The throwing of a stone in a lake (can be approximated as hydrostatic case) creates ripples in the water. The ripples or the disturbance associated with this is elliptical and travels uniformly in all the directions.
Now if I put an analogous model where heat transfer is involved in a rectangular plate with higher and lower thermal diffusivity. The plate with higher diffusivity will have more penetration of the outer wall temperatures and that is absolutely fine with the physics of heat transfer.
Any physical phenomena where we have higher diffusivity will tend to have deeper penetration.
But then why in case of a static fluid, the disturbance created by a stone travels larger distance when the fluid viscosity is low?
I can argue that with as viscosity increases, the losses associated increase as well and hence disturbance die out quickly.
But where am I wrong if I try to put it like " higher viscosity meaning higher diffusivity which means the disturbance must travel longer distance" ?
Thanks
Please read these informations in this wesite, it may be helpful for your topic. Good luck.
http://labman.phys.utk.edu/phys136/modules/m1/Viscous%20fluids.htm
first, the disturbance caused by a stone in a fluid at a rest is a typical case of wave propagation, governed by hyperbolic equations. Hyperbolic equations generally appears when the viscosity is totally disregarded in the physical model (inviscid flow).
You can thing that in real flows the viscosity of a fluid is fixed but when the energy is associated tos small wavelenght they will dissipated when the local Re number is O(1).
Therefore, the more the viscosity is high, the faster the local Re number reaches O(1).
Hi Filippo,
So if the disturbance generated by stone in the water is hyperbolic, why it travels equally in all the direction, similar to an elliptical phenomenon?
Also what is the reason for transfer of disturbance. It cannot be convective diffusion since the fluid is not in motion.
in hyperbolic equations it travels at a finite velocity and only along some directions, that is the difference! Think about an acoustic source at the rest: it propagates the disturbance isotropically at the the velocity of sound. For elliptic equtions the solution says the a disturbance propagates immediately everywhere, no privileged directions exist
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