Microbubble drag reduction (MBDR) is an effective method to improve the efficiency of fluid systems. MBDR is a field that has been extensively studied in the past, and experimental values of up to 80% to 90% drag reduction have been obtained. The effectiveness and simplicity of MBDR makes it a viable method for real world applications, particularly in naval applications where it can reduce the drag between the surface of ships and the surrounding water. A two dimensional single phase model was created in ANSYS Fluent to effectively model the behavior of bubble laden flow over a flat plate. This model was used to analyze the effectiveness of MBDR based on the following factors: Reynolds number, types of gas injected, upstream flow velocity, upstream fluid type, density ratio, flow rate of injected gas, using air as the upstream injected fluid.
This study aims to advance our understanding of the inner-core dynamics of tropical cyclones (TCs) from the perspective of vortex Rossby waves (VRWs) through investigating wave kinematics, propagation feature, and wave-mean-flow interaction in three dimensional TC-like baroclinic vortices. Using the Wenzel-Kramers-Brillouin analysis in the asymmetric balanced model framework, the generalized wave dispersion relation, group velocities, and stagnation radius/height of VRW wave-packets in both pseudo-height and isentropic coordinates are derived. It is found that the VRW dispersion relation associated with baroclinic vortices in an isentropic coordinate has the same format as that of barotropic vortices in a pseudo-height coordinate. However, baroclinicity causes the vertical wavenumber to increase, resulting in wave propagation features different from those in barotropic vortices. The stagnation radius and height are strictly constrained by the geometry of the 'critical’ surface determined by the initial properties of wave-packets and basic-state vortices. Baroclinicity substantially promotes the vertical propagation of VRWs but suppresses the corresponding wave radial propagation under the constraint of the ‘critical’ surface. Asymmetries excited at the surface are trapped in the low layer with substantial radial propagation, whereas the waves excited in the low to mid-troposphere in the vortex inner-core region can effectively propagate upward but their radial propagation is suppressed. Only low azimuthal wavenumber asymmetries can have meaningful radial and vertical propagation.
The theoretical prediction of wave kinematics is confirmed by the non-hydrostatic simulations performed by the Weather Research and Forecasting (WRF) model. The WRF simulations show that the VRWs in baroclinic vortices can be classified into a surface quasi-barotropic regime and an upper baroclinic regime. The distinct wave kinematics in these two regimes results in different wave-mean-flow interaction. The former causes a strong vortex spin-up just outside the center of the initial asymmetry similar to those in barotropic vortices, whereas the latter confines the mean angular momentum inside the center of initial asymmetry but substantially supports the upward transport of angular momentum. The vortex intensification in baroclinic vortices is shown to be governed by the tilting of wave phase, the radial and vertical eddy momentum fluxes, and the vortex symmetric response to asymmetric momentum forcing.