It seems that the instability in fluid dynamics always accompanied with the appearence of vortex/roll structure. Is it right?

If it is wrong, please give us an example.

Thanks.

(1). I don't think so. (2). When I was an instructor at a university fluid mechanics lab, there was an experiment on laminar flow to turbulent flow in a channel. (3). In the experiment, color dye was injected in the center of the channel where the flow was initially laminar. As the dye move downstream, it will stay laminar for a distance from the entrance. Then the turbuent motion will set in rather quickly and the color dye will spread out quickly to fill the whole channel. (4). There was no organized vortex/roll structure. (5). But if you first set the laminar flow into vortex motion, after a while, it will burst into random motion and the rotating vortex will suddenly disappear. (6). Most of the time, the flow behind a cylinder will show organized vortices, and two stream mixing or edge of the jet mixing layer will also show organized vortex motion. (7). So, I would say that, organized vortex motion can later develope into turbulent flows, and turbulent flows will always display in the form of random vortex motion. But organized vortex motion can also stay laminar, if the Reynolds number is low. And in turbulent flows, you can see both the random vortices and sometimes the organized vortex structures in mean flows. (8), In the farfield of jet and wake, you will see the random vortices, but not the organized vortex. (9). In the confined boundary layer flows, such as flow between two rotating cylinders, one can see both the vortices and the development into turbulent flows. I think, the boundary conditions have a strong effect on the development of the flows and I don't know whether there is a clear cut process or steps for the flow to become turbulent. (10). And if that is the case, then the most nature way to describe the motion of the flow will be the vorticity equation, not the momentum equation. I don't have a concrete answer here. I think, it is still an open question. You are free to make any comment.

THere are different kinds of flows (e.g. two-dimensional, three-dimensional, compressible, incompressible, etc...) and therefore there are many different kinds of instabilities of flow, some with vortices, some with streamwise vortices, some with rolling vortices (cell-like) etc...

Your question is not very specific and so the answer to it cannot be specific neither.

Some flows are unstable because of an object, a boundary, in contact with the fluid. Then you have the formation of a boundary layer (sometimes itself turbulent) and the detachement of the boundary layer itself from the surface of contact induces the flow to roll (the flow in the boundary layer is slow, while away from it is fast, therefore the differential velocity induces the 'rolling' of the flow) and to form vortices (the von Karman vortex street in the wake of a cylinder for example). When the surface of contact (the boundary layer) is curved, centrifugal forces are acting and can induces a centrifugal instability. For example between concentric rotating cylinders (the Couette flow) Taylor vortices first develop, and as the instability increases (velocities increase) the flow becomes turbulent. Here you have first the formation of (Taylor) vortices and then transition to turbulence. In other cases, like in the water table experiment, an object induces difference in pressure in the flow and induce the flowing fluid to move from the high pressure to the low pressure. This movement can generate vorticity, and a streamwise vortex forms in the flow. Downstream from the streamwise vortex, the flow becomes turbulent and the streamwise vortex transfer energy from the stable laminar flow to the unstable turbulent region. The same pressure imbalance happens at the end of the wings of an airplane and creates two streamwise vortices and turbulence behind the airplane. That's why small airplanes cannot fly behind big airplanes (e.g. at takeoff, etc..). VOrtices are a feature (mostly) of incompressible 3D flows and 2D flows. For compressible flows, when the speed becomes sonic and supersonic, shocks and shock fronts are the dominant features.

A vortex is defined as a coherent structure in the flow that can stay for a while. A fully turbulent flow might not have any vortex at all, in that sens that if there are only transient rolling patterns in the flow that dissappear very quickly. In these case they are refered to as Eddies, rather than vortices. So also it is not clear whether you just meant Eddy or coherent vortex.

If your question was about the transition of the flow from laminar to turbulent, then the answer for incompressible flows is pretty simple. In 3D incompressible flows (most of our lives flows, from air, water, etc.. to weather), the destabilization (transition of the flow from laminar to turbulence due to a finite-amplitude perturbation) process that leads to turbulence is associated with streamwise vortices.

To summarize, the instability of flows is not especially associated with vortex/roll structure. Hwoever, vortex/roll structure are easily formed in (incompressible) flows. (The simplest picture I can give you is the following: since the flow is incompressible, when you 'push' it, the only way it can make place to your pushing action is by moving around the pushing object in some manner or another, and this moving around of the flow looks like rolling and vortices. ) So the vortex/roll structure are not especially the source of the instability, but usually mainly a consequence of it. When the flow is fully turbulent vortices are not especially observed, but only transient patterns are observed: the flow is basically chaotic. In this case you will not see the vortex/roll pattern (open your tap to a maximum and let the water flow in your glass - what do you see? - chaos).

Hi! i was reading you answer to the earlier question and it triggers me (as i'm not an expert in this field), we usually put a borderline in the Reynolds number as to when the flow will become turbulent, which some books say about a million. Could turbulent eddies be detected in this Re region, say a small aircraft is flying at this Re #. If it could, then why is it that most literature focuses on the flow structure behind bluff bodies..cyl, prisms, etc and not of airfoil at high AOA. I can see that they usually assume the flow across airfoil at high AOA is similar to the flow across cyl. in the transverse dir., but isn't the separation/transition point diff?

thanx in advance!

-yin-