Chapter 2 lecture notes Flashcards
Motion in the atmospheric boundary layer is generally
turbulent.
Most turbulent flows of interest, including those in the ABL have a number of common characteristics:
- 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
Non-turbulent flows are called
laminar. In laminar flow, a perfect frictionless fluid would experience no tangential force at a boundary.
Non-turbulent flows are called laminar. In laminar flow, a perfect frictionless fluid would experience no tangential force at a boundary.
ļ In contrast, a real fluid experiences
such tangential forces.
Such tangential forces are also referred to as
shearing stresses that are related to the fluid viscosity,
the frictional shearing stress unit
(frictional force per unit area) in Nm-2
the dynamic viscosity unit
kgm-1s-1
If we measure the flow with a fast-responding anemometer, we will find that the velocity
fluctuates with time in a seemingly random manner. Air temperature, humidity, and other scalars also exhibit irregular temporal fluctuations.
Details of the flow are
impossible to predict
Details of the flow are impossible to predict. Hence
we quantify the mean state of the atmosphere by performing averaging operation on the atmospheric properties
This averaging operation is called
block averaging
In field observations or modeling studies, time series data are obtained at
discrete sampling intervals, tf
In field observations or modeling studies, time series data are obtained at
discrete sampling intervals, tf . This interval is
constant in field measurements but can be variable in modeling studies.
A typical averaging length is
30 min
a typical sampling interval is
0.1 s
the molecular friction force are now expressed with
mean flow quantities
The extra terms in the parentheses consist of
spatial derivatives of Reynolds variances (e.g., -uā2) and covariances (e.g., -š¢āš£ā²). 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.
Resulting from averaging of the nonlinear terms, such as š¢ šš¤āšš§ , in the original equations, the Reynolds velocity covariances represent
turbulent momentum fluxes or transport of momentum by turbulent eddies.
Once again, the Reynolds averaging operation has produced additional terms.
ļ These terms consist of
spatial derivatives of velocity-scalar covariances and are given in the parentheses on the right side of the equations.
These terms consist of spatial derivatives of velocity-scalar covariances and are given in the parentheses on the right side of the equations.
ļ In analogy to molecular diffusion, these covariances represent
turbulent transport of water vapor and potential temperature
In other words, the result of velocity and scalar fluctuations is
a diffusive transport of energy and materials in the atmosphere.
Turbulent transport is one factor contributing to
the local time rate of change in the mean scalar quantities.
Other contributors of the temporal change are
horizontal and vertical advection and molecular diffusion (1st term on the right).
Surface boundary conditions strongly affect
the vertical distributions of velocity, temperature, and gaseous abundance in the atmospheric boundary layer.
The vertical gradients of these quantities are generally
much larger than their horizontal gradients
From now on, we will also ignore the molecular terms because
they are much smaller in magnitude than their turbulent counterparts.
To study flow dynamics in a neutral boundary layer,
the two momentum equations (Eqns. 10 and 11) will suffice. I
In neutral stability,
turbulence is generated by vertical wind shear, and buoyancy does not play a role.
If the atmosphere is stratified, or if we are interested in heat and water vapor transport,
we will also need Eqns. 13 and 14 to account for buoyancy generation and destruction of turbulence and to quantify the transport processes.
A fundamental challenge in the studies of turbulent flow is
that the number of unknowns exceeds the number of mean equations
This closure problem arises from
the fact Reynolds averaging generates variances and covariances from nonlinear terms in the instant equations.
The additional equations, called turbulence closure parameterizations, are not derived from fundamental laws of thermodynamics and physics. Rather they are
empirical equations
The most common parameterization scheme relates a
Reynolds covariance to the spatial gradient of the relevant mean quantity.
The free parameter in these equations, K, is termed eddy diffusivity, having the dimensions of
m2 s-1
The parameterizing equations 15ā18 state that the
strength of turbulent diffusion is proportional to the spatial gradient of the mean state quantity of interest
The negative sign in these equations ensures that
the diffusion flux is directed down the gradient from a position of higher to a position of lower momentum, temperature, or gaseous concentration.
The negative sign means a ā¦ā¦ā¦ typically for ā¦ā¦ā¦..
downward heat flux, from hot to cold. This is typical for statically stable ABL
Kinetic energy is the
energy of motion
These kinetic energy quantities are in dimensions of
m2s-2
To obtain kinetic energy density in the familiar SI energy units of
Jm-3
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
multiply them by the air density š in kgm-3.
The TKE is
the smallest of all the energies (IE, APE, TKE and EKE) in the atmosphere.
The total TKE in the atmospheric boundary layer is about
300 Jm-2
The TKE in the air column above the boundary layer may be probably
several times smaller than the TKE in the boundary layer
ā¦ā¦ā¦ā¦ā¦ā¦ā¦ā¦ā¦ā¦ā¦ that makes the boundary layer uniquely different from the rest of the atmosphere
It is this small energy
