Large eddy simulations of stratified turbulence: the dynamic Smagorinsky model

Khani, Sina; Waite, Michael L.

doi:10.1017/jfm.2015.249

Cited by 33 publications

(34 citation statements)

References 41 publications

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“…'). Recent work on large eddy simulation of stratified turbulence has shown that eddy viscosity models without any explicit Ri dependence work well as long as L b is sufficiently resolved (Khani andWaite 2014, 2015).…”

Section: Discussionmentioning

confidence: 99%

Dependence of Model Energy Spectra on Vertical Resolution

Waite

2016

Monthly Weather Review

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Many high-resolution atmospheric models can reproduce the qualitative shape of the atmospheric kinetic energy spectrum, which has a power-law slope of 23 at large horizontal scales that shallows to approximately 25/3 in the mesoscale. This paper investigates the possible dependence of model energy spectra on the vertical grid resolution. Idealized simulations forced by relaxation to a baroclinically unstable jet are performed for a wide range of vertical grid spacings Dz. Energy spectra are converged for Dz & 200 m but are very sensitive to resolution with 500 m # Dz # 2 km. The nature of this sensitivity depends on the vertical mixing scheme. With no vertical mixing or with weak, stability-dependent mixing, the mesoscale spectra are artificially amplified by low resolution: they are shallower and extend to larger scales than in the converged simulations. By contrast, vertical hyperviscosity with fixed grid-scale damping rate has the opposite effect: underresolved spectra are spuriously steepened. High-resolution spectra are converged except for the stability-dependent mixing case, which are damped by excessive mixing due to enhanced shear over a wide range of horizontal scales. It is shown that converged spectra require resolution of all vertical scales associated with the resolved horizontal structures: these include quasigeostrophic scales for large-scale motions with small Rossby number and the buoyancy scale for small-scale motions at large Rossby number. It is speculated that some model energy spectra may be contaminated by low vertical resolution, and it is recommended that vertical-resolution sensitivity tests always be performed.

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Section: Discussionmentioning

confidence: 99%

Dependence of Model Energy Spectra on Vertical Resolution

Waite

2016

Monthly Weather Review

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“…Information about the dynamics of the local energy transfer is therefore lost, and in practice, the averaging procedure removes the local effect of backscatter, because the averaged c s is usually positive (e.g. [7,[9][10][11][12]). …”

Section: Introductionmentioning

confidence: 99%

“…The performance of different eddy viscosity SGS models (the Smagorinsky, dynamic Smagorinsky and Kraichnan models) has recently been studied in LES of stratified turbulence with isotropic grid resolution [10,22]. In all cases, it is shown that LES must resolve the buoyancy scale L b = 2π u rms /N to capture the fundamental large scale characteristics of stratified turbulence.…”

Section: Introductionmentioning

confidence: 99%

“…Here, u rms and N are the root-mean-square velocity and buoyancy frequency. The resolution criterion for LES of stratified turbulence depends on the SGS model: it requires ∆ < 0.47L b for the Kraichnan model, ∆ < 0.24L b for the dynamic Smagorinsky model and ∆ < 0.17L b for the regular Smagorinsky model (where ∆ is the grid spacing, [10,22]). These criteria are obtained by studying the capability of different SGS models to capture three fundamental features of stratified turbulence: layered structures that break down into Kelvin-Helmholtz (KH) instabilities and small-scale turbulence when shear is large; horizontal wavenumber energy spectra with an approximately − 5/3 power law at large scales along with a bump (or shallowness) around k b ; and the resolution of regions with small and negative Richardson number, which demonstrate the presence of KH instabilities, overturning and small-scale turbulence.…”

Section: Introductionmentioning

confidence: 99%

“…[14,15,[17][18][19][20][23][24][25][26]). The importance of L b implies that LES of stratified turbulence does not require resolution of the smaller Ozmidov scale L o = 2π (ϵ/N 3 ) 1/2 , where ϵ is the kinetic energy molecular dissipation rate [10,22]. As a result, the potential of employing LES with much coarser grids than DNS is promising.…”

Section: Introductionmentioning

confidence: 99%

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Backscatter in stratified turbulence

Khani

Waite

2016

European Journal of Mechanics - B/Fluids

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a b s t r a c tIn this paper, kinetic and potential energy transfers around a spectral test filter scale in direct numerical simulations of decaying stratified turbulence are studied in both physical and spectral domains. It is shown that while the domain-averaged effective subgrid scale energy transfer in physical space is a net downscale cascade, it is actually a combination of large values of downscale and upscale transfer, i.e. forward-and backscatter, in which the forward scatter is slightly dominant. Our results suggest that spectral backscatter in stratified turbulence depends on the buoyancy Reynolds number Re b and the filtering scale ∆ test . When the test filter scale ∆ test is around the dissipation scale L d , transfer spectra show spectral backscatter from sub-filter to intermediate scales, as reported elsewhere. However, we find that this spectral backscatter is due to viscous effects at vertical scales around the test filter. It is also shown that there is a non-local energy transfer from scales larger than the buoyancy scale L b to small scales. The effective turbulent Prandtl number spectra demonstrate that the assumption Pr t ≈ 1 is reasonable for the local energy transfer.

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Resolution and domain‐size sensitivity in implicit large‐eddy simulation of the stratocumulus‐topped boundary layer

Pedersen

Malinowski

Grabowski

2016

J Adv Model Earth Syst

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As a complement to measurements, numerical modeling facilitates improved understanding of the complex turbulent processes in the stratocumulus-topped boundary layer (STBL). Due to limited computational resources simulations are often run at too coarse resolutions to resolve details of cloud-top turbulence and potentially in computational domains too small to account for the largest scales of boundary layer circulations. The effects of such deficiencies are not fully understood. Here the influence of resolution/ anisotropy of the computational grid and domain size in under-resolved implicit large-eddy simulation of the STBL is investigated. The performed simulations are based on data from the first research flight of the DYCOMS-II campaign. Regarding cloud cover and domain-averaged liquid water path, simulations with horizontal/vertical grid spacing of 35/5 m, 70/10 m, and 105/15 m are found to agree better with measurements than more computationally expensive simulations with isotropic grid boxes, e.g., with 10/10 m or 15/15 m grid spacing. While decreasing the vertical grid spacing allows more representative simulation of the thin, turbulent, stably stratified interfacial layer between the STBL and the free troposphere, coarsening the horizontal resolution dampens vertical velocity fluctuations in this region and mimics the observed anisotropy of stably stratified small-scale turbulence near the cloud top. The size of the computational domain is found to have almost no impact on mean cloud properties. However, increasing it from 3:533:5 km 2 to 14314 km 2 does lead to the occurrence of larger coherent updraft structures. Increasing it further to 21321 km 2 shows little or no increase in the updraft size.

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Large eddy simulations of stratified turbulence: the dynamic Smagorinsky model

Cited by 33 publications

References 41 publications

Dependence of Model Energy Spectra on Vertical Resolution

Dependence of Model Energy Spectra on Vertical Resolution

Backscatter in stratified turbulence

Resolution and domain‐size sensitivity in implicit large‐eddy simulation of the stratocumulus‐topped boundary layer

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