Boundar Layer Meteorology Lecture 2

• Review chapter 1 of Garratt• Terminology and Notation Review• Some non-dimensional numbers• Reynolds Averaging

Review chapter 1 of Garratt

• Inner and outer layers (what’s with this, is the outer layer really part of the boundary layer?)

• Seasonal and geographic variations of the boundary layer’s character.

Modeled Boundary Layer Depth

Modeled Boundary Layer Depth

Observed Boundary Layer Depth

Terminology•Boundary Layer Regions:

•Surface Layer•Mixed Layer•Residual Layer•Stable (Nocturnal Boundary) Layer•Entrainment Zone•Ekman Layer (Outer Layer)•Surface Layer

Boundary Layer Regions

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Notation

• Variables: T, Tv ,, v , , q, x, y, z,

• Viscosity: = du/dy; Tkg/(m s)=Pa/s– Kinetmatic viscosity: m2/s

• Summation (Einstein) notation: see Stull handout (pp. 57-74). Note definitions of the Kronecker delta (and distinction between it and the unit vector), and the alternating unit tensor (Levi-Civita symbol) used to express the cross product.

Some Non-Dimensional Numbers

• Reynolds number: Re = VL/ – Reynolds number is ratio of acceleration (or “inertial

force”) to friction force. It governs transition to turbulence (at high Reynolds numbers , e.g. about 2300 for pipes; highly variable!).

• Richardson numbers: ratio of

– Flux

– Gradient: Ri = (g/ddz)/(du/dz)2

– Bulk

Reynolds averaging and Reynolds Stresses

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define : u = u + ′ u

u = 1t1

u dtt0

t0 +t1

∫

′ u = 0

t1 should be enough larger than t2 so that the average is independent of time.

Reynolds averaging and Reynolds Stresses

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uv = (u + ′ u )(v + ′ v )

= u v + u ′ v + ′ u v + ′ u ′ v

= u v + ′ u ′ v

∴uv = u v + ′ u ′ v

Understanding Reynolds Stress

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