Linear Convection Grid Dependence Problem

The figure shown below illustrates the variation of velocity after 0.4 seconds with the grid size, as the grid size increases from 21 to 81 the velocity profile start taking its original form but at a grid size of 161, the grid becomes finer some instabilities start forming and systems become unstablehttps://drive.google.com/open?id=175t4A3jXD5IysU-t_G5ntWuRhb7MokAo