In fluid, collective response of fluid elements about its an equilibrium position originates wave like structures. This wave like motion is result of the oscillatory motions of the fluid elements. In this motion, inertial as well as restoring forces are playing a role. This is the case when the pressure force (may be internal or external) on the group of fluid elements is uniform. In the other case, fluid elements start to rotate (clockwise or anti) if there is a shear in the pressure force. In rotatory motion, the fluid elements start to move along any closed path. It is only possible when the fluid elements lost its restoring force. I have understand the mathematical formulation for such types of motion but unable to understand the physical picture. Why fluid elements lost its restoring force only in the shear pressure forces? Can anyone explains such type of motion and clear my doubt?
it is because fundamentally fluids do not support shear forces! And after initiating a rotatory motion fluids do come to rest as a result of the viscous damping of the fluid-motion. I hope I have understood your problem correctly.
Look at this doc (introductory fluid mechanics) it may be helpful for your topic. Good luck.
@ Zoubair, The article you have attached has absolutely no connection to the question asked. If you think it has, please explain.
@ Vikash, I have changed it, I want attache a book (introductory fluid mechanics) it may be useful :) :)
About what a restoring force in the liquid are you saying? A fundamental property of a fluid is a property to change its shape, and therefore the mutual position of the fluid elements, without any restriction. The restoring force arises in a solid, if you try to shift some atom from its equilibrium position with respect to the lattice. But not in the liquid, wherein no crystal lattice.
Generally, the restoring force can occur in fluid when there are an additional force, which makes the medium heterogeneous. For example, it happens if the cavity is heated from outside under the gravity or when there exists the interface.
Thnks Dmitry bratsun for your wonderful answering.
I am asking in context to dusty plasma. dusty plasma is charged micronsized particles. it is considered as a fluid. Dust particles are in equilibrium under certain conditions (no net forces on particles). If i displace the particles from it equilibrium position, they will start to oscillate around its equilibrium position because of restoring force (provided by electrons and ions) and inertial force of dust particles. This oscillatory motion of dust grains are seems as wave like pattern. In this , i think, coupling between the dust grains (coulomb interactions) play a crucial role. If i reduce the coupling strength among the dust grains then the situation is somewhat different. Now, the dust grains are lost its restoring force and turn towards the rotatory motions.
My question is that which factor is more dominate ( shear pressure or weak interaction among particles) to turn the duty medium into rotatory motion rather than simple oscillatory motion? Is it possible to create similar types of the vortex motion in the fluid ? if you find some work (in fluid or any medium) which shows the multiple vortex (similar types) then please send me link.
Now I can see your problem is very special and it is unusual for hydrodynamics. If the solid particles are held in place by some force, then their behavior is rather similar to the behavior of solid lattice. I remind you that the oscillations in the lattice described by the classical theory of phonons. An interesting feature of your problem is that the solid particles are simultaneously under the influence of vortex motion in a fluid, which can disrupt the order of particles. Then you need to look for works on the dynamics of phonons near the critical point of transition solid state to the liquid state. At least it will give you an idea of how to describe the situation in your task.
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