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Note that the inertia force is in front of the phase of the drag force: the flow velocity is a sine wave, while the local acceleration is a cosine wave as a function of time. In fluid dynamics the Morison equation is a semi-empirical equation for the inline force on a body in oscillatory flow.
f is the source function (driving force), u is the displacement vector. By using ∇ × (∇ × u) = ∇(∇ ⋅ u) − ∇ ⋅ ∇ u = ∇(∇ ⋅ u) − ∆u, the elastic wave equation can be rewritten into the more common form of the Navier–Cauchy equation. Note that in the elastic wave equation, both force and displacement are vector ...
A shock wave is a type of propagating disturbance. When a wave moves faster than the local speed of sound in a fluid, it is a shock wave. Like an ordinary wave, a shock wave carries energy and can propagate through a medium; however, it is characterized by an abrupt, nearly discontinuous change in pressure, temperature and density of the medium ...
The phase velocity is the rate at which the phase of the wave propagates in space. The group velocity is the rate at which the wave envelope, i.e. the changes in amplitude, propagates. The wave envelope is the profile of the wave amplitudes; all transverse displacements are bound by the envelope profile.
A linearly polarized electromagnetic plane wave propagating parallel to the z-axis is a possible solution for the electromagnetic wave equations in free space. The electric field, E, and the magnetic field, B, are perpendicular to each other and the direction of propagation. Maxwell's equations can be combined to derive wave equations.
Like all waves, mechanical waves transport energy. This energy propagates in the same direction as the wave. A wave requires an initial energy input; once this initial energy is added, the wave travels through the medium until all its energy is transferred. In contrast, electromagnetic waves require no medium, but can still travel through one.
Mathematically, the simplest kind of transverse wave is a plane linearly polarized sinusoidal one. "Plane" here means that the direction of propagation is unchanging and the same over the whole medium; "linearly polarized" means that the direction of displacement too is unchanging and the same over the whole medium; and the magnitude of the displacement is a sinusoidal function only of time ...
This wind wave model generates forecasts of wave conditions through the use of wave-action conservation and the wind-field forecasts (from weather forecasting models). [1] In continuum mechanics, wave action refers to a conservable measure of the wave part of a motion. [2] For small-amplitude and slowly varying waves, the wave action density is ...