Turbulent Stress Profiles Research Articles

Stress equation based scaling framework for adverse pressure gradient turbulent boundary layers

This paper provides a framework for estimating appropriate turbulent velocity scales in adverse pressure gradient turbulent boundary layers (APG TBLs) via a study of the mean stress balance. We examine the velocity scales of APG TBLs using the relationship between the Reynolds shear stress and pressure stress. It is reasoned that as distance from the wall increases the velocity scaling transitions from one dominated by the wall-shear-stress velocity scale, uτ, to a scaling dominated by the pressure stress. A velocity scale, uhyb, is proposed that varies with distance from the wall and combines the wall-shear-stress velocity with a pressure-stress-based velocity. This investigation uses new high Reynolds number (7000≲Reτ≲7800) experimental measurements, existing lower Reynolds number experimental (600≲Reτ≲2000) and computational (Reτ<700) data sets. The proposed velocity scale realizes similarity in the turbulent stress profiles to a degree that is superior to that achievable via any wall-distance-independent velocity scale when considering the full extent of the flow domain.

Direct numerical simulation of stratified Ekman layers over a periodic rough surface

Abstract

Compressible mixing layer in shock-induced separation

Unsteadiness in separated shock–boundary layer interactions have been previously analysed in order to propose a scenario of entrainment–discharge as the origin of unsteadiness. It was assumed that the fluid in the separated zone is entrained by the free shear layer formed at its edge, and that this layer follows the properties of the canonical mixing layer. This last point is addressed by reanalysing the velocity measurements in an oblique shock reflection at a nominal Mach number of 2.3 and for two cases of flow deviation ($8^{\circ }$ and $9.5^{\circ }$). The rate of spatial growth of this layer is evaluated from the spatial growth of the turbulent stress profiles. Moreover, the entrainment velocity at the edge of the layer is determined from the mean velocity profiles. It is shown that the values of turbulent shear stress, spreading rate and entrainment velocity are consistent, and that they follow the classical laws for turbulent transport in compressible shear layers. Moreover, the measurements suggest that the vertical normal stress is sensitive to compressibility, so that the anisotropy of turbulence is affected by high Mach numbers. Dimensional considerations proposed by Brown &amp; Roshko (J. Fluid Mech., vol. 64, 1974, 775–781) are reformulated to explain this observed trend.

Self-similar behavior of turbulent impinging jet based upon outer scaling and dynamics of secondary peak in heat transfer

The flow field of an impinging wall jet created by the impingement of a turbulent axisymmetric jet normal to a flat surface was characterized by the particle image velocimetry technique. Experimental data is analyzed to explore two basic features of the impinging jet: first, to bring out unexplored aspects which are responsible for secondary peak in heat transfer distribution and to understand the reason for discrepancies in the existing observations about the peaks in heat transfer. Second, to analyze the self-similarity of radial wall jet based upon outer scaling. Measurements of the cross-wise mean velocity and turbulence statistics were initially used to explain the dynamics of secondary peak. Our results show that flow separation/reattachment occurs along the surface. At the reattachment location an intense increase in crosswise velocity, normal stresses and higher mixing are evident, which would lead to a peak in heat transfer. The separation/reattachment location is further found to depend upon the specific stage of vortical structure and is a function of surface spacing. The location of maximum value of mean cross-wise velocity and normal stress is located at the intersection of inner and outer shear layers. While the maximum Reynolds shear stress location is shifted to the outer shear layer and is located between the location of maximum velocity and jet half-width. The impinging jet exhibits a self-similar behavior as evident by the collapse of mean velocity and turbulent stress profiles when scaled with appropriate parameters. The outer scaling is able to bring out the self-similar profile of mean velocity and normal stresses. However, the shear stress profile does not show the self-similar behavior by the use of outer scaling. Data in the inner shear layer show small scatter compared to the outer shear layer especially close to the surface. The results show that the outer scales are not suitable to scale the data in the inner layer. It is also observed that the presence of vortical structure in wall jet delays attainment of self-similarity and the location beyond which self-similarity is observed is a function of surface spacing. These results aid in interpretation of heat transfer behavior from a flat surface and provide comprehensive benchmark data for theoretical modeling of the flow.

Transport of magnetic flux and the vertical structure of accretion discs – II. Vertical profile of the diffusion coefficients

We investigate the radial transport of magnetic flux in a thin accretion disc, the turbulence being modelled by effective diffusion coefficients (viscosity and resistivity). Both turbulent diffusion and advection by the accretion flow contribute to flux transport, and they are likely to act in opposition. We study the consequences of the vertical variation of the diffusion coefficients, due to a varying strength of the turbulence. For this purpose, we consider three different vertical profiles of these coefficients. The first one is aimed at mimicking the turbulent stress profile observed in numerical simulations of MHD turbulence in stratified discs. This enables us to confirm the robustness of the main result of Paper I obtained for uniform diffusion coefficients that, for weak magnetic fields, the contribution of the accretion flow to the transport velocity of magnetic flux is much larger than the transport velocity of mass. We then consider the presence of a dead zone around the equatorial plane, where the physical resistivity is high while the turbulent viscosity is low. We find that it amplifies the previous effect: weak magnetic fields can be advected orders of magnitude faster than mass, for dead zones with a large vertical extension. The ratio of advection to diffusion, determining the maximum inclination of the field at the surface of the disc, is however not much affected. Finally, we study the effect of a non-turbulent layer at the surface of the disc, which has been suggested as a way to reduce the diffusion of the magnetic flux. We find that the reduction of the diffusion requires the conducting layer to extend below the height at which the magnetic pressure equals the thermal pressure. As a consequence, if the absence of turbulence is caused by the large-scale magnetic field, the highly conducting layer is inefficient at reducing the diffusion.

A method for separating shock wave motion and turbulence in LDV measurements

Two-component laser Doppler velocimetry (LDV) measurements were made in a planar, two-dimensional flow containing an unsteady oblique shock wave formed by the convergence of two supersonic streams past a thick plate. High-speed wall pressure measurements locate the shock wave and, consequently, allow separation of the effects of shock wave motion from the turbulence fluctuations in the LDV measurements of the shock-separated free shear layer. In the current flow isolating the large-scale changes in the position of the shock from the turbulence primarily reduces the experimental scatter rather than significantly changing the shapes or magnitudes of the turbulent stress profiles. Changes in the direction of shock motion do not significantly affect the mean velocity, but do affect the turbulent stresses.

Turbulence characteristics of a boundary layer over a two-dimensional bump

The turbulent flow development was examined for a two-dimensional boundary layer over a bump. The upstream boundary layer had a momentum-thickness. Reynolds number of approximately 4030. The ratios of upstream boundary layer thickness to bump height and convex radius of curvature were 1.5 and 0.06, respectively. The bump was defined by three tangential circular arcs, which subjected the flow to alternating signs of pressure gradient and surface curvature. The boundary layer grew rapidly on the downstream side of the bump but did not separate. The mean velocity profiles deviated significantly from the law of the wall above the bump. The change from concave to convex surface curvature near the leading edge triggered an internal boundary layer, as shown by knee points in the turbulent stress profiles. The internal layer grew rapidly away from the wall on the downstream side of the bump owing to the adverse pressure gradient. The effect of convex surface curvature was considered small since the flow behaviour was generally explained by the effects due to streamwise pressure gradient. A second internal layer was triggered by the change from convex to concave curvature near the trailing edge. The boundary layer recovered rapidly in the downstream section and approached typical flat-plate boundary layer behaviour at the last measurement location.

The turbulent near wake of a flat plate at low Reynolds number

Mean-velocity and turbulence measurements have been made in the turbulent near wake of a flat plate at various Reynolds numbers in order to investigate the low-Reynolds-number effects in this region. The results indicate that the low-Reynolds-number effects are significant enough to partially explain the discrepancies in the existing mean-velocity data. It has been found that, while the Reynolds-number-independent, inner-law similarity of the boundary layers continues to exist, the width of the inner wake that develops within the inner-law region scales with the outer variable. Therefore, the mean velocity near the wake centreline depends on the Reynolds number. It is conjectured that this is due to the influence of the large eddies of the outer layer on the spreading of the inner wake.Measured turbulence quantities indicate that sudden changes occurring just downstream of the trailing edge are independent of the Reynolds number, but the subsequent development of the turbulent stress profiles depends on the Reynolds number. The Reynolds shear stress and the mean-velocity profiles within the inner wake show approximate similarity.

Fundamental studies on the control of turbulent boundary layers. Computation of effects on the characteristics of boundary layers, pressure decrease near the entrance convex curvature passage, and adverse pressure gradient along the convex curvature surface.

A Simple type (Model 2) of the turbulent stress model developed by Launder, Reece and Rodi is adopted changing to a high-Reynolds-number turbulence model, to estimate the accelerated effects for double conditions: convex curvature, and adverse pressure gradient. To evaluate the accuracies of the model and the numerical computation method, the velocity profiles, turbulent stress profiles and quantities of turbulent energy production terms are calculated, and compared with the experimental values for CASE IIP. The condition CASE IIP consists of two conditions: convex curvature radius R=500mm, and weak adverse pressure gradient dcp/dx=0.2674(1/m). As a result, it is clarified that the effects of the double conditions are more accelerated than the total of the individual effects, and the boundary layers on the convex surface are highly developed.

Dynamics and thermodynamics of the ice/upper ocean system in the marginal ice zone of the Greenland Sea

Measurements were made of the ice/upper ocean system in the marginal ice zone of the Greenland Sea during a 4‐day storm in which wind blew the ice south across a frontal region, coinciding with the ice edge that had existed when the storm began. In response to wind stress of about 0.2 Pa, a turbulent boundary layer developed under the ice that exhibited marked Ekman rotation in both mean velocity (average surface speed about 0.17 m s−1, deflection angle about 33°) and turbulent stress profiles (typical Reynolds stress about 0.1 Pa). Ablation of the ice undersurface increased rapidly after crossing the surface temperature front, and the observed melt rate corresponded with direct heat flux measurements in the oceanic boundary layer, with maximum upward heat flux of about 200 W m−2. We discuss overall momentum and energy balances, interpret observed boundary layer measurements with a numerical model, and show that molecular effects are important for heat and mass transport at the hydraulically rough ice‐ocean interface. We also develop a simple model for predicting ice melt from interfacial stress and temperature and salinity of the mixed layer.

Investigation by laser Doppler anemometry of the turbulent flow around cylindrical obstacles on a rough surface

Mean flow and turbulence measurements were made in the separated region and around a vertical cylindrical obstacle submerged in a turbulent boundary layer and mounted on an irregularly rough surface. Solid cylinders and cylinders with a concentric cavity at the top were used as the isolated obstacles. The experiment demonstrated that the presence of a cavity enhanced turbulent stresses just above the cylinder. Double-peaked turbulent stress profiles could be found in the separated zone, which could be interpreted in terms of a double-vortex model.