A report on Standing wave and Hydraulic jump

Animation of a standing wave ( red ) created by the superposition of a left traveling ( blue ) and right traveling ( green ) wave
A raft encountering a hydraulic jump on Canolfan Tryweryn in Wales.
Longitudinal standing wave
Figure 2: A common example of a hydraulic jump is the roughly circular stationary wave that forms around the central stream of water. The jump is at the transition between the point where the circle appears still and where the turbulence is visible.
Transient analysis of a damped traveling wave reflecting at a boundary
Figure 3: A tidal bore in Alaska showing a turbulent shock-wave-like front. At this point the water is relatively shallow and the fractional change in elevation is large.
Standing wave in stationary medium. The red dots represent the wave nodes.
Figure 4: An undular front on a tidal bore. At this point the water is relatively deep and the fractional change in elevation is small.
A standing wave (black) depicted as the sum of two propagating waves traveling in opposite directions (red and blue).
Figure 5: Series of roll waves moving down a spillway, where they terminate in a stationary hydraulic jump.
Electric force vector (E) and magnetic force vector (H) of a standing wave.
Naturally occurring hydraulic jump observed on the Upper Spokane Falls north channel.
Standing waves in a string – the fundamental mode and the first 5 harmonics.
Saint Anthony Falls on the Mississippi River showing a pronounced hydraulic jump.
A standing wave on a circular membrane, an example of standing waves in two dimensions. This is the fundamental mode.
Supercritical flow down the Cleveland Dam spillway at the head of the Capilano River in North Vancouver, British Columbia, Canada.
A higher harmonic standing wave on a disk with two nodal lines crossing at the center.
Energy dissipation using hydraulic jump.
Kayak playing on the transition between the turbulent flow and the recirculation region in the pier wake.

Standing waves and hydraulic jumps also form on fast flowing river rapids and tidal currents such as the Saltstraumen maelstrom.

- Standing wave

When this occurs, the water slows in a rather abrupt rise (a step or standing wave) on the liquid surface.

- Hydraulic jump
Animation of a standing wave ( red ) created by the superposition of a left traveling ( blue ) and right traveling ( green ) wave

2 related topics with Alpha

Overall

Surface waves in water showing water ripples

Wave

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Propagating dynamic disturbance of one or more quantities.

Propagating dynamic disturbance of one or more quantities.

Surface waves in water showing water ripples
Example of biological waves expanding over the brain cortex, an example of spreading depolarizations.
Wavelength λ, can be measured between any two corresponding points on a waveform
Animation of two waves, the green wave moves to the right while blue wave moves to the left, the net red wave amplitude at each point is the sum of the amplitudes of the individual waves. Note that f(x,t) + g(x,t) = u(x,t)
Sine, square, triangle and sawtooth waveforms.
Amplitude modulation can be achieved through f(x,t) = 1.00×sin(2π/0.10×(x−1.00×t)) and g(x,t) = 1.00×sin(2π/0.11×(x−1.00×t))only the resultant is visible to improve clarity of waveform.
Illustration of the envelope (the slowly varying red curve) of an amplitude-modulated wave. The fast varying blue curve is the carrier wave, which is being modulated.
The red square moves with the phase velocity, while the green circles propagate with the group velocity
A wave with the group and phase velocities going in different directions
Standing wave. The red dots represent the wave nodes
Light beam exhibiting reflection, refraction, transmission and dispersion when encountering a prism
Sinusoidal traveling plane wave entering a region of lower wave velocity at an angle, illustrating the decrease in wavelength and change of direction (refraction) that results.
Identical waves from two sources undergoing interference. Observed at the bottom one sees 5 positions where the waves add in phase, but in between which they are out of phase and cancel.
Schematic of light being dispersed by a prism. Click to see animation.
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Formation of a shock wave by a plane.
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A propagating wave packet; in general, the envelope of the wave packet moves at a different speed than the constituent waves.
Animation showing the effect of a cross-polarized gravitational wave on a ring of test particles
One-dimensional standing waves; the fundamental mode and the first 5 overtones.
A two-dimensional standing wave on a disk; this is the fundamental mode.
A standing wave on a disk with two nodal lines crossing at the center; this is an overtone.

When the entire waveform moves in one direction, it is said to be a traveling wave; by contrast, a pair of superimposed periodic waves traveling in opposite directions makes a standing wave.

On the other hand, some waves have envelopes which do not move at all such as standing waves (which are fundamental to music) and hydraulic jumps.

Surfer on the Eisbach, Englischer Garten, Munich, Germany.

River surfing

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Surfer on the Eisbach, Englischer Garten, Munich, Germany.
Surfing a standing wave on the Eisbach.
Surfers on the Severn bore

River surfing is the sport of surfing either standing waves, tidal bores or upstream waves in rivers.

It is a form of hydraulic jump.