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If the bluff structure is not mounted rigidly and the frequency of vortex shedding matches the resonance frequency of the structure, then the structure can begin to resonate, vibrating with harmonic oscillations driven by the energy of the flow. This vibration is the cause for overhead power line wires humming in the wind, [1] and for the ...
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 ...
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 ...
An example for an eddy is a vortex which produces such deviation. However, there are other types of eddies that are not simple vortices. For example, a Rossby wave is an eddy [3] which is an undulation that is a deviation from mean flow, but does not have the local closed streamlines of a vortex.
Turbulence kinetic energy is then transferred down the turbulence energy cascade, and is dissipated by viscous forces at the Kolmogorov scale. This process of production, transport and dissipation can be expressed as: D k D t + ∇ ⋅ T ′ = P − ε , {\displaystyle {\frac {Dk}{Dt}}+\nabla \cdot T'=P-\varepsilon ,} where: [ 1 ]
The main physical phenomenon of the vortex tube is the temperature separation between the cold vortex core and the warm vortex periphery. The "vortex tube effect" is fully explained with the work equation of Euler, [3] also known as Euler's turbine equation, which can be written in its most general vectorial form as: [4]
Continuous vortex sheet approximation by panel method. Roll-up of a vortex sheet due to an initial sinusoidal perturbation. Note that the integral in the above equation is a Cauchy principal value integral. The initial condition for a flat vortex sheet with constant strength is (,) =. The flat vortex sheet is an equilibrium solution.