Richtmyer-Meshkov (RM) instability occurs when one fluid is impulsively accelerated into a second fluid, such that ρ1 ρ2. This research numerically investigates RM instabilities between incompressible media, similar to the experiments reported by Niederhaus & Jacobs . A two-dimensional, finite-volume numerical algorithm has been developed to solve the variable density Navier-Stokes equations explicitly on a Cartesian, co-located grid. In previous calculations, no physical viscosity was implemented; however, small scale fluctuations were damped by the numerical algorithm. In contrast, current simulations incorporate the physical viscosities reported by Niederhaus & Jacobs  and are explicitly used. Calculations of volume fraction and momentum advections are second-order accurate in space. Unphysical oscillations due to the higher-order advection scheme are minimized through the use of a Van Leer flux limiting algorithm. An initial velocity impulse  has been used to model the impulsive acceleration history found in the experiments of Niederhaus & Jacobs . Both inviscid and viscous simulations result in similar growth rates for the interpenetration of one fluid into another. However, the inviscid simulations (i.e. no explicit viscosity) are unable to capture the full dynamics of the internal vortex structure that exists between the two fluids due to the absence of viscous effects.