Fluid mechanics is so interesting. I shifted paradigms to fluid mechanics about a fortnight ago or so, and am in that stage of correcting old views to the new paradigm, and rooting out those unchallenged assumptions or axioms.
Newton's bucket, for example. I gave an explanation of water climbing the bucket wall based on what little I understood of Bernoulli's observations. I know I explained the movement as a pressure induced reaction to low pressure forming at the rotating rim. The central high pressure then spirals out to form some equilibrium. However when this equilibrium is formed it is a dynamic one, and the pressures in the dynamic equilibrium in the fluid boundary support the reverse view to a low pressure in a faster moving streamline! In fact the situation is more complex. The fluid takes on a particular form . This form is a dynamic equilibrium! It is hard to grasp what that means!
For example a mountain is for all intents and purposes a static equilibrium, and this is where the difficulty lies. Particle and rigid body physics dominates where it should not. The more general view of form has to be a fluid mechanical one. A form has to be accepted as a dynamic equilibrium. We can almost get rid of the emphasis that form is due to static equilibria! These are my assertions.
Thus the water climbs the bucket wall because the water is a bubble! The spin of the bubble is torqued and the atmospheric pressure is able to press on the spots where low internal pressures form, squeezing the bubble toward the higher pressure areas at the rim to form a dynamic equilibrium. They in turn press on the lower pressure areas. These lower pressure areas exist in a skin surrounding the higher pressure areas and this skin is highly dynamic and intensely powerful in a Dirac delta function sense. Fluids appear to press up against a rigid boundary directly. The reality is more complex, and it becomes significant in a dynamic system to apprehend these complexities.
Fluids, because they deform are naturally best described by a deformation mechanics. The term " Wave" I believe has become too indistinct to be useful. Even the Wave" on a pond surface is not a wave – which almost universally means a sine curve disposition in space, not time. These displacements are better characterised as deformations.
The Question is: how does a deformation propagate? How is it to be described spatially?
The deformations in fluids are very exciting and very interesting .
There are several concepts that have to be let go in order to embrace a fluid mechanic paradigm, and a lot of distinctions and experiences to apprehend. I think the first is to let go of traditional Newtonian mechanics and to return to Newton's metaphysical principles and thoroughly examine these.
Those who have read my blogs know I have been doing this from a historical perspective since I started to study Newton. However, in making a paradigm shift this has to be done in earnest, rigorously and at every level.
Newton himself carried forward many metaphysical ideas from those that went before him, from ancient Greek and roman philosophers to the philosophy of his peers and contemporaries. Thus much work has to be done in the long historical trail Newton followed, besides Newton's own insights and comprehensions.
Why bother? Has not modern science done this work in Einstein? Have not Bohr and Rutherford revised the ancient views eliminating irrational myths? Has not Darwin set modern culture straight on zoological and biological diversity? The flat answer is no, and the explanation is that it is all smoke and mirrors. Since the wars we have been fed a regular propaganda diet about science and technology which requires historical research and analysis to apprehend the scale of. We may in fact go back as far as the troubled times of the Prussian Renaissance with the philosophical controversies of Kant and Schilling and the Grassmanns to see how positions were established and defended on religious and geopolitical grounds, enforced by cultural and social stratification. We may also see the rise of the commercial barons and large scale industrial enterprises impacting on society and culture as a commercial resource under the propaganda heading of progress.
Plagiarism long an academic sin becomes enhanced into industrial espionage, a commercial and national concern . Social engineering principles become paramount to ensure a nation could compete in an industrial landscape. Global economics, long a concern of empires, now became commercial concerns. Adam Smith's and Keynes Economics, Karl Marx economic structural analysis all shaped commercial and political ideology into our times?
Thus we find that the mataphysics of science though still debated received scant technological or commercial or governmental interest. The only interested parties were faith groups and structure, which spread across a much more diverse range of beliefs as one of the consequences of this upheaval.
While we are freer , in the west to examine and develop our own ideas from all that has gone before and our own empirical data, there is now no central religious body or governmental body to enforce a consensus. Instead market and evolutionary forces are allowed to work, with those in power cherry picking the best results of that process.. These things have to be carefully picked so as not to destabilise the power structures currently in place.
Many of us, brought up on modern myths and legends should perhaps return to the Grimm fairy tales for a more balanced apprehension of the situation we are in. Even the Tanakh teaches us to be aware of propaganda and myth making, but we may perhaps immediately grasp the significance of the Three little pigs!
In making a paradigm shift therefore it is as well to remind oneself continually that both myths. And facts are products of the human imagination.