Convective mixed layer buoyant is the driving mechanisms

turbulence is not random but organized into structures such as thermal and plumes

unstableASL

dust devils, buoyant vertical plumes convergence lines

streamwise rolls LS thermals mesoscale convetion patterns

intermittency KH and gravity waves clouds

buoyancy favor mixing in the vertical direction while shear favor mixing in the horizontal plane

Free atmosphere Entrainment zone Mixed layer (strong convective mixing bring high momentum fluids to the ground: larger surface winds as compared to the night ASL (RH, T, wind magnit. ~ constant with z) Surface layer -> dθ/dz=0 -> θmax

strong wind -> well approximated by the modified log law (MO similarity)

A super-adiabatic lapse rate occurs when the temperature decreases with height at a rate of greater than 10 degrees Celsius per kilometer. A super-adiabatic lapse rate is usually caused by intense solar heating at the surface. Especially when the winds are light and the soils are dry heat from the sun will build at the surface (all radiative heating into sensible - not latent- heat flux). A super-adiabatic lapse rate is common in the Southwest U.S. in the summer 1) skies are clear (maximum insolation), 2) wind speeds are low (limited vertical mixing) 3) soils are dry (no evaporative cooling).

moisture depends on history effects (available water in the ground) entrainment of dry air at zi force w’q’~0 at the top heat is transferred by conduction in the micro layer and by eddy/turbulent diffusion in the ASL wind gusts depends on the passage of thermal structures

wind

Plumes

coherent vertical motion of warm rising air with diameter and depth of O(ASL depth)~100m

plumes~100m

merge into thermals ~1Km

sharp trailing edge (microfront)

Plumes travel horizonthally with Uconv~ Uave|vert.plume ext This implies that at the surface plumes travel >> than the local U(z~surf) !(Taylor assumption?)+ typical inclination angle are 450 with weak winds, in the plane they show 8:1 aspect ratio ~ 70

40m

~500m

W~1m/s

450 450

450

what can we learn from the spanwise alignment of structures ?

it does have consequences on the detection of ramp-like structures as perceived by a met tower or PIV field

authors reports that 40% of the planar area in the CBL is occupied by plumes

same structure is visible tracking temperature differences

sketches & measurements of plumes

dominant convection θ*=0.33, u*=0.6

updraft

turbulence in the ramp>> w’ up to 5m/s as compared to a mean(W)~1m/s

As the plume propagates faster than the local mean velocity it entrains warm air on the diffused (leading edge) front and lift it up (updraft), creating a sharp warm trailing edge (Stull>vacuum cleaner analogy is interesting)

strong heat flux

wind planar view U,V Y

(no

rth

)

x (east)

surface convergence bands suggest upward motion / updraft curtains/ rising thermals (continuity) the scale here ~2Km is >> than plumes schematic representation of plumes

and radiative cooling structures from zi

DUST devils

u~10m/s << 100m/s (tornadoes)

diameter O(10m)

depth=O(100m)

2m/s 4m/s upw

As plumes, it travels with a mean velocity averaged over its vertical profile thus, it is much faster than the surface wind

Models for Mixed Layer growth BLACKBOARD entrainment models (messy)

warm air rising cold air downward

Thermals

vert. scale ~zi horiz. scale~1.5zi

d~100m early morning d~2Km ML in equil.

Remember the ML scaling conv. velocity scale w*=[g/θV <w’ θ’V>zi]

1/3 (z indep.) θML

* = <w’ θ’V>surf /w* ; t*=zi /w* ~ 15min

horiz. flow converg.

horiz. flow diverg.

horizontal flow convergence

horizontal flow divergence

top of the ML

just above the ASL

θ’>0 w’> 0

θ’<0 w’<0

JPDF

JPDF

thermals rising above zi and sinking down

~zi

~zi

horiz. flow converg.

horiz. flow diverg. probabilistic description of thermals

z/zi=1.13 z/zi=0.95 z/zi=0.58 z/zi=0.26

We discuss how thermal overshooting z>zi and convective penetration increased zi by entraining FA air into the ML. Moisture (and lack of moisture ) can be used as a tracer to identify sources on convective motions 1) moist air from the ASL, trapped in an upward thermal is often found at top of the ML 2) dry air entrained from FA rarely travels lower than 0.5zi

3) mixing on top of thermals provides seeding turbulence for KH / shear instabilities 4) some thermals gain most of the buoyancy from their moisture content (θV increases)

(gas->liquid->heat release->T up)

thermal core: undiluted air weak mixing

in the FA weak mixing

strong horiz. mixing due to upward warm and downward cold

Covection + shear : Horizontal Roll vortices

strong wind+surface heating -> streamwise rolls cloud streets form above the updraft regions, if surface moisture is available

rolls are visualized by clouds (i.e. vapor condensation) when cold air fronts travel over water bodies, in general clouds always suggest upward motions and humid air condensation

Mesoscale cellular convection

“ honeycomb “ cloud pattern external ring of updraft around a downdraft core

These open cells have size ~ 10-100Km and depth ~2-3 Km

aspect ratio of 10--30:1

very different with typical Rayleigh-Benard (RB) convection cells of aspect ratio ~ 1:1

The Rayleigh number controlling the heat transfer for non turbulent

flows: Ra = 𝑔∆𝜃 ℎ3

𝜃 𝜐𝜐𝜃

Δ𝜃 difference across the convective layer of depth h 𝜐, 𝜐𝜃 =molecular viscosity, thermal diffusivity. Extending this to atmospheric turbulence is not trivial: Ra indicates if heat transfer is dominated by thermal convection (Ra>>!) as opposed to conduction (Ra<<!). At high Ra , we should see convective cells (even in turb flows with eddy viscosity and diffusivity)

NASA

Entrainment zone (EZ)

Region of statistically stable air at the top of the ML where there is entrainment of FA air downward and thermal overshooting upward

The bottom of EZ is difficult to quantify: due to penetrative convection and downward entrainment of colder air the heat flux, at h0 < θ’vw’> becomes negative the top of EZ is defined by the envelope of the thermals

The average ML depth -> zi is defined as the quote where 50% of the air in the plane has FA characteristics

3 characteristics air types: 1) FA, undiluted, 2) SL, in the core of

thermals (undiluted) 3) mixture air (mixing)

KH waves The air in the entrainment zone is statistically stable, thus subjected to the shear layer instabilities related to wind shear on top of the ML layer: KH wavelength ~ O (depth of the EZ) ~ depth of the stable air layer (remember we have a density gradient!) alternatively KH waves at a smaller scale can form on top of overshooting thermals

Gravity / thermal/interface waves

1) Gravity (internal) waves induced by thermals that penetrate in the stable air of free Atm. and Entrainment Zone. As thermals advect with a vertically averaged mean velocity, at the top they travel slower than the local mean velocity U(z=zi) they act as a physical obstruction to the flow. This generate convection waves 2) the thermal waves propagating away from the source/thermal)with no wind we have 3) Interfacial wave vwave=1—4m/s; λ=5-15Km

NASA: investigating turbulence from breaking gravity waves that are generated by rapidly rising deep convection. This image from NASA's MODIS instrument shows gravity waves over the ocean. Atmospheric gravity waves (also called atmospheric internal waves) occur either when a uniform layer of air blows over a large obstacle, like a mountain or island or when rapidly rising, deep convection perturbs a stable layer from below (here). When the air hits any obstacle or is disturbed by rising convection from below generate a wave pattern. In addition , wave clouds can form as well, creating potential turbulence for aircraft.