  Wave localization induced by spatial disorder is ubiquitous in physics. Here,
we study the temporal analog of such phenomenon on water waves. Our time
disordered media consists in a collection of temporal interfaces achieved
through electrostriction between water surface and an electrode. The wave field
observed is the result of the interferences between reflected and refracted
waves on the interfaces. Although no eigenmode can be associated to the wave
field, several common features between space and time emerge. The waves grow
exponentially depending on the noise level in agreement with a 2D matrix
evolution model such as in the spatial case. The relative position of the
momentum-gap appearing in the time modulated systems plays a central role in
the wave field evolution. When tuning the excitation to compensate for the
damping, transient waves, localized in time, appear on the liquid surface. They
result from a particular history of the multiples interferences produced by a
specific sequence of time boundaries.
