skip to main content

Title: Impact of Stratification Mechanisms on Turbulent Characteristics of Stable Open-Channel Flows

Flow over a surface can be stratified by imposing a fixed mean vertical temperature (density) gradient profile throughout or via cooling at the surface. These distinct mechanisms can act simultaneously to establish a stable stratification in a flow. Here, we perform a series of direct numerical simulations of open-channel flows to study adaptation of a neutrally stratified turbulent flow under the combined or independent action of the aforementioned mechanisms. We force the fully developed flow with a constant mass flow rate. This flow forcing technique enables us to keep the bulk Reynolds number constant throughout our investigation and avoid complications arising from the acceleration of the bulk flow if a constant pressure gradient approach were to be adopted to force the flow instead. When both stratification mechanisms are active, the dimensionless stratification perturbation number emerges as an external flow control parameter, in addition to the Reynolds, Froude, and Prandtl numbers. We demonstrate that significant deviations from the Monin–Obukhov similarity formulation are possible when both types of stratification mechanisms are active within an otherwise weakly stable flow, even when the flux Richardson number is well below 0.2. An extended version of the similarity theory due to Zilitinkevich and Calanca shows promise in predicting the dimensionless shear for cases where both types of stratification mechanisms are active, but the extended theory is less accurate for gradients of scalar. The degree of deviation from neutral dimensionless shear as a function of the vertical coordinate emerges as a qualitative measure of the strength of stable stratification for all the cases investigated in this study.

more » « less
Award ID(s):
Author(s) / Creator(s):
Publisher / Repository:
American Meteorological Society
Date Published:
Journal Name:
Journal of the Atmospheric Sciences
Page Range / eLocation ID:
p. 205-225
Medium: X
Sponsoring Org:
National Science Foundation
More Like this
  1. Abstract Direct numerical simulations are performed to compare the evolution of turbulent stratified shear layers with different density gradient profiles at a high Reynolds number. The density profiles include uniform stratification, two-layer hyperbolic tangent profile and a composite of these two profiles. All profiles have the same initial bulk Richardson number ( $$Ri_{b,0}$$ R i b , 0 ); however, the minimum gradient Richardson number and the distribution of density gradient across the shear layer are varied among the cases. The objective of the study is to provide a comparative analysis of the evolution of the shear layers in term of shear layer growth, turbulent kinetic energy as well as the mixing efficiency and its parameterization. The evolution of the shear layers in all cases shows the development of Kelvin–Helmholtz billows, the transition to turbulence by secondary instabilities followed by the decay of turbulence. Comparison among the cases reveals that the amount of turbulent mixing varies with the density gradient distribution inside the shear layer. The minimum gradient Richardson number and the initial bulk Richardson number do not correlate well with the integrated TKE production, dissipation and buoyancy flux. The bulk mixing efficiency for fixed $$Ri_{b,0}$$ R i b , 0 is found to be highest in the case with two-layer density profile and lowest in the case with uniform stratification. However, the parameterizations of the flux coefficient based on buoyancy Reynolds number and the ratio of Ozmidov and Ellison scales show similar scaling in all cases. 
    more » « less
  2. Direct numerical simulations are performed to investigate a stratified shear layer at high Reynolds number ( $Re$ ) in a study where the Richardson number ( $Ri$ ) is varied among cases. Unlike previous work on a two-layer configuration in which the shear layer resides between two layers with constant density, an unbounded fluid with uniform stratification is considered here. The evolution of the shear layer includes a primary Kelvin–Helmholtz shear instability followed by a wide range of secondary shear and convective instabilities, similar to the two-layer configuration. During transition to turbulence, the shear layers at low $Ri$ exhibit a period of thickness contraction (not observed at lower $Re$ ) when the momentum and buoyancy fluxes are counter-gradient. The behaviour in the turbulent regime is significantly different from the case with a two-layer density profile. The transition layers, which are zones with elevated shear and stratification that form at the shear-layer edges, are stronger and also able to support a significant internal wave flux. After the shear layer becomes turbulent, mixing in the transition layers is shown to be more efficient than that which develops in the centre of the shear layer. Overall, the cumulative mixing efficiency ( $E^C$ ) is larger than the often assumed value of 1/6. Also, $E^C$ is found to be smaller than that in the two-layer configuration at moderate Ri . It is relatively less sensitive to background stratification, exhibiting little variation for $0.08 \leqslant Ri \leqslant 0.2$ . The dependence of mixing efficiency on buoyancy Reynolds number during the turbulence phase is qualitatively similar to homogeneous sheared turbulence. 
    more » « less
  3. Abstract

    In this study we examined a data set of nearly two‐year collection and investigated the effects of low‐level jets (LLJ) on near‐surface turbulence, especially wind direction changes, in the nocturnal boundary layer. Typically, nocturnal boundary layer is thermally stratified and stable. When wind profiles exhibit low gradient (in the absence of LLJ), it is characterized by very weak turbulence and very large, abrupt, but intermittent wind direction changes (∆WD) in the layers near the surface. In contrast, presence of LLJs can cause dramatic changes through inducing wind velocity shears, enhancing vertical mixing, and weakening the thermal stratification underneath. Ultimately, bulk Richardson number (Rb) is reduced and weakly stable conditions prevail, leading to active turbulence, close coupling across the layers between the LLJ height and ground surface, relatively large vertical momentum and sensible heat fluxes, and suppressed ∆WD values.Rbcan be a useful parameter in assessing turbulence strength and ∆WD as well. The dependence of ∆WD onRbappears to be well defined under weakly stable conditions (0.0 < Rb ≤ 0.25) and ∆WD is generally confined to small values. However, the relationship between ΔWD andRbbreaks whenRbincreases, especiallyRb > 1.0 (very stable conditions), under which ΔWD varies across a very wide range and the potential for large ΔWD increases greatly. Our findings have provided important implications to the plume dispersion in the nocturnal boundary layers.

    more » « less
  4. Stably stratified roughness sublayer flows are ubiquitous yet remain difficult to represent in models and to interpret using field experiments. Here, continuous high‐frequency potential temperature profiles from the forest floor up to 6.5 times the canopy height observed with distributed temperature sensing (DTS) are used to link eddy topology to roughness sublayer stability correction functions and coupling between air layers within and above the canopy. The experiments are conducted at two forest stands classified as hydrodynamically sparse and dense. Near‐continuous profiles of eddy sizes (length scales) and effective mixing lengths for heat are derived from the observed profiles using a novel conditional sampling approach. The approach utilizes potential temperature isoline fluctuations from a statically stable background state. The transport of potential temperature by an observed eddy is assumed to be conserved (adiabatic movement) and we assume that irreversible heat exchange between the eddy and the surrounding background occurs along the (vertical) periphery of the eddy. This assumption is analogous to Prandtl's mixing‐length concept, where momentum is transported rapidly vertically and then equilibrated with the local mean velocity gradient. A distinct dependence of the derived length scales on background stratification, height above ground, and canopy characteristics emerges from the observed profiles. Implications of these findings for (1) the failure of Monin–Obukhov similarity in the roughness sublayer and (2) above‐canopy flow coupling to the forest floor are examined. The findings have practical applications in terms of analysing similar DTS data sets with the proposed approach, modelling roughness sublayer flows, and interpreting nocturnal eddy covariance measurements above tall forested canopies. 
    more » « less
  5. Since the generation of green and clean renewable energy is a major concern in the modern era, solar energy conversion technologies such as the solar chimney power plant are gaining more attention. In order to accurately predict the performance of these power plants, hydrodynamic instabilities that can lead to large-scale coherent structures which affect the mean flow, have to be identified and their onset has to be predicted accurately. The thermal stratification of the collector flow (resulting from the temperature difference between the heated bottom surface and the cooled top surface) together with the opposing gravity can lead to buoyancy-driven instability. As the flow accelerates inside the collector, the Reynolds number can get large enough for viscous (Tollmien-Schlichting) instability to occur. A new highly accurate compact finite difference Navier-Stokes code in cylindrical coordinates has been developed for the spatial stability analysis of such radial flows. The new code was validated for a square channel flow. Stability results for different stable and unstable Reynolds/Rayleigh number combinations were in good agreement with temporal stability simulations as well as linear stability theory. To investigate the radial flow effect, spatial stability simulations were then carried out for a computational domain with constant streamwise extent and different outflow radii. The Reynolds and Rayleigh number were chosen such that buoyancy-driven instability occured. For cases with significant radial flow effect, the spatial growth rates of the azimuthal modes were found to vary considerably in the streamwise direction. 
    more » « less