  We present WASP-43b climate simulations with deep wind jets (down to 700~bar)
that are linked to retrograde (westward) flow at the equatorial day side for
$p<0.1$~bar. Retrograde flow inhibits efficient eastward heat transport and
naturally explains the small hotspot shift and large day-night-side gradient of
WASP-43b ($P_{\text{orb}}=P_{\text{rot}}=0.8135$~days) observed with Spitzer.
We find that deep wind jets are mainly associated with very fast rotations
($P_{\text{rot}}=P_{\text{orb}}\leq 1.5$~days) which correspond to the Rhines
length smaller than $2$ planetary radii. We also diagnose wave activity that
likely gives rise to deviations from superrotation. Further, we show that we
can achieve full steady state in our climate simulations by imposing a deep
forcing regime for $p>10$~bar: convergence time scale
$\tau_{\text{conv}}=10^6-10^8$~s to a common adiabat, as well as linear drag at
depth ($p\geq 200$~bar), which mimics to first order magnetic drag. Lower
boundary stability and the deep forcing assumptions were also tested with
climate simulations for HD~209458b ($P_{\text{orb}}=P_{\text{rot}}=3.5$~days).
HD~209458b simulations always show shallow wind jets (never deeper than
100~bar) and unperturbed superrotation. If we impose a fast rotation
($P_{\text{orb}}=P_{\text{rot}}=0.8135$~days), also the HD~209458b-like
simulation shows equatorial retrograde flow at the day side. We conclude that
the placement of the lower boundary at $p=200$~bar is justified for slow
rotators like HD~209458b, but we suggest that it has to be placed deeper for
fast-rotating, dense hot Jupiters ($P_{\text{orb}}\leq 1.5$~days) like
WASP-43b. Our study highlights that the deep atmosphere may have a strong
influence on the observable atmospheric flow in some hot Jupiters.
