Parametrizing the Energy Dissipation Rate in Stably Stratified Flows

DeMarco

2020

Environ Fluid Mech

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In this study, we explore several integral and outer length scales of turbulence which can be formulated by using the dissipation of temperature fluctuations () and other relevant variables. Our analyses directly lead to simple yet non-trivial parameterizations for both spatially-averaged and the structure parameter of temperature (C 2 T). For our purposes, we make use of high-fidelity data from direct numerical simulations of stratified channel flows.

“…Using the DNS database of the current study, Basu et al [10] recently found that = 0.23eS and = 0.63 2 w S for 0 < Ri g < 0.2 . If we insert these formulations in Eq.…”

Section: Structure Parameter Of Temperature ( C 2 T )mentioning

confidence: 54%

“…Recently, Basu et al [10] found that for 0 < Ri g < 0.2 , = 0.23eS and = 0.63 2 w S . Thus, one can easily deduce that 2 w ∕e = 0.365 .…”

Section: Appendix 1: Bolgiano-obukhov Length Scalementioning

confidence: 99%

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On the dissipation rate of temperature fluctuations in stably stratified flows

DeMarco

2020

Environ Fluid Mech

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“…We would like to point out that in the appendices of Basu et al [6,7] we have summarized the characteristics of Hunt, buoyancy, Ellison, Bolgiano, Ozmidov, and several other length scales. For brevity, we do not repeat them here.…”

Section: A Hybrid Length Scalementioning

confidence: 99%

“…1). More recently, Basu et al [7] utilized a database of direct numerical simulations and found: for 0 < Ri g < 0.2 . TKE is denoted by e .…”

Section: Energy Dissipation Ratementioning

confidence: 99%

Turbulent Prandtl number and characteristic length scales in stably stratified flows: steady-state analytical solutions

Holtslag

2021

Environ Fluid Mech

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In this study, the stability dependence of turbulent Prandtl number ($$Pr_t$$ P r t ) is quantified via a novel and simple analytical approach. Based on the variance and flux budget equations, a hybrid length scale formulation is first proposed and its functional relationships to well-known length scales are established. Next, the ratios of these length scales are utilized to derive an explicit relationship between $$Pr_t$$ P r t and gradient Richardson number. In addition, theoretical predictions are made for several key turbulence variables (e.g., dissipation rates, normalized fluxes). The results from our proposed approach are compared against other competing formulations as well as published datasets. Overall, the agreement between the different approaches is rather good despite their different theoretical foundations and assumptions.

Addressing the Grid-Size Sensitivity Issue in Large-Eddy Simulations of Stable Boundary Layers

Dai

Boundary-Layer Meteorol

Maronga

et al. 2020

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We have identified certain fundamental limitations of a mixing-length parametrization used in a popular turbulent kinetic energy-based subgrid-scale model. Replacing this parametrization with a more physically realistic one significantly improves the overall quality of the largeeddy simulation (LES) of stable boundary layers. For the range of grid sizes considered here (specifically, 1 m-12.5 m), the revision dramatically reduces the grid-size sensitivity of the simulations. Most importantly, the revised scheme allows us to reliably estimate the firstand second-order statistics of a well-known LES intercomparison case, even with a coarse grid size of O(10 m).