1. (a) Write the expression for a horizontal wind vector in Cartesian coordinates using unit vectors i and j. Then consider the wind barb below. (b) State the wind direction using the meteorological convention (cardinal degrees), and (c) calculate the u and v components in terms of this angle. Write down the intermediate trigonometric functions. (d) Write the equation for the wind magnitude |||| in terms of u and v and state its value. Give your answers in units of m s-¹. (e) draw the wind vector.
1. (a) Write the expression for a horizontal wind vector in Cartesian coordinates using unit vectors i and j. Then consider the wind barb below. (b) State the wind direction using the meteorological convention (cardinal degrees), and (c) calculate the u and v components in terms of this angle. Write down the intermediate trigonometric functions. (d) Write the equation for the wind magnitude |||| in terms of u and v and state its value. Give your answers in units of m s-¹. (e) draw the wind vector.
Related questions
Question
Answer all parts of the questions please and ask what it is asking
Transcribed Image Text:1. (a) Write the expression for a horizontal wind vector in Cartesian coordinates using unit vectors i and
j. Then consider the wind barb below. (b) State the wind direction using the meteorological convention
(cardinal degrees), and (c) calculate the u and v components in terms of this angle. Write down the
intermediate trigonometric functions. (d) Write the equation for the wind magnitude |||| in terms of u and
v and state its value. Give your answers in units of m s-¹. (e) draw the wind vector.
2. Show that the vertical component of the pressure gradient force can be written as:
F₂
1 др
pəz
m
=
Like we did in class, include a sketch of the parcel volume and forces necessary to derive this equation (but
in the vertical direction). Write the intermediate equation F, that sums the forces on the top and bottom
of the parcel.
3. An air parcel initially at rest is subjected to a constant pressure gradient force in the x direction, as
it accelerates over some distance Ar during a time interval At. Write the relationship between force and
acceleration for this problem, considering only the pressure gradient force for now. Assume pressure only
varies in the direction and does not change in time. (a) Integrate the equation to solve for the parcel's u
velocity at the end of At. (b) Then come up with a way to write At in terms of Ax and use this expression to
solve for u in terms of the pressure difference over the distance traveled. (c) Assuming the pressure difference
is 4 hPa, estimate the value of u. (d) If pressure increases in the x direction, what is the sign of the u wind
component? Hint: If you're really stuck, you could try a different approach to find u by thinking about the
kinetic energy of the parcel and the work done by the pressure gradient force.
Fra = v
4. Using the concept of dimensional homogeneity, point out what may be confusing about the way the
frictional force equation (1.5) is written in Holton and Hakim. To do this, write out the dimensions of both
sides of the equation. It's enough to look at the x component, given below:
J²u J²u J²u
+ +
əz²
მე-2 dy²
Then, state how we have to define Fr to have the dimensions of the right hand side be the same as those
on left hand side of the equation.
5. Draw a vertical wind profile near Earth's surface that would be consistent with a frictional deceleration
of zonal wind speed according to the equation in (4) above. State why it is consistent with deceleration.
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 4 steps with 5 images
