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

Lee, Sungwon; Gohari, Alireza; Sarkar, Sutanu

doi:10.1017/jfm.2020.590

Cited by 7 publications

(6 citation statements)

References 66 publications

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“…We note that the intermittency profiles observed in figure 4( a ) show a remarkable resemblance to that of the intermittency observed in studies of neutrally stratified Ekman flow (Ansorge & Mellado 2014, 2016; Lee, Gohari & Sarkar 2020). In atmospheric literature such intermittency is classified as ‘external’: that is, the flow is separated into in an inner turbulent flow near the wall and an outer or external non-turbulent flow above.…”

Section: Turbulent/non-turbulent Identification Algorithmsupporting

confidence: 76%

Intermittency and critical mixing in internally heated stratified channel flow

2023

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Through direct numerical simulations we investigate the effects of spatiotemporal intermittency as a result of stable stratification in surface heated stratified open channel flow. By adapting the density inversion criterion method of Portwood et al. [J. Fluid Mech., vol. 807, 2016, R2] for our flow, we demonstrate that the flow may be robustly separated into regions of active turbulence for which $Re_B \gtrsim {O}(10)$ and surrounding quiescent fluid, where $Re_B$ is the buoyancy Reynolds number. The intermittency in the flow spontaneously manifests as a deformed horizontal interface between the upper quiescent and lower turbulent flow, characterised by vigorous mixing from ‘overturning’ shear instabilities. The resulting vertical intermittency profile is accurately predicted by a local Monin–Obukhov length normalised by viscous wall units $\varLambda ^+$ such that the flow displays intermittency within the parameter range of $2.5 \lesssim \varLambda ^+ \lesssim 260$ . By considering conditional averages of the ‘turbulent’ and ‘quiescent’ flow separately, we find the ‘turbulent’ flow within this region to be described by constant critical gradient Richardson and turbulent Froude numbers of $Ri_{g,c} \approx 0.2$ and $Fr_c \approx 0.3$ . We find that the turbulent flow continues to display a $\varGamma \sim Fr^{-1}$ relationship when $Fr < Fr_c$ , whereas the quiescent flow shows no correlation between $\varGamma$ and $Fr$ , where $\varGamma$ is the flux coefficient. Hence, we demonstrate directly that for our flow, the emergence of an asymptotic ‘saturated’ $\varGamma$ regime in the limit of a low ‘global’ $Fr$ occurs due to intermittency and increasing contributions to measurements of $\varGamma$ from the quiescent flow.

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Section: Turbulent/non-turbulent Identification Algorithmsupporting

confidence: 76%

Intermittency and critical mixing in internally heated stratified channel flow

2023

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“…The spatio‐temporal evolution of the flow is computed with the nondimensional incompressible Navier–Stokes system of equations for Newtonian fluids, in conjunction with a scalar transport equation for the buoyancy field simplified with the Boussinesq approximation. Following previous works (Coleman et al, 1992; Ansorge and Mellado, 2014; Lee et al, 2020), the equations for the stratified Ekman boundary layer (EBL) problem can be written as

\frac{\partial {u}_i}{\partial {x}_i}\kern0.5em =0,\kern1.00em

\kern-.5em \frac{\partial {u}_i}{\partial t}+\frac{1}{2}\left({u}_j\frac{\partial {u}_i}{\partial {x}_j}+\frac{\partial {u}_i{u}_j}{\partial {x}_j}\right)=\frac{1}{\mathit{\operatorname{Re}}}\frac{\partial^2{u}_i}{\partial {x}_j\partial {x}_j}-\frac{\partial p}{\partial {x}_i}+{f}_i+{e}_i^{\mathrm{g}} bR\mathrm{i},

\begin{matrix} alignleft \\ align-1 \frac{\partial b}{\partial t} + u_{j} \frac{\partial b}{\partial x_{j}} \end{matrix}

…”

Section: Problem Definitionmentioning

confidence: 83%

“…The spatio-temporal evolution of the flow is computed with the nondimensional incompressible Navier-Stokes system of equations for Newtonian fluids, in conjunction with a scalar transport equation for the buoyancy field simplified with the Boussinesq approximation. Following previous works (Coleman et al, 1992;Ansorge and Mellado, 2014;Lee et al, 2020), the equations for the stratified Ekman boundary layer (EBL) problem can be written as…”

Section: Governing Equationsmentioning

confidence: 99%

Horizontal meandering in direct numerical simulations of the stable boundary layer

Stefanello

Frantz

Acevedo

et al. 2022

Quart J Royal Meteoro Soc

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Large‐scale nonturbulent motions are investigated using high‐resolution direct numerical simulations of the turbulent Ekman layer at a moderate Reynolds number. In particular, the role of stable stratification effects in the generation and amplification of large‐scale oscillations in the wind‐speed components and buoyancy is analysed. Eulerian autocorrelation functions (EAFs) and spectral analysis help to describe and characterize such modes as meandering‐like structures. Focus is given to the strong stability cases, where vertical turbulent motions are damped and large‐scale modes drive near‐wall patterns of flow laminarization. Horizontal meandering arises in the near‐wall region when the ratio of vertical wind‐speed variance to horizontal wind‐speed variance decreases to small orders of magnitude. In the case of strong stratification, the characteristic features of meandering motion were identified as negative lobes in the EAF, with corresponding low‐frequency peaks in the horizontal wind speed and buoyancy spectra. The Ekman configuration used reproduced the development of meandering‐like structures satisfactorily in strong stable conditions, as indicated by field observations of the stable boundary layer and its dependence on the level of stratification. At strong stability, the Rotta model constant, which represents the relationship between the dissipation and return to isotropy terms in the velocity variance budget, is shown to vary with stability.

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“…Note that with this definition, the laminar and dispersive fluxes are also explicitly included in the framework, while the original MOST is based on homogeneous flow at infinite Reynolds number and therefore only includes the turbulent fluxes (Shah & Bou-Zeid 2014). Nevertheless, recent DNS studies involving heterogeneous surfaces have also incorporated laminar and (implicit) dispersive fluxes in their comparisons to MOST (Lee, Gohari & Sarkar 2020; Mironov & Sullivan 2023). Figure 7( a ) shows profiles of the local Obukhov length scale for the present simulations with .…”

Section: Resultsmentioning

confidence: 99%

Secondary flows induced by two-dimensional surface temperature heterogeneity in stably stratified channel flow

Bon,

Broos,

Cal

et al. 2023

J. Fluid Mech.

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The structure and impact of thermally induced secondary motions in stably stratified channel flows with two-dimensional surface temperature inhomogeneities is studied using direct numerical simulation (DNS). Starting from a configuration with only spanwise varying surface temperature, where the streamwise direction is homogeneous (Bon & Meyers, J. Fluid Mech., 2022, pp. 1–38), we study cases where the periodic temperature strip length $l_x/h$ (with $h$ the half-channel height) assumes finite values. The patch width ( $l_y/h =\{{\rm \pi} /4, {\rm \pi}/8$ }) and length are varied at fixed stability and two different Reynolds numbers. Results indicate that for the investigated patch widths, the streamwise development of the secondary flows depends on the patch aspect ratio ( $a=l_x/l_y$ ), while they reach a fully developed state after approximately $25l_y$ . The strength of the secondary motions, and their impact on momentum and heat transfer through the dispersive fluxes, is strongly reduced as the length of the temperature strips decreases, and becomes negligible when $a\lesssim 1$ . We demonstrate that upward dispersive and turbulent heat transport in locally unstably stratified regions above the high-temperature patches lead to reduced overall downward heat transfer. Comparison to local Monin–Obukhov similarity theory (MOST) reveals that scaled velocity and temperature gradients in homogeneous stably stratified channel flow at $Re_\tau =550$ agree reasonably well with empirical correlations obtained from meteorological data. For thermally heterogeneous cases with strips of finite length, the similarity functions only collapse higher above the surface, where dispersive fluxes are negligible. Lastly, we show that mean profiles of all simulations collapse when using outer-layer scaling based on displacement thickness.

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

Abstract: Abstract

Cited by 7 publications

References 66 publications

Intermittency and critical mixing in internally heated stratified channel flow

Intermittency and critical mixing in internally heated stratified channel flow

Horizontal meandering in direct numerical simulations of the stable boundary layer

Secondary flows induced by two-dimensional surface temperature heterogeneity in stably stratified channel flow

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