Finite Difference Method in Fluid Potential Function and Velocity Calculation

There is no deterministic solution for many fluid problems but by applying analytical solutions many of them are approximated. In this study an implicit finite difference method presented which solves the potential function and further expanded to drive out the velocity components in 2D-space by applying a point-by-point swiping approach. The results showed the rotational behavior of both potential function as well as velocity components while encountering central obstacle.

3D Structure of Striations in the North Pacific

Ocean striations are composed of alternating quasi-zonal band-like flows; this kind of organized structure of currents be found in all world’s oceans and seas. Previous studies have mainly been focused on the mechanisms of their generation and propagation. This study uses the spatial high-pass filtering to obtain the three-dimensional structure of ocean striations in the North Pacific in both the z-coordinate and σ-coordinate based on 10-yr averaged SODA3 data. First, we identify an ideal-fluid potential density domain where the striations are undisturbed by the surface forcing and boundary effects. Second, using the isopycnal layer analysis, we show that on isopycnal surfaces the orientations of striations nearly follow the potential vorticity (PV) contours, while in the meridional-vertical plane the central positions of striations are generally aligned with the latitude of zero gradient of the relative PV. Our analysis provides a simple dynamical interpretation and better understanding for the role of ocean striations.

Swimming, flying, and diving behaviors from a unified 2D potential model

Animals swim in water, fly in air, or dive into water to find mates, chase prey, or escape from predators. Even though these locomotion modes are phenomenologically distinct, we can rationalize the underlying hydrodynamic forces using a unified fluid potential model. First, we review the previously known complex potential of a moving thin plate to describe circulation and pressure around the body. Then, the impact force in diving or thrust force in swimming and flying are evaluated from the potential flow model. For the impact force, we show that the slamming or impact force of various ellipsoid-shaped bodies of animals increases with animal weight, however, the impact pressure does not vary much. For fliers, birds and bats follow a linear correlation between thrust lift force and animal weight. For swimming animals, we present a scaling of swimming speed as a balance of thrust force with drag, which is verified with biological data. Under this framework, three distinct animal behaviors (i.e., swimming, flying, and diving) are similar in that a thin appendage displaces and pressurizes a fluid, but different in regards to the surroundings, being either fully immersed in a fluid or at a fluid interface.