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Lettris is a curious tetris-clone game where all the bricks have the same square shape but different content. Each square carries a letter. To make squares disappear and save space for other squares you have to assemble English words (left, right, up, down) from the falling squares.
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1.(physics) a wave that is hypothesized to propagate gravity and to travel at the speed of light
mathématiques appliquées (fr)[Classe]
physics; natural philosophy[ClasseHyper.]
natural philosophy, physics[Domaine]
gravity wave (n.)
When a fluid element is displaced on an interface or internally to a region with a different density, gravity tries to restore the parcel toward equilibrium resulting in an oscillation about the equilibrium state or wave orbit. Gravity waves on an air–sea interface are called surface gravity waves or surface waves while internal gravity waves are called internal waves. Wind-generated waves on the water surface are examples of gravity waves, and tsunamis and ocean tides are others.
Wind-generated gravity waves on the free surface of the Earth's ponds, lakes, seas and oceans have a period of between 0.3 and 30 seconds (3 Hz to 0.03 Hz). Shorter waves are also affected by surface tension and are called gravity–capillary waves and (if hardly influenced by gravity) capillary waves. Alternatively, so-called infragravity waves, which are due to subharmonic nonlinear wave interaction with the wind waves, have periods longer than the accompanying wind-generated waves.
In the Earth's atmosphere, gravity waves are a mechanism for the transfer of momentum from the troposphere to the stratosphere. Gravity waves are generated in the troposphere by frontal systems or by airflow over mountains. At first, waves propagate through the atmosphere without appreciable change in mean velocity. But as the waves reach more rarefied air at higher altitudes, their amplitude increases, and nonlinear effects cause the waves to break, transferring their momentum to the mean flow.
The phase speed of a linear gravity wave with wavenumber is given by the formula
where g is the acceleration due to gravity. When surface tension is important, this is modified to
where σ is the surface tension coefficient, ρ is the density, and k is the wavenumber (spatial frequency) of the disturbance.
Since is the phase speed in terms of the angular frequency and the wavenumber, the gravity wave angular frequency can be expressed as
The group velocity of a wave (that is, the speed at which a wave packet travels) is given by
and thus for a gravity wave,
The group velocity is one half the phase velocity. A wave in which the group and phase velocities differ is called dispersive.
High tide does not occur when the moon is at its zenith, but about 6 hours later, which means the moon is always maximally out of phase with the tides that it causes. This delay is called the lunitidal interval. The main cause is that the extremely long wavelength gravity waves that transport the water don't travel fast enough to keep up with the earth's rotation. The oceans have a depth , where is the length of these waves; hence the case of propagation in shallow water applies and their speed is proportional to . These lunitidal waves travel at over 500 mph, but they would need to travel at slightly more than 1000 mph to keep up with the earth's rotation, since the equator moves 25,000 miles in 24 hours. If the oceans were four times as deep the lunitidal interval would vanish and the tides would be in phase with the moon.
Wind waves, as their name suggests, are generated by wind transferring energy from the atmosphere to the ocean's surface, and capillary-gravity waves play an essential role in this effect. There are two distinct mechanisms involved, called after their proponents, Phillips and Miles.
In the work of Phillips, the ocean surface is imagined to be initially flat (glassy), and a turbulent wind blows over the surface. When a flow is turbulent, one observes a randomly fluctuating velocity field superimposed on a mean flow (contrast with a laminar flow, in which the fluid motion is ordered and smooth). The fluctuating velocity field gives rise to fluctuating stresses (both tangential and normal) that act on the air-water interface. The normal stress, or fluctuating pressure acts as a forcing term (much like pushing a swing introduces a forcing term). If the frequency and wavenumber of this forcing term match a mode of vibration of the capillary-gravity wave (as derived above), then there is a resonance, and the wave grows in amplitude. As with other resonance effects, the amplitude of this wave grows linearly with time.
The air-water interface is now endowed with a surface roughness due to the capillary-gravity waves, and a second phase of wave growth takes place. A wave established on the surface either spontaneously as described above, or in laboratory conditions, interacts with the turbulent mean flow in a manner described by Miles. This is the so-called critical-layer mechanism. A critical layer forms at a height where the wave speed c equals the mean turbulent flow U. As the flow is turbulent, its mean profile is logarithmic, and its second derivative is thus negative. This is precisely the condition for the mean flow to impart its energy to the interface through the critical layer. This supply of energy to the interface is destabilizing and causes the amplitude of the wave on the interface to grow in time. As in other examples of linear instability, the growth rate of the disturbance in this phase is exponential in time.
This Miles–Phillips Mechanism process can continue until an equilibrium is reached, or until the wind stops transferring energy to the waves (i.e., blowing them along) or when they run out of ocean distance, also known as fetch length.
When the wavelength of a gravity wave is less than twice the depth of the ocean or lake its behavior is governed by the nonlinear Schrodinger equation and its speed is proportional to . This means that different waves can travel at different speeds. Just by chance it can happen that several peaks, traveling at different speeds arrive simultaneously at the location of an unfortunate ship. If the combined height of the different peaks is a little more than twice that of normal storm waves it is considered a rogue wave and will usually sink the ship. This is one way in which rogue waves can arise. By contrast, the more familiar sound and light waves satisfy linear differential equations, so their speed is independent of wavelength. Experiments in large tanks with wave generating machines are used with models of ships to study rogue waves. The wave machines can generate waves of several different wavelengths simultaneously, and when these wavelengths are less than twice the depth of the tank the above phenomenon can be observed.
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