Oceanic Rossby Waves
For example, this momentum transfer is partly responsible for the driving of the Quasi-Biennial Oscillation , and in the mesosphere , it is thought to be the major driving force of the Semi-Annual Oscillation. Thus, this process plays a key role in the dynamics of the middle atmosphere. The effect of gravity waves in clouds can look like altostratus undulatus clouds , and are sometimes confused with them, but the formation mechanism is different.
When surface tension is important, this is modified to. The gravity wave represents a perturbation around a stationary state, in which there is no velocity.
If no fluid is to leak out of the bottom, we must have the condition. The perturbed pressures are evaluated in terms of streamfunctions, using the horizontal momentum equation of the linearised Euler equations for the perturbations,. The group velocity of a wave that is, the speed at which a wave packet travels is given by. The group velocity is one half the phase velocity.
A wave in which the group and phase velocities differ is called dispersive. Gravity waves traveling in shallow water where the depth is much less than the wavelength , are nondispersive : the phase and group velocities are identical and independent of wavelength and frequency. When the water depth is h ,. 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.
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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. 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. 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. From Wikipedia, the free encyclopedia. This article is about the movement of fluids.
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