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THE PHENOMENON OF TURBULENCE
The phenomenon of turbulence has been studied by a number of scientists over more than 150 years. Unfortunately for most of this time he could not give a satisfactory explanation. It was not until the decade 1980-1990 that has finally begun to understand the phenomenon of turbulence in terms of chaos.
When the water of a river flowing its banks know that there are different forms of flow. If the water velocity is small, then this flow is regular; when the water passes through a rock in the river, just it surrounds it and the flow continues regularly. It is said that the flow is laminar, since its movement is as if a set of sheets of water flow over one another.
However, increasing the water reaches a certain speed when the flow becomes highly irregular. We realize that the stone skirting swirls occur. If the water velocity is much higher still, swirls appear within eddies. In these conditions the water flow is turbulent.
The initial description of these phenomena, corresponding to hydrodynamics, was made by applying Newton's laws of motion to fluids. Thus an equation was found to be nonlinear. In the literature this equation is called Navier-Stokes. As has happened with most nonlinear equations, the Navier-Stokes could not be solved exactly.
In the case where the liquid velocity is very small, the nonlinear term in the Navier-Stokes turns out to be extremely small and may not take into account, thus obtaining a linear equation, which itself has been unable to resolve. Under these conditions we are in the laminar regime. The properties of the laminar flows are obtained and are fairly well known. In fact, much of the technology based on the hydrodynamics has been developed from the solutions of the Navier-Stokes linearized.
An example of a well turbulence occurs when water is heated in an oven. As is known, if the water is allowed to warm long enough, it increases its temperature and begin to see a movement in the water, which is called convection. The cause of convection is because the portion closest to the flame heats water and therefore its volume increases. When this expansion occur, this water becomes lighter than colder water above. Therefore, cold water is heavier and moves downward, displacing the warm, which in turn moves up. Thus a circular bottom-up and top-down type movement is generated.
As the temperature continues to rise, the movement is very irregular, and when this happens, is said to have begun turbulence.
In the decade of 1980-1990 some very careful work on turbulence due to temperature variations were made. To study this phenomenon a liquid is enclosed in a small capsule and fixed temperature difference between the upper and lower surfaces of the capsule is maintained. The lower surface is maintained hotter than the top. This temperature difference causes liquid at the bottom expands, becoming lighter than the above. This starts down and the bottom up, ie, convection occurs. If the lengths of the container have well-defined values, the liquid movement is performed around cylindrical paths (Figure 34).
After a while, if not change the temperature difference between both sides, the movement is steady, which means that the rotation becomes newspaper; the liquid takes time to turn around. In this experiment measured flow time or period.
The experiment was carried out by gradually changing the temperature difference between the faces of the capsule. For each value of this difference it is wait long enough until it reaches a steady state and the period of the motion is recorded.
Figure 34. In certain circumstances the convective motion occurs in cylindrical paths.
What was found is that by increasing the temperature difference comes a time when two periods, ie appear, there are two times of rotation, and not just that, but one of the times is the same as previously, and the other has valordoble the former. This means that a phenomenon of bifurcation (see Section VIII) is presented.
To further increase the temperature difference comes another time appear four times, or four periods, ie, another fork occurs. Continuing in this way are the features discussed in Chapter VIII, on the road to chaos. We must say that in this particular case the temperature difference between the faces of the capsule is the analogue of the quantity q with which worked in equation (6) of Chapter VIII. Greater temperature difference corresponds to a larger
value of this parameter
One way which was adequately present the results was doing an analysis of periods but not frequency. In Figure 35 a succession of frequencies displayed for each fixed value of the temperature difference, that is, the q value is displayed. First, when the value of the difference is small enough, only one frequency (that is, one period); to increase this difference, there comes a time when two frequencies (Figure 35 (a)), equal to the previous and the other half just appear. To further increase the temperature difference four frequencies, the
initial, an equal half, other peer-to-quarter and another value equal to one eighth of the initial value (Figure 35 (b)) appear. If the difference in temperature continues to rise, they appear more and more frequency precisely the values associated with the branches. Finally, there comes a time when there are frequencies of all values (Figure 35 (c)). It has come to the chaotic regime. In this situation, the fluid within the turbulent regime starts. Therefore, it has been shown that turbulence is associated precisely describe the chaos in Chapter VIII.
There have been several similar experiments, with conditions that generate turbulence. The analysis of the results, from the point of view just considered, show that the turbulence is initiated when the chaos begins. The relationship between turbulence and chaos in a fluid is the subject of active research today.
EL FENOMENO DE LA TURBULENCIA
La turbulencia ha sido estudiado por un buen número de científicos a lo largo de más de 150 años, Cuando el agua de un río fluye por su cauce sabemos que existen diferentes formas de flujo. Si la velocidad del agua es pequeña, entonces este flujo es regular; al aumentar la velocidad del agua llega cierto momento en que el flujo se vuelve altamente irregular. Esto es hidrodinámico. Aplicando las leyes del movimiento de Newton a los fluidos. Las propiedades de los flujos laminares se han obtenido y se conocen bastante bien. De hecho, gran parte de la tecnología basada en la hidrodinámica. En 1980-1990 se hicieron varios trabajos muy cuidadosos sobre la turbulencia debida a variaciones de la temperatura. La superficie inferior se mantiene más caliente que la superior. Esta diferencia de temperatura causa que el líquido en la parte inferior se expanda, volviéndose más ligero que el de arriba. Éste empieza a bajar y el de abajo sube, es decir, ocurre la convección. Si no hay diferencia de temperatura entre ambas caras, el movimiento se hace estacionario. Al seguir aumentando la diferencia de temperatura llega otro momento en que parecen cuatro tiempos-turbulencias. Con condiciones que generan turbulencias. Los análisis de los resultados obtenidos, bajo el punto de vista que acabamos de considerar, indican que al iniciarse la turbulencia es cuando empieza el caos.
REFERENCIAS.
http://bibliotecadigital.ilce.edu.mx/sites/ciencia/volumen3/ciencia3/150/htm/sec_18.htm