  The Seebeck coefficient $S$ of the cuprate YBa$_{2}$Cu$_{3}$O$_{y}$ was
measured in magnetic fields large enough to suppress superconductivity, at hole
dopings $p = 0.11$ and $p = 0.12$, for heat currents along the $a$ and $b$
directions of the orthorhombic crystal structure. For both directions, $S/T$
decreases and becomes negative at low temperature, a signature that the Fermi
surface undergoes a reconstruction due to broken translational symmetry. Above
a clear threshold field, a strong new feature appears in $S_{\rm b}$, for
conduction along the $b$ axis only. We attribute this feature to the onset of
3D-coherent unidirectional charge-density-wave modulations seen by x-ray
diffraction, also along the $b$ axis only. Because these modulations have a
sharp onset temperature well below the temperature where $S/T$ starts to drop
towards negative values, we infer that they are not the cause of Fermi-surface
reconstruction. Instead, the reconstruction must be caused by the quasi-2D
bidirectional modulations that develop at significantly higher temperature.
