Accuracy of the 2D+$t$ Approximation for Turbulent Wakes in Stratified Flows

Wakes in the ocean can be produced by a stationary object in a current or by a moving object in stationary water. When viewed in a reference frame moving with the object, the wake can persist thousands of object diameters downstream. Due to the extensive domain, an unsteady two-dimensional (2D+$t$) computation is often used to sweep downstream through the wake development. The 2D+$t$ computation approximates the development of the wake at a fixed location as an object moves past but applies cyclical boundary conditions in the streamwise direction. A Parabolized Navier-Stokes (PNS) method has the same numerical efficiency as the 2D+$t$ method but includes additional streamwise gradient terms found in the three-dimensional governing equations. The present paper investigates the accuracy of the 2D+$t$ approximation for stratified turbulent wake flows for a range of Froude numbers and Reynolds numbers. The 2D+$t$ results are compared with results from 3D Navier-Stokes computations and results from PNS computations to identify criteria at which the 2D+$t$ method will yield accurate results.