shear of both the layer and underlying basement develops, which is further followed by a vertically nonuniform shear caused by the activation of the deep fault. For the studied object, irreversible fracture deformations on macro- and microlevels arise as early as the initial stage of loading under the action of gravitational stresses. These deformations continue evolving on the megascopic level in the course of horizontal shearing that is quasi-uniform both along the depth and laterally. The final formation of the structural ensemble occurs after a long stage of horizontal displacement of the blocks of the crystalline basement—the stage of localized shear. The theoretical analysis of the evolution of the stress state and morphology of the failure structures established the presence of numerous fractures with the normal dip-slip components in the intermediate-depth part of the rock mass, which are formed at the stages of uniform and localized horizontal shearing. The fractures with a strike-slip component mainly arise in the upper and near-axial deep parts of the section.

Tropical cyclone convection: the effects of ambient vertical vorticity

AbstractWe present idealized numerical model experiments to isolate and quantify the influence of ambient vertical vorticity on the dynamics of deep convection, such as that in the inner‐core region of a tropical depression. The vertical vorticity is represented either by a uniform horizontal shear, a uniform solid‐body rotation, or a combination of both. We show that the growing convective cells amplify locally the ambient rotation at low levels by more than an order of magnitude and that this vorticity, which is produced by the stretching of existing ambient vorticity, persists long after the initial updraught has decayed. Significant amplification of vorticity occurs even for a background rotation rate typical of the undisturbed tropical atmosphere and even for clouds of only moderate vertical extent. This finding has important implications for tropical cyclogenesis and provides a basis for a unified theory of tropical cyclogenesis and tropical cyclone intensification.The presence of ambient vertical vorticity reduces the updraught strength, slightly more when the vorticity is associated with horizontal shear than when it is associated with solid‐body rotation on account of enhanced entrainment. The reduction of the updraught strength can be attributed to the reduction of the lateral inflow by the centrifugal and Coriolis forces. Despite the significant amplification of vorticity, the sum of the centrifugal and Coriolis forces is mostly small compared with the lateral pressure gradient. Thus, at the level of background rotation studied, the Rossby elasticity effects in the updraught postulated by Montgomery et al. are not large, but may be important for higher levels of background rotation. The simulations ignore several processes that are likely to be important in reality, such as ambient vertical shear and surface friction, but they provide important benchmark calculations for interpreting the additional complexity arising from the inclusion of these effects. Copyright © 2011 Royal Meteorological Society

Shear‐driven magnetic buoyancy oscillations

AbstractThe effects of uniform horizontal shear on a stably stratified layer of gas is studied. The system is initially destabilized by a magnetically buoyant flux tube pointing in the cross‐stream direction. The shear amplifies the initial field to Lundquist numbers of about 200–400, but then its value drops to about 100–300, depending on the value of the sub‐adiabatic gradient. The larger values correspond to cases where the stratification is strongly stable and nearly isothermal. At the end of the runs the magnetic field is nearly axisymmetric, i.e. uniform in the streamwise direction. In view of Cowling's theorem the sustainment of the field remains a puzzle and may be due to subtle numerical effects that have not yet been identified in detail. In the final state the strength of the magnetic field decreases with height in such a way that the field is expected to be unstable. Low amplitude oscillations are seen in the vertical velocity even at late times, suggesting that they might be persistent (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Large-scale dynamos in turbulent convection with shear

Aims. To study the existence of large-scale convective dynamos under the influence of shear and rotation. Methods. Three-dimensional numerical simulations of penetrative compressible convection with uniform horizontal shear are used to study dynamo action and the generation of large-scale magnetic fields. We consider cases where the magnetic Reynolds number is either marginal or moderately supercritical with respect to small-scale dynamo action in the absence of shear and rotation. Our magnetic Reynolds number is based on the wavenumber of the depth of the convectively unstable layer. The effects of magnetic helicity fluxes are studied by comparing results for the magnetic field with open and closed boundaries. Results. Without shear no large-scale dynamos are found even if the ingredients necessary for the α-effect (rotation and stratification) are present in the system. When uniform horizontal shear is added, a large-scale magnetic field develops, provided the boundaries are open. In this case the mean magnetic field contains a significant fraction of the total field. For those runs where the magnetic Reynolds number is between 60 and 250, an additional small-scale dynamo is expected to be excited, but the field distribution is found to be similar to cases with smaller magnetic Reynolds number where the small-scale dynamo is not excited. In the case of closed (perfectly conducting) boundaries, magnetic helicity fluxes are suppressed and no large-scale fields are found. Similarly, poor large-scale field development is seen when vertical shear is used in combination with periodic boundary conditions in the horizontal directions. If, however, open (normal-field) boundary conditions are used in the x-direction, a large-scale field develops. These results support the notion that shear not only helps to generate the field, but it also plays a crucial role in driving magnetic helicity fluxes out of the system along the isocontours of shear, thereby allowing efficient dynamo action.

Vertical scale selection in inertial instability

The linear instability of a barotropic flow with uniform horizontal shear in a stratified rotating fluid is investigated with respect to perturbations invariant in the alongflow direction. The flow can be inertially unstable if there is sufficiently strong anticyclonic shear, but only for sufficiently high Reynolds numbers Re. We determine the critical Reynolds numbers required for amplification of the instability as a function of Prandtl number, strength of the stratification and magnitude of the shear. The vertical scales at the onset of the instability are calculated. For Prandtl number P < 1.44 instability always sets in through stationary overturning motions, for P > 1.44 it may also commence through overstable (oscillatory) motions. For Re exceeding the critical value, we determine the vertical scale of the most rapidly amplifying modes and the corresponding growth rates and how they vary with Re, P, the shear and the strength of stratification.

A Direct Numerical Study of Transport and Anisotropy in a Stably Stratified Turbulent Flow with Uniform Horizontal Shear

Direct numerical simulations of homogeneous turbulence in stably stratified shear flow have been performed to aid the understanding of turbulence and turbulent mixing in geophysical flow. Two cases are compared. In the first case, which has been studied in the past, the mean velocity has vertical shear and the mean density is vertically stably stratified. In the second case, which has not been studied systematically before, the mean velocity has horizontal shear and the mean density is again vertically stably stratified. The critical value of the gradient Richardson number, for which a constant turbulence level is obtained, is found to be an order of magnitude larger in the horizontal shear case. The turbulent transport coefficients of momentum and vertical mass transfer are also an order of magnitude larger in the horizontal shear case. The anisotropy of the turbulence intensities are found to be in the range expected of flows with mean shear with no major qualitative change in the range of Richardson numbers studied here. However, the anisotropy of the turbulent dissipation rate is strongly affected by stratification with the vertical component dominating the others.