  Two-dimensional numerical simulations have been performed to understand the
effect of wall proximity on the vortex-induced vibrations (VIV) of an
elastically mounted circular cylinder having two degrees of freedom for gap
ratios g/D = {0.1,0.2,0.3,0.4,0.5,0.6}, where D is the cylinder diameter, and g
is the gap between the cylinder's bottom surface and the wall. Parametric
simulations have been performed using a quasi-monolithic coupled
fluid-structure interaction solver with exact interface tracking for Re = 100
and m*=10 over a range of U* to present the effect of the wall's proximity on
the vibration response, vortex structures, force dynamics, pressure
distribution, the phase between the hydrodynamic forces and displacements, and
finally different VIV branching response regimes. The numerical simulations
reveal that as the gap ratio reduces, the maximum transverse vibration
amplitude reduces, and the lock-in region widens. Periodic vortex shedding with
a single "S" vortex street has been observed for all gap ratios g/D = 0.1 to
0.6. It has also been observed that the wall proximity affects the mean lift
coefficient not only in the lock-in region but also in the pre and post lock-in
regions. In the lock-in region, the response dynamics of the vibrating cylinder
can be characterized into two branches, with the transition between the
branches marked by a sudden jump in the phase angle $\Phi$ between the lift and
transverse displacement from 0 to a value slightly greater than $\pi$. As the
gap ratio reduces, the widening of the lock-in region is accompanied by the
widening of the IInd response branch and a narrowing down of the Ist response
branch. For the gap ratio of g/D = 0.1, the Ist branch vanishes entirely. This
work is directly relevant to the design, maintenance, and fatigue life
estimation of underwater pipelines/cables laid on the seabed.
