9 de diciembre

A flow is known as laminar when it is regular (that it does not present too many space or temporal variations), very often stationary. It acts in fact of a stable solution of the Navier-Stokes equations, with the direction where if the flow is modified, it turns over towards the laminar solution.

The Viscosité stabilizes and regularizes the flows in a general way. A fluid having an important viscosity will run out in a laminar way. A flow is characterized by its Reynolds number, who allows to make an idea of its stability: when this number is small, the flow is laminar, when it is large, the flow is in general unstable and turbulent.

The transition between the stable flows and the even turbulent unstable flows (chaotic) is an important subject of study.

The most current questions

Why a flow become does non stationary for a stationary forcing?

The study of the passage of a laminar flow to a turbulent flow when the Reynolds number increases, could be made in certain cases while being based on the dynamic system theory (junctions). Instabilities are directly associated at the end nonlinear inertial of transport by convection of the Navier-Stokes equation. The non stationary answer to a stationary excitation testifies to the nonlinear character of the dynamics of the fluids.

If Re < 1, the equation is linear because the diffusive phenomena dominate. It is about the adimensionnée form of the Navier-Stokes equation.
If Re >> 1, the equation is nonlinear because the phenomena convectifs dominate. Nonthe linearities will produce: non stationary effects for a stationary forcing, cracks of symmetries compared to the boundary conditions initial, in other terms, turbulence. This brutal change which takes place corresponds in the passing of the means of diffusive transport dominating with the means of convectif transport dominating.

Which is the mechanism of dissipation of the kinetic energy in a turbulent flow and laminar?

The tensor of the gradients speed is written as the sum of a symmetrical tensor and an antisymmetric tensor: the tensor of the rates of deformation is directly related to the kinetic dissipation of energy in the form of heat whereas the tensor of the rates of rotation is connected to the swirls. In an unspecified flow, there is a distribution of deformation (which dissipates energy) and a contribution of rotation (which does not dissipate).

Turbulence makes it possible to dissipate the kinetic energy more effectively than a laminar flow.

In turbulent mode, the kinetic energy provided to the flow with large scales (typically size of the flow) is transmitted towards the small scales by the mechanism of cascade of energy: movements whirling on the scale of the average flow are vortex generator on scales a little smaller which themselves generate movements on smaller scales etc This process of cascade of energy finishes finally when the excited movements of very small size are dissipated in heat under the effect of molecular viscosity. One can thus say, in a certain manner, that dissipation takes place by transfer of energy towards the small scales in a turbulent flow. It is not the case in laminar mode where dissipation operates directly with large scales.

How the small swirls formed are in turbulence and which is their role in dissipation?

An average flow forms small structures by the mechanism of stretching of the vorticity. These small structures correspond to the field fluctuating of the decomposition of Reynolds. Energy thus passed from the average flow towards these tubes which have strong gradients, turn quickly and are small, therefore they dissipate energy effectively.

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