The drag on a vertically moving grid of bars in a linearly stratified fluid

Abstract

We present the results of an investigation of the drag force on a horizontal grid of bars moving vertically through a stratified fluid. A novel approach was used to calculate the drag, based on measurements of the terminal velocity of a freely rising grid. In the homogeneous case the drag coefficient of the grid is found to be approximately constant for a range of grid-based Reynolds numbers. In the presence of a linear stratification, the drag on the grid was found to be significantly larger than in the homogeneous case. This increase is interpreted as being due to the additional buoyancy force required to displace fluid elements in the wake of the grid from their equilibrium positions. A buoyancy drag has been defined as the additional drag force due to the stratification. The buoyancy drag coefficient is relatively insensitive to grid Reynolds number Re _g=W _g M/ν and is shown to be a function of overall Richardson number Ri _o=N ² M ²/W ² _g, where N is the buoyancy frequency of the stratification, W _g is the vertical velocity of the grid, M is the grid mesh size, and ν is the kinematic viscosity of the fluid. The additional drag force varies as $Ri_{\rm{o}}^{1/2}$suggesting that, as Ri _o increases, a larger proportion of energy imparted to the fluid by the grid is initially in the form of potential energy caused by the displacement of the isopycnal surfaces. A simple model of this process is described.