Numerical study of some neutrally and unstably stratified boundary-layer flows over a valley at small Richardson number

A unified linear viscous stability theory is developed for a certain class of stratified parallel channel and boundary-layer flows with Prandtl number equal to unity. Results are presented for plane Poiseuille flow and the asymptotic suction boundary-layer profile, which show that the asymptotic behaviour of both branches of the curve of neutral stability has a universal character. For velocity profiles without inflexion points it is found that a mode of instability disappears as η, the local Richardson number evaluated at the critical point, approaches 0.0554 from below. Calculations for Grohne's inflexion-point profile show both major and minor curves of neutral stability for 0 < η [les ] 0.0554; for\[ 0.0554 < \eta < 0.0773 \]there is only a single curve of neutral stability; and, for η > 0.0773, the curves of neutral stability become closed, with complete stabilization being achieved for a value of η of about 0·107.

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Numerical Study of Yawed Wind Turbine Under Unstable Atmospheric Boundary Layer Flows

10.1115/1.0001146v ◽

2021 ◽

Author(s):

Decheng Wan ◽

Dezhi Wei

Keyword(s):

Boundary Layer ◽

Atmospheric Boundary Layer ◽

Wind Turbine ◽

Numerical Study ◽

Boundary Layer Flows

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Inviscid vortex motions in weakly three-dimensional boundary layers and their relation with instabilities in stratified shear flows

Proceedings of the Royal Society of London. Series A: Mathematical and Physical Sciences ◽

10.1098/rspa.1993.0041 ◽

1993 ◽

Vol 440 (1910) ◽

pp. 701-710 ◽

Cited By ~ 9

Keyword(s):

Boundary Layer ◽

Boundary Layers ◽

Richardson Number ◽

Shear Flows ◽

Three Dimensional ◽

Governing Equations ◽

Boundary Layer Flows ◽

Dimensional Boundary ◽

Definition Of ◽

Inviscid Instability

In this paper we consider the inviscid instability of three-dimensional boundary-layer flows with a small crossflow over locally concave or convex walls, along with the inviscid instability of stratified shear flows. We show how these two problems are closely related through the forms of their governing equations. A proposed definition of a generalized Richardson number for the neutrally stable inviscid vortex motions is given. Implications of the similarity between the two problems are discussed.

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COEFFICIENTS OF EDDY DIFFUSION OF MOMENTUM AND HEAT IN ATMOSPHERIC BOUNDARY LAYER: NUMERICAL STUDY

Interexpo GEO-Siberia ◽

10.33764/2618-981x-2020-4-1-74-82 ◽

2020 ◽

Vol 4 (1) ◽

pp. 74-82

Author(s):

Lyudmila I. Kurbatskaya

Keyword(s):

Boundary Layer ◽

Atmospheric Boundary Layer ◽

Richardson Number ◽

Transient Flow ◽

Numerical Study ◽

Stable State ◽

Eddy Diffusion ◽

Strong Mixing ◽

Turbulent Eddy ◽

Gradient Richardson Number

The changes in turbulent eddy mixing in the atmospheric boundary layer (ABL) are investigated with the use of the mesoscale RANS turbulence model with account for effects of internal gravitational waves, which support momentum transfer under condition of very stable stratification. A focus was put on analysis of behavior of the coefficients of vertical eddy diffusion of momentum and heat. The behavior of the turbulent eddy mixing parameters was found to be consistent with measurements in the laboratory and atmosphere. In particular, the flow Richardson number () during the transient flow to a strongly stable state can behave nonmonotonically, growing with increasing gradient Richardson number () to the state of saturation at a certain gradient Richardson number ( Ri@ 1 ), which separates two different turbulent regimes: strong mixing and weak mixing.

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