Atmospheric Boundary Layer and Turbulence

1.1 Definition of the Atmospheric Boundary Layer:

(3 sentences)

The lowest region of the Troposphere where interactions between the surface and atmosphere induce turbulent responses within an hour or less timescale.

Turbulent responses exchange of heat, moisture, mass, and momentum (HMMM) caused by frictional drag, ET, heat transfer, pollutants, or terrain-induced flow modification.

The variation in Boundary Layer (BL) vertical depth are influenced by surface properties and roughness, latitude, diurnal variations, and seasonality.

1.2 Wind and Flow

(5 sentences)

The winds found in the BL can be classified as the mean wind, turbulence, and waves which can all exist simultaneously in the BL.

Mean wind dominates horizontally and is responsible for sharp horizontal transport, the vertical mean winds component is much smaller.

The perturbations compose of turbulence and waves are defined as deviations from the mean.

Turbulence dominates vertically, waves are effective transport of momentum and energy, but poor transport of scalar properties (heat, humidity, and mass).

There are two mathematical terms arise when studying mean wind and perturbation: nonlinear where variables interact with turbulence $\overline{u'w'}$, or linear where variables interact with waves $\bar{U}{u'}$.

1.3 Turbulent Transport

(2 sentences)

Turbulence is several orders of magnitude more efficient at transporting properties than molecular diffusivity, allowing expeditious response within the BL to surface forcings. Different size eddies of irregular swirling motion superimposed on the mean wind generated by solar heating (thermals), frictional drag (wind shear), or obstacles (turbulent wakes).

1.4 Taylor's Hypothesis

(2 sentences)

Taylor’s hypothesis is only when turbulent intensity is small relative to mean wind speed, the mean wind can be used to calculate turbulence as a function of time.

Taylor's simplification useful for cases where turbulent eddies temporal evolution takes longer than the time eddy advect past a sensor.

1.5 Virtual Potential Temperature

Explain why it’s used.

(6 sentences)

Two categories of turbulence exists, mechanical turbulence generated by mean wind, and convective turbulence generated by buoyancy.

WV is less dense than air, any pedigree of unsaturated moist air is more buoyant than pure dry air if temperature and pressure kept constant.

Liquid water aloft brought about through phase changes introduce density variations (water loading) which causes a downward force and thus expansion of VT definition to include liquid water mixing ratio: $T_{v}=T(1+0.61q+l)$
Turbulent environments shift air parcels (sat or unsat) across pressure levels, changing actual temperature and $T_v$, which is computationally difficult.

Consider the parcel moving adiabatically through Virtual Potential Temperature eliminates changes in pressure levels. $\theta_v = \theta (1+0.61q)$

In unsaturated air, $\theta_v$ indicates if enough moisture triggers convective turbulence. In saturated air, $\theta_v$ indicates if rain + cloud weight will cause downdraft (sinking motion) regardless if air is warm (positively buoyant).

1.5 Virtual Potential Temperature

Problem. Given a temperature at $25 \degree$ C and a mixing ratio of $q=20$ g/kg measured at a pressure of 90 kPa (900 mb), find the virtual potential temperature.

Discuss findings (1 sentences).

$\theta = T(p_0/p)^(0.286) = (273.15+25)(100/90)^(0.286) = 307.28$ K

$\theta_v = \theta(1+0.61q) = 307.28(1+0.61(20 \cdot 10^{-4})) = 311.03$ K
Notice that we needed to convert to Kelvin and kg/kg!!!

Moisture acts like heat, helping the parcel rise until it condenses and WV becomes liquid beginning the water loading processes and shrinking the 4 K advantage.

1.6 Depth and Structure:

ABL depth over oceans

(4 sentences)

Over oceans, with high heat capacity of water and constant mixing of sea surface, the ABL depth varies slowly spatially and temporally compared to terrestrial layers.

As an air mass moves over a sea surface with different temperatures, it undergoes modification until reaching equilibrium with the SST.

Once this steady state is reached, the ABL depth is very uniform and typically varies by 10% over horizontal distances of 1000 km.

This steady state is interrupted by oceanic fronts where sharp SST cause rapid changes in forcings and ABL depth.

1.6 Depth and Structure:

ABL Sublayers and only surface layer

(2 sentences)

BL Sublayers are defined by how they modify vertical property fluxes.

The surface layer experiences constant vertical HMMM fluxes with height.

1.6 Depth and Structure:

Mixed Layer

(6 sentences)

Mixed Layer experiences turbulent vertical fluxes, either mechanical or convective in nature.

Depth growth through entrainment reaching maxima in the afternoon, convective turbulence from surface surface heat flux (warm upward thermals) and cloud top radiative cooling (cool downward thermals) which can occur simultaneously.

The mean virtual PT, mixing ratio, and momentum are independent of height due to vigorous turbulent mixing, however HMMM fluxes can differ directionally.

In the presence of daytime convection, momentum is transported downward, while heat / moisture fluxes are transported upward.

ML wind speeds are sub geostrophic crossing isobars at a small angle towards LP.

The mean MR along with PT identify the ML top, and in the event thermals with sufficient moisture reach the LCL, clouds form.

1.6 Depth and Structure:

Entrainment Zone

(3 sentences)

The entrainment zone is a transition between boundary layer air and free atmospheric air, and sharp changes in HMMM properties: mixing ratio decreases, and PT increases, while the magnitude of heat, moisture, momentum fluxes by turbulence decrease.

Free atmospheric air (mass) can be incorporated into the BL.

A stable layer (temperature inversion) which restraints thermal turbulence and traps pollutants, its name is from the entrainment (capture) of FA dry air into the ABL.

Concept

Richardson Number

(1 equation, 2 main points, 3 scenarios, 8 sentences)

• Turbulence indicator

• Stability Index
  $Ri = \frac{g}{T_0} \frac{\frac{\partial \theta_v}{\partial z}}{\left(\frac{\partial U}{\partial z}\right)^2}$

There are different scenarios resulting from changes stability (numerator) and mechanical shear (denominator):

• Ri = 0 indicates neutral stability and the presence of mechanical turbulence. Air flow is turbulent.

• Ri < 0 indicate an unstable environment produced either by mechanical turbulence and convection, or dominate presence of convection. Wind flow in the BL with negative Ri is turbulent.

• 0 < Ri < 0.25 where 0.25 is the critical threshold defines the largest value for a Ri where air flow is still classified as turbulent. Positive Richardson numbers indicate stable environments, and typical values can range from 0.1 - 10. As Richard number value increases, mechanical turbulence is weakening and stratification intensifies, resulting in inhibition of vertical mixing.

1.6 Depth and Structure:

Residual Layer

(2 sentences)

Thirty minutes before sunset, terrestrial cooling due to OLR cools the surface faster than near-surface air, resulting in very stable boundary layer, suppression of turbulence HMMM fluxes begins which mechanically uncouple the surface from the former ML.

Processes in this neutrally stratified layer are guided by the mean wind speed (advection), and depending on moisture content retained in RL, moisture could be used as a passive tracer since RL VPT remain nearly adiabatic.

Concept

Dalton’s Laws

(3 sentences)

Dalton's Laws state:

1) each gas obeys its own equation of state,

2) each gas completely occupies the volume at the temperature of the mixture,

3) the total pressure of the mixture of gasses is the sum of all partial pressures of individual gases.

Concept

Gas Constant

(2 sentences)

The specific gas constant signifies how much energy per kg and degree of the specific gas.

The universal gas constant is 8314.3 J/(K mol), dry air gas constant is 287 J/(K kg), and water vapor gas constant is 461 J/(K kg).

Concept

First Law of Thermodynamics

(2 equations, 2 sentences)

The conservation of energy for a thermodynamic system. Head added to a system is equal to the change of Internal energy of system and the work done by the system.

$$dh = du +dw \rightarrow \text{ Or} \rightarrow dq = du +dw$$