  We study the effect of varying sound speed on clustering dark energy in the
Dirac-Born-Infeld (DBI) scenario. The DBI action is included in the class of
$k$-essence models, and it has an important role in describing the effective
degrees of freedom of D-branes in the string theory. In the DBI setup, we take
the anti-de Sitter (AdS) warp factor $f(\phi)=f_0\, \phi^{-4}$, and investigate
the self-interacting quartic potential $V(\phi)=\lambda\phi^{4}/4$. We
calculate the full expression of the effective sound speed for our model, and
show that it can evolve with time during the cosmological evolution. Besides,
the adiabatic sound speed evolves with time here, and this influences the
background dynamics to some extent. We show that the effective sound speed is
very close to the adiabatic sound speed. We examine the effect of the variable
sound speed on growth of the perturbations in both the linear and non-linear
regimes. In the linear regime, we apply the Pseudo-Newtonian formalism, and
show that dark energy suppresses the growth of perturbations at low redshifts.
From study the Integrated Sachs-Wolf (ISW) effect in our setup, we see that the
model manifests some deviation from the concordance $\Lambda$CDM model. In the
non-linear regime, we follow the approach of spherical collapse model, and
calculate the linear overdensity, the virial overdensity, overdensity at the
turn around and the rate of expansion of collapsed region. We further compute
relative number density of halo objects above a given mass in our setting, and
show that the number of structures with respect to the $\Lambda$CDM model is
reduced more in the high mass tail at high redshifts.
