doc/overview/kinematic_bound.rst

f67abf1ee3 Jeff*0001 Kinematic Boundary conditions
                0002 -----------------------------
                0003
                0004 Vertical
                0005 ~~~~~~~~
                0006
                0007 at fixed and moving :math:`r` surfaces we set (see :numref:`zandp-vert-coord`):
                0008
                0009 .. math::
0bad585a21 Navi*0010    \dot{r}=0 \text{ at } r=R_{\rm fixed}(x, y)\text{  (ocean bottom, top of the atmosphere)}
f67abf1ee3 Jeff*0011    :label: fixedbc
                0012
                0013 .. math::
0bad585a21 Navi*0014    \dot{r}=\frac{Dr}{Dt} \text{ at } r=R_{\rm moving}(x, y)\text{  (ocean surface, bottom of the atmosphere)}
f67abf1ee3 Jeff*0015    :label: movingbc
                0016
                0017 Here
                0018
0bad585a21 Navi*0019 .. math:: R_{\rm moving}=R_{o} + \eta
f67abf1ee3 Jeff*0020
                ** Warning **Wide character in print at /usr/local/share/lxr/source line 1030, <$git> line 22.


0021 where :math:`R_{o}(x,y)` is the ‘:math:`r-`\ value’ (height or pressure,
                ** Warning **Wide character in print at /usr/local/share/lxr/source line 1030, <$git> line 23.


0022 depending on whether we are in the atmosphere or ocean) of the ‘moving
                ** Warning **Wide character in print at /usr/local/share/lxr/source line 1030, <$git> line 24.


0023 surface’ in the resting fluid and :math:`\eta` is the departure from
                0024 :math:`R_{o}(x,y)` in the presence of motion.
                0025
                0026 Horizontal
                0027 ~~~~~~~~~~
                0028
                0029 .. math:: \vec{\mathbf{v}}\cdot \vec{\mathbf{n}}=0
                0030    :label: noflow
                0031
                0032 where :math:`\vec{\mathbf{n}}` is the normal to a solid boundary.
                0033