Direct numerical simulation of stationary homogeneous stratified sheared turbulence

Abstract

Using direct numerical simulation, we investigate stationary and homogeneous shear-driven turbulence in various stratifications, ranging from neutral to very stable. To attain and maintain a stationary flow, we throttle the mean shear so that the net production stays constant for all times. This results in a flow that is characterized solely by its mean shear and its mean buoyancy gradient, independent of initial conditions. The method of throttling is validated by comparison with experimental spectra in the case of neutral stratification. With increasing stratification comes the emergence of vertically sheared large-scale horizontal motions that preclude a straightforward interpretation of flow statistics. However, once these motions are excluded, simply by subtracting the horizontal average, the underlying flow appears amenable to the standard methods of turbulence analysis. It is shown that a direct acknowledgement of the confining influence of the periodic simulation box can lead to a meaningful physical interpretation of the large scales. Once an appropriate confinement scale is identified, many features, including horizontal spectra, flux–gradient relationships and length scales, of stratified sheared turbulence can be readily understood, both qualitatively and quantitatively, in terms of Monin–Obukhov similarity theory. Finally, the similarity-theory framework is used to interpret the scaling of the vertical diapycnal diffusivity in stratified turbulence.

Analyses of external and global intermittency in the logarithmic layer of Ekman flow

“…Implications for parameterizing turbulence in the atmospheric boundary layer Our findings with regards to the turbulence structure under strong stratification have implications for the parameterization of exchange coefficients in the stable boundary layer. In agreement with previous work on the boundary layer and canonical flow configurations under stable stratification (Flores & Riley 2011;Brethouwer et al 2012;Chung & Matheou 2012;Deusebio, Caulfied & Taylor 2015), the present results show that the absence of turbulence in extended regions of flow, even close to the surface, is a ubiquitous phenomenon under very strong stratification. Once turbulence cannot be fully sustained, the turbulent area fraction and the relative size of the non-turbulent region is determined by the stratification strength, which is most appropriately parameterized in terms of the Obukhov length expressed in wall units L + O (Flores & Riley 2011;Deusebio et al 2015).…”

Turbulent Winds and Temperature Fronts in Large-Eddy Simulations of the Stable Atmospheric Boundary Layer

“…Finally, a comparison of the wind, temperature, and Richardson number profiles from simulations B and Bw are nearly identical; this demonstrates that the smaller computational domain 400 3 m is adequate for capturing the largest scales of motion in our SBL and that the solution mesh sensitivity is due entirely to small scales. DNS of stratified homogeneous shear flow show a dependence on the computational domain size (Chung and Matheou 2012) and large scales are also reported in DNS of a stably stratified Ekman layer with zero buoyancy gradient aloft by Ansorge and Mellado (2014). We believe that their results are a consequence of the problem posing; these DNS do not contain a stably stratified capping inversion or a LLJ.…”

“…In our simulations, n t decreases by more than a factor of 8.5 and the standard deviation of the spatial temperature gradients increases by more than a factor of 5 as the mesh varies from D 5 2 to 0.39 m. A sensitivity of the frontal width to viscosity is supported to a limited extent by the measurements of decaying turbulence by Tong and Warhaft (1994), who find that their passive scalar fronts become sharper and more intense as the molecular Reynolds number increases (Warhaft 2000, p. 215). We are aware that warm-cool temperature fronts are also found in idealized low-Re direct numerical simulations of homogeneous shear flows (no walls); for example, see Gerz et al (1994), Warhaft (2000), and Chung and Matheou (2012). The warm-cool fronts found here are cousins to those in homogeneous shear flows but differ because of the presence of a rough wall, the vertically varying stratification N 2 , and the presence of a stably stratified capping inversion.…”

“…Their temperature front appears to be part of the family of clifframp structures observed by Thorpe and Hall (1980) in a lake under moderate wind conditions and by Gao et al (1989) above a forest under slightly unstable conditions. Chung and Matheou (2012) also find clifframp fronts in direct numerical simulations (DNS) of stably stratified shear flow with no solid boundaries; their flow visualization also reveals that the fronts tilt farther forward (or downstream) and can become intermittent with increasing stratification. The dynamics behind the cliff-ramp fronts in boundary layers is not completely explained but is possibly linked to hairpin packets found in neutral wall-bounded flows as discussed by Adrian (2007).…”

Physics of Stratocumulus Top (POST): turbulence characteristics

“…Knowing the Kolmogorov microscale allows the characterization of small-scale turbulence in TISL and CTMSL by means of buoyancy and shear Reynolds numbers, Re B and Re S (for details consult, e.g., Chung and Matheou, 2012), from the following formulas:…”