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Vortex-induced vibration (VIV) is an important source of fatigue damage of offshore oil exploration drilling, export, production risers, including steel catenary risers (SCRs) and tension leg platform (TLP) tendons or tethers. These slender structures experience both current flow and top-end vessel motions, which both give rise to the flow ...
Fig. 1 The vector field of two-dimensional magnetic skyrmions: a) a hedgehog skyrmion and b) a spiral skyrmion. In physics, magnetic skyrmions (occasionally described as 'vortices,' [1] or 'vortex-like' [2] configurations) are statically stable solitons which have been predicted theoretically [1] [3] [4] and observed experimentally [5] [6] [7] in condensed matter systems.
The Scruton number (Sc) is an important parameter for vortex-induced vibration (excitation) of structures, vibrations caused by rain or wind, dry inclined cable galloping, and wake galloping, the unstable airflow that forms around bridge cables and other cylindrically-structured buildings. [1]
Exact solutions to classical nonlinear magnetic equations include the Landau–Lifshitz equation, the continuum Heisenberg model, the Ishimori equation, and the nonlinear Schrödinger equation. Vortex rings are torus-shaped vortices where the axis of rotation is a continuous closed curve. Smoke rings and bubble rings are two well-known examples.
Continuous charge distribution. The volume charge density ρ is the amount of charge per unit volume (cube), surface charge density σ is amount per unit surface area (circle) with outward unit normal nĚ‚, d is the dipole moment between two point charges, the volume density of these is the polarization density P.
The vorticity equation of fluid dynamics describes the evolution of the vorticity ω of a particle of a fluid as it moves with its flow; that is, the local rotation of the fluid (in terms of vector calculus this is the curl of the flow velocity). The governing equation is:
A vortex tube is the surface in the continuum formed by all vortex lines passing through a given (reducible) closed curve in the continuum. The 'strength' of a vortex tube (also called vortex flux ) [ 11 ] is the integral of the vorticity across a cross-section of the tube, and is the same everywhere along the tube (because vorticity has zero ...
This vibration is the cause for overhead power line wires humming in the wind, [1] and for the fluttering of automobile whip radio antennas at some speeds. Tall chimneys constructed of thin-walled steel tubes can be sufficiently flexible that, in air flow with a speed in the critical range, vortex shedding can drive the chimney into violent ...