Chapter 2 lecture notes

Question 1

Motion in the atmospheric boundary layer is generally

Answer 1

turbulent.

Question 2

Most turbulent flows of interest, including those in the ABL have a number of common characteristics:

Answer 2

• the flows are rotational and three dimensional (vorticity fluctuations are therefore important);
• the flows are dissipative, so that energy must be supplied to maintain the turbulence;
• (iii) the fluid motions are unpredictable in detail;
• (iv) the rates of transfer and mixing are several orders of magnitude greater than the rate of molecular diffusion

Question 3

Non-turbulent flows are called

Answer 3

laminar. In laminar flow, a perfect frictionless fluid would experience no tangential force at a boundary.

Question 4

Non-turbulent flows are called laminar. In laminar flow, a perfect frictionless fluid would experience no tangential force at a boundary.

 In contrast, a real fluid experiences

Answer 4

such tangential forces.

Question 5

Such tangential forces are also referred to as

Answer 5

shearing stresses that are related to the fluid viscosity,

Question 6

the frictional shearing stress unit

Answer 6

(frictional force per unit area) in Nm^-2

Question 7

the dynamic viscosity unit

Answer 7

kgm^-1s^-1

Question 8

If we measure the flow with a fast-responding anemometer, we will find that the velocity

Answer 8

fluctuates with time in a seemingly random manner. Air temperature, humidity, and other scalars also exhibit irregular temporal fluctuations.

Question 9

Details of the flow are

Answer 9

impossible to predict

Question 10

Details of the flow are impossible to predict. Hence

Answer 10

we quantify the mean state of the atmosphere by performing averaging operation on the atmospheric properties

Question 11

This averaging operation is called

Answer 11

block averaging

Question 12

In field observations or modeling studies, time series data are obtained at

Answer 12

discrete sampling intervals, t_f

Question 13

In field observations or modeling studies, time series data are obtained at

discrete sampling intervals, tf . This interval is

Answer 13

constant in field measurements but can be variable in modeling studies.

Question 14

A typical averaging length is

Answer 14

30 min

Question 15

a typical sampling interval is

Answer 15

0.1 s

Question 16

the molecular friction force are now expressed with

Answer 16

mean flow quantities

Question 17

The extra terms in the parentheses consist of

Answer 17

spatial derivatives of Reynolds variances (e.g., -u’²) and covariances (e.g., -𝑢’𝑣′). Like molecular friction, these terms act as retarding forces on the mean motion. Thus, a consequence of velocity fluctuations is that they slow down the air motion.

Question 18

Resulting from averaging of the nonlinear terms, such as 𝑢 𝜕𝑤⁄𝜕𝑧 , in the original equations, the Reynolds velocity covariances represent

Answer 18

turbulent momentum fluxes or transport of momentum by turbulent eddies.

Question 19

Once again, the Reynolds averaging operation has produced additional terms.

 These terms consist of

Answer 19

spatial derivatives of velocity-scalar covariances and are given in the parentheses on the right side of the equations.

Question 20

These terms consist of spatial derivatives of velocity-scalar covariances and are given in the parentheses on the right side of the equations.

 In analogy to molecular diffusion, these covariances represent

Answer 20

turbulent transport of water vapor and potential temperature

Question 21

In other words, the result of velocity and scalar fluctuations is

Answer 21

a diffusive transport of energy and materials in the atmosphere.

Question 22

Turbulent transport is one factor contributing to

Answer 22

the local time rate of change in the mean scalar quantities.

Question 23

Other contributors of the temporal change are

Answer 23

horizontal and vertical advection and molecular diffusion (1st term on the right).

Question 24

Surface boundary conditions strongly affect

Answer 24

the vertical distributions of velocity, temperature, and gaseous abundance in the atmospheric boundary layer.

Question 25

The vertical gradients of these quantities are generally

Answer 25

much larger than their horizontal gradients

Question 26

From now on, we will also ignore the molecular terms because

Answer 26

they are much smaller in magnitude than their turbulent counterparts.

Question 27

To study flow dynamics in a neutral boundary layer,

Answer 27

the two momentum equations (Eqns. 10 and 11) will suffice. I

Question 28

In neutral stability,

Answer 28

turbulence is generated by vertical wind shear, and buoyancy does not play a role.

Question 29

If the atmosphere is stratified, or if we are interested in heat and water vapor transport,

Answer 29

we will also need Eqns. 13 and 14 to account for buoyancy generation and destruction of turbulence and to quantify the transport processes.

Question 30

A fundamental challenge in the studies of turbulent flow is

Answer 30

that the number of unknowns exceeds the number of mean equations

Question 31

This closure problem arises from

Answer 31

the fact Reynolds averaging generates variances and covariances from nonlinear terms in the instant equations.

Question 32

The additional equations, called turbulence closure parameterizations, are not derived from fundamental laws of thermodynamics and physics. Rather they are

Answer 32

empirical equations

Question 33

The most common parameterization scheme relates a

Answer 33

Reynolds covariance to the spatial gradient of the relevant mean quantity.

Question 34

The free parameter in these equations, K, is termed eddy diffusivity, having the dimensions of

Answer 34

m² s^-1

Question 35

The parameterizing equations 15–18 state that the

Answer 35

strength of turbulent diffusion is proportional to the spatial gradient of the mean state quantity of interest

Question 36

The negative sign in these equations ensures that

Answer 36

the diffusion flux is directed down the gradient from a position of higher to a position of lower momentum, temperature, or gaseous concentration.

Question 37

The negative sign means a ……… typically for ………..

Answer 37

downward heat flux, from hot to cold. This is typical for statically stable ABL

Question 38

Kinetic energy is the

Answer 38

energy of motion

Question 39

These kinetic energy quantities are in dimensions of

Answer 39

m²s^-2

Question 40

To obtain kinetic energy density in the familiar SI energy units of

Answer 40

Jm^-3

Question 41

These kinetic energy quantities are in dimensions of m2s-2. To obtain kinetic energy density in the familiar SI energy units of Jm-3, we should

Answer 41

multiply them by the air density 𝜌 in kgm^-3.

Question 42

The TKE is

Answer 42

the smallest of all the energies (IE, APE, TKE and EKE) in the atmosphere.

Question 43

The total TKE in the atmospheric boundary layer is about

Answer 43

300 Jm^-2

Question 44

The TKE in the air column above the boundary layer may be probably

Answer 44

several times smaller than the TKE in the boundary layer

Question 45

…………………………… that makes the boundary layer uniquely different from the rest of the atmosphere

Answer 45

It is this small energy