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We describe a 2.5D MHD simulation describing the evolution of cool jetstriggered by initial vertical velocity perturbations in the solar chromosphere.We implement random velocity pulses of amplitude 20-50 km/s between 1 Mm and1.5 Mm, along with various switch-off periods between 50 s and 300 s. Theapplied vertical velocity pulses create a series of magnetoacoustic shockssteepening above TR. These shocks interact with each other in the inner corona,leading to complex localized velocity fields. The upward propagation of suchperturbations creates low-pressure regions behind them, which propel a varietyof cool jets and plasma flows. We study the transverse oscillations of arepresentative cool jet J1 , which moves up to the height of 6.2 Mm above theTR from its origin point. During its evolution, the plasma flows make the spineof jet J1 radially inhomogeneous, which is visible in the density and Alfv\'enspeed smoothly varying across the jet. The highly dense J1 supports thepropagating transverse wave of period of approximately 195 s with a phase speedof about 125 km/s. In the distance-time map of density, it is manifested as atransverse kink wave. However, the careful investigation of the distance-timemaps of the x- and z-components of velocity reveals that these transverse wavesare actually the mixed Alfv\'enic modes. The transverse wave shows evidence ofdamping in the jet. We conclude that the cross-field structuring of the densityand characteristic Alfv\'en speed within J1 causes the onset of the resonantconversion and leakage of the wave energy outward to dissipate these transverseoscillations via resonant absorption. The wave energy flux is estimated asapproximately of 1.0 x 10^6 ergs cm^{-2} s^{-1}. This energy, if it dissipatesthrough the resonant absorption into the corona where the jet is propagated, issufficient energy for the localized coronal heating.

Numerical Simulations of the Decaying Transverse Oscillations in the Cool Jet