Vphi

Vphi, often written as Vφ or vφ, denotes the azimuthal component of a vector in cylindrical coordinates (r, φ, z). It describes motion in the tangential direction around the z-axis and is a standard quantity in fields that model rotation and swirling flows, such as fluid dynamics, plasma physics, and astrophysics.

The velocity field is usually expressed as V = V_r e_r + V_φ e_φ + V_z e_z, with e_r and e_φ the radial and azimuthal unit vectors. The component V_φ can be related to Cartesian components by V_φ = -V_x sinφ + V_y cosφ. The relations V_r = V_x cosφ + V_y sinφ and the inverse V_x = V_r cosφ - V_φ sinφ, V_y = V_r sinφ + V_φ cosφ also hold.

In astronomy and geophysics, v_φ is used to characterize rotational speeds, such as the circumferential velocity in galaxies, accretion disks, or atmospheric and oceanic flows around an axis. In programming and data analysis, Vφ is a common variable name representing the azimuthal velocity component in simulations or plots. See also the concepts of phi (angle), cylindrical coordinates, velocity components, and vector fields.