Question

3. (6 points) Thermal wind balance (a) The horizontal equation of motion valid for large scales in isobaric coordinates can be written as \frac{d\vec{V}}{dt} = -\nabla_p \phi - f \hat{k} \times \vec{V} Starting from there, show the steps required to find the geostrophic wind \vec{V}_g and then take its vertical (pressure) derivative to derive thermal wind balance: \frac{\partial \vec{V}_g}{\partial p} = \frac{\hat{k}}{f} \times \nabla_p \frac{\partial \phi}{\partial p} = \frac{-R}{f p} \hat{k} \times \nabla_p T State the assumptions you invoke along the way. (b) Use the TWB equation to conceptually explain how we may diagnose the \"polar\" westerly jet aloft at midlatitudes. (c) Explain the difference between a barotropic and baroclinic atmosphere and what these concepts imply for vertical wind shear.

          3. (6 points) Thermal wind balance
(a) The horizontal equation of motion valid for large scales in isobaric coordinates
can be written as
\frac{d\vec{V}}{dt} = -\nabla_p \phi - f \hat{k} \times \vec{V}
Starting from there, show the steps required to find the geostrophic wind \vec{V}_g and
then take its vertical (pressure) derivative to derive thermal wind balance:
\frac{\partial \vec{V}_g}{\partial p} = \frac{\hat{k}}{f} \times \nabla_p \frac{\partial \phi}{\partial p} = \frac{-R}{f p} \hat{k} \times \nabla_p T
State the assumptions you invoke along the way.
(b) Use the TWB equation to conceptually explain how we may diagnose the \"polar\"
westerly jet aloft at midlatitudes.
(c) Explain the difference between a barotropic and baroclinic atmosphere and what
these concepts imply for vertical wind shear.

3. (6 points) Thermal wind balance
(a) The horizontal equation of motion valid for large scales in isobaric coordinates
can be written as
(dV⃗)/(dt) = -ϕ- f k̂ ×V⃗
Starting from there, show the steps required to find the geostrophic wind V⃗g and
then take its vertical (pressure) derivative to derive thermal wind balance:
(∂V⃗g)/(∂p) = (k̂)/(f) ×(∂ϕ)/(∂p) = (-R)/(f p) k̂ ×T
State the assumptions you invoke along the way.
(b) Use the TWB equation to conceptually explain how we may diagnose the p̈olarẅesterly jet aloft at midlatitudes.
(c) Explain the difference between a barotropic and baroclinic atmosphere and what
these concepts imply for vertical wind shear.

Added by Nicol-S N.

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