τ xz = τ measured close to the the surface (often at z=5m) these three scales represent inner unit or near wall normalization

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Colleen McCormick
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1 τ xz = τ measured close to the the surface (often at z=5m) these three scales represent inner unit or near wall normalization

2 Note that w *3 /z i is used to normalized the TKE equation in case of free convection (pp.156) Remember : for i =3, with weak wind and strong thermals we have: w2 t ~ g θ v (w θ v ): we can derive w*!

3 u * DAY DAY u * w * w * u DAY DAY * u * w * w * note that the peak of thermal activity in a clear sky day is quite consistent (14:00), while u* is expected to vary more with the wind magnitude (u* ~O(0.1)m/s, weak wind conditions)

Now we need to find an objective way to define if the turbulence is mostly generated by thermal and free convection or by wind shear TKE is not sustainable shear dominates thermals dominate Since the

4 Now we need to find an objective way to define if the turbulence is mostly generated by thermal and free convection or by wind shear TKE is not sustainable shear dominates thermals dominate Since the <w θ > term is a source or sink or turbulence in the TKE equation depending on the thermal stability, we note that: laminar flow in the stable BL will remain laminar while turbulent flow in the unstable BL will remain turbulent.

5 Static stability: in the absence of wind, air motion depends on the occurrence of thermals and convective motions. Note that to actually form thermals, a perturbation is required (such as in any unstable system). In the atmosphere thermal convection is triggered by radiative heating or surface roughness heterogeneity Statically stable air implies that denser air stays on the ground and no motion is induced. Mean shear is the driving force, but TKE is damped. Statically unstable air implies that warmer and less dense air on the ground tends to move up because of buoyancy, until locally neutral conditions are restored. Mean shear is the driving force, TKE is enhanced.

KH Instabilities : how in stable air, shear is able to induce

KH instability developing into waves that roll and brakes leading to a

6 KH Instabilities : how in stable air, shear is able to induce turbulence(dynamical not static process) lighter fluid shear denser fluid KH instability developing into waves that roll and brakes leading to a diffuse (non sharp) interface and a reduced shear Typical forcing, i.e. strong sources of shear: nocturnal jet/catabatic winds jet stream large scale vortex shedding may give rise to detached regions of decaying turbulence Timeea Vinerean

7 the static stability is defined based on the local air density gradient. Is it correct? Fig 1b: based on the local stability we would classify the center part of the mixed layer (daytime BL) as neutral However it depends on the occurrence of thermals or any other vertical motion able to perturb the conditions at which an air parcel would move from a certain vertical location. adiabatic lapse rate vs neutral stability according to the unsaturated or dry adiabatic lapse rate, the temperature of an air parcel decreases as it is moving upward (towards lower pressure regions) adiabatically (with its temperature decreasing due to expansion (change in ambient pressure eq. of state, not due to heat exchange ). So air temperature properties in static equilibrium depend on the vertical location (in the absence of other vertical motion) However if thermals form and grow below the local (z) layer I am considering, I do not have anymore a correct measure of static stability neutral stability requires an adiabatic lapse rate and the absence of buoyancy or convective motions. So we have two ways to assess local thermal stability correctly: 1) knowing the stability conditions of the whole air column 2) measuring directly the buoyancy term to quantify convective motions Figure 1

8 More ambiguities: in the convective mixed layer the rise of thermals is responsible for the constant θ v profile. Thermals keep rising and mix the air column due to excess buoyancy and inertia (in the vertical direction). Constant θ v thus is not a sufficient condition to define the neutral state the local lapse rate, therefore does not allow for a univocal definition of thermal stability. The sign of <w θ v > estimated at the surface provides a better measure of thermal stability in a static sense

9 Correct dynamic quantification of thermal stability u w <0, w θ <0 w θ =0 u w <0, w θ >0 Note : in the ASL Reynolds is high enough, so the question is on sustaining of turbulence originally proposed by Richardson R f > 1 implies that buoyancy is dampening turbulence more, as compared to how much the shear is sustaining it

10 this is an anticipation of the closure strategy, replacing turbulent fluxes e.g. <u w > with a mean flow gradient, e.g. du/dz you may remember; 1) the definition of turbulent or eddy viscosity 2) the physical understanding that strong eddies (uw correlated) form in regions of strong gradients same criterion for the flux Richardson number low Ri shear production is high high Ri temp. is stably strat (increase with z) critical value for the onset of KH waves, Rc suggests a minimum shear to destabilize a given density profile through interface perturbation

11 Bulk Richardson number R b = g θ v z θ v U 2 + V 2 usually it is defined using the two layers delimiting the air column of interest, e.g. from the ground to a given height it is a bulk or integral measure of the thermal stability regime When Bulk Richardson could be used?

12 Obukhov length scale this is a parameterized near wall TKE production to make the equation dimensionless du/dz=u * /kz, uw=u * 2 for z=l in the stable boundary layer, =1, so the destruction of TKE by buoyancy is matched by near wall TKE production. for 0 < z < L shear production sustain turbulence

day: L<0 L = u 3 θ v kg ( w θ v ) surf night: L>0 night: L>0 note that while L varies due to thermal conditions, z varies in the vertical direction: if z ~0, i.e. at the ground, z/l will be small no matter what.

13 day: L<0 L = u 3 θ v kg ( w θ v ) surf night: L>0 night: L>0 note that while L varies due to thermal conditions, z varies in the vertical direction: if z ~0, i.e. at the ground, z/l will be small no matter what. Therefore, indication for neutral conditions z/l <0.1 are matched very close to the ground where turbulence is mostly generated by shear the discontinuity is due to the change in the sign of the heat flux when the sun starts heating the ground. As <w θ > (small value during the transition) is at the denominator, the magnitude of L increases drastically (but z/l 0 near neutral) generally z/l is estimated by a sonic anemometer at a given location. That location is important

measurements: 31 log-spaced wall-normal locations 5kHz sample frequency Tmax 210 s u* estimated from Sonic anemometers

14 Experiments in the near neutral ASL Metzger et al km fetch, Predominant wind from north U(z=5m) 5 m/s δ m δ+= δu τ /ν O(10 6 ) Simultaneous hotwire measurements: 31 log-spaced wall-normal locations 5kHz sample frequency Tmax 210 s u* estimated from Sonic anemometers During evening, nearly neutral period, friction velocity, heat and momentum fluxes from sonic anemometer array SLTEST University of Utah Metzger, Klewicki Mean and fluctuating velocity profiles

L = u 3 θ v kg ( w θ v ) surf Stability in the convective boundary layer given the definition of convective velocity scale we can rewrite : z/l = k z w 3 z i u 3 in unstable conditions z/l is

15 L = u 3 θ v kg ( w θ v ) surf Stability in the convective boundary layer given the definition of convective velocity scale we can rewrite : z/l = k z w 3 z i u 3 in unstable conditions z/l is negative z/l > 1 when w * >>u * Note that the more z z i (inversion layer) the less strong w* has to be to establish dominant thermal effects over mechanical effects. normalized TKE terms during daytime E.g. for w * ~ 2u * z/l~ -8 kz/z i =-1 at z ~ z i / 4. Even for such a weak convection scale, ¾ of the mixed layer (z> z i /4 ) are dominated by buoyancy

16 Ri, Rf, z/l are essentially interchangeable, but be careful about the use of 1) surface or 2) z-dependent heat flux

18 Mean velocity profile in the Atmospheric Boundary layer Experimentally it was found that the velocity profile exhibit significant difference depending on the thermal stability Note: In log scale the mean velocity (log law) is a line

19 Thermal control in the SAFL atmospheric boundary layer neutral convective stable (Howard K.B., Chamorro L.P., Guala M. BLM 2016) Top tip stable neutral convective Bottom tip o Neutral - Stable - Convective

20 Convective Stable U/U hub

21 The shape of the mean velocity profile depends thus on thermal stability, which means that its gradient can be parameterized as a function of z/l Note that for z/l 0 (thermally neutral regime) we got back: u*/kz=du/dz leading to the log law... OK

The Stable Boundary layer

The Stable Boundary layer the statistically stable or stratified regime occurs when surface is cooler than the air The stable BL forms at night over land (Nocturnal Boundary Layer) or when warm air travels