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\title{Overview of the dynamics of the Brewer-Dobson stratospheric
  circulation}
\author{Eli, EPS281r (taken from EPS231 notes)}
\maketitle

Based on Vallis' atmosphere-ocean fluid dynamics textbook

  \begin{itemize}
  \item Zonal stratospheric circulation (Vallis Fig 13.12, and p 568):
    shortwave (SW) absorption near summer pole leads to a reversed
    temperature gradient in summer hemisphere: e.g., $T_y<0$ in
    southern hemisphere during Jan.  This leads to
    $u_z{\propto}T_y/f_0>0$ in southern hemisphere July, and using
    $u=0$ at top of stratosphere we get $u<0$ (easterlies) during
    summer (Jan) in the southern hemisphere stratosphere.  Similarly,
    $u<0$ (easterlies) during summer (July) in northern hemisphere.
  \item Winter hemisphere (northern Jan, southern July) has no SW at
    pole, temperature gradient is not reversed and winds are
    westerlies there.
  \item Rossby waves propagating vertically from the troposphere
    cannot propagate into easterlies, therefore can only reach
    stratosphere in the winter hemisphere.
  \item Brewer-Dobson stratospheric circulation: zonally averaged
    momentum balance is $-f_0\overline{v}^*=\overline{v'q'}$ (Vallis,
    eqn 13.88; $q'=\zeta'+f\partial_z(b'/N^2)$, see chapter 7.2).
    Assuming the potential vorticity flux is down gradient
    (equatorward, because the gradient is dominated by $\beta$), the
    rhs is negative, so that the mean flow $\overline{v}^*>0$ is
    poleward.
  \item B-D circulation warms the pole and cools the equator in the
    stratosphere (Vallis eqn 13.89):
    $N^2\overline{w}^*=\frac{\theta_E-\theta}{\tau}$, together with
    positive $w$ in tropics and negative in polar areas forced by
    poleward B-D meridional flow.  This leads to $\theta<\theta_E$
    (cooling!) at equator (where $\overline{w}^*>0$) and
    $\theta>\theta_E$ (warming!) at pole (where $\overline{w}^*<0$).
  \end{itemize}

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