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Asymptotic behaviour of the Direct Interaction Approximation.

Asymptotic behaviour of the Direct Interaction Approximation. As mentioned previously, Kraichnan’s asymptotic solution of the DIA, for high Reynolds numbers and large wavenumbers, did not agree with the observed asymptotic behaviour of turbulence. His expression for the spectrum was , where is the root-mean-square velocity and is a constant. In 1964 (see [1] for theContinue reading Asymptotic behaviour of the Direct Interaction Approximation.

A brief summary of two-point renormalized perturbation theories.

A brief summary of two-point renormalized perturbation theories. In the previous post we discussed the introduction of Kraichnan’s DIA, based on a combination of a mean-field assumption and a new kind of perturbation theory, and how it was supported by Wyld’s formalism, itself based on a conventional perturbation expansion of the NSE. This was notContinue reading A brief summary of two-point renormalized perturbation theories.

Marseille (1961): a paradoxical outcome.

Marseille (1961): a paradoxical outcome. When I was first at Edinburgh, in the early 1970s, a number of samizdat-like documents, of entirely mysterious provenance, were being passed around. One that came my way, was a paper by Lumley which contained some rather interesting ideas for treating the problem of turbulent diffusion. I expect that itContinue reading Marseille (1961): a paradoxical outcome.

Which Navier-Stokes equation do you use?

Which Navier-Stokes equation do you use? In the first half of 1999, a major turbulence programme was held at the Isaac Newton Institute in Cambridge. On those days when there were no lectures or seminars during the morning, a large group of us used to meet for coffee and discussions. In my view these discussionsContinue reading Which Navier-Stokes equation do you use?

Turbulence as a quantum field theory: 2

Turbulence as a quantum field theory: 2 In the previous post, we specified the problem of stationary, isotropic turbulence, and discussed the nature of turbulence phenomenology, insofar as it is relevant to taking our first steps in a field-theoretic approach. Now we will extend that specification in order to allow us to concentrate on renormalizationContinue reading Turbulence as a quantum field theory: 2

Turbulence as a quantum field theory: 1

Turbulence as a quantum field theory: 1 In the late 1940s, the remarkable success of arbitrary renormalization procedures in quantum electrodynamics in giving an accurate picture of the interaction between matter and the electromagnetic field, led on to the development of quantum field theory. The basis of the method was perturbation theory, which is essentiallyContinue reading Turbulence as a quantum field theory: 1

Is there an alternative infinite Reynolds number limit?

Is there an alternative infinite Reynolds number limit? I first became conscious of the term dissipation anomaly in January 2006, at a summer school, where the lecturer preceding me laid heavy emphasis on the term, drawing an analogy with the concept of anomaly in quantum field theory, as he did so. It seemed that thisContinue reading Is there an alternative infinite Reynolds number limit?

What relevance has theoretical physics to turbulence theory?

What relevance has theoretical physics to turbulence theory? The question is of course rhetorical, as I intend to answer it. But I have to pause on the thought that it is also unsatisfactory in some respects. So why ask it then? Well my reply to that is that various turbulence researchers have over the yearsContinue reading What relevance has theoretical physics to turbulence theory?

The Kolmogorov `5/3’ spectrum and why it is important

The Kolmogorov `5/3’ spectrum and why it is important An intriguing aspect of the Kolmogorov inertial range spectrum is that it was not actually derived by Kolmogorov. This fact was unknown to me when, as a new postgraduate student, I first encountered the `5/3’ spectrum in 1966. At that time, all work on the statisticalContinue reading The Kolmogorov `5/3’ spectrum and why it is important

Scientific discussion in the turbulence community.

Scientific discussion in the turbulence community. Shortly after I retired, I began a two-year travel fellowship, with the hope of having interesting discussions on various aspects of turbulence. I’m sure that I had many interesting discussions, particularly in trying out some new and half-baked ideas that I had about that time, but what really sticksContinue reading Scientific discussion in the turbulence community.

Intermittency corrections (sic) and the perversity of group think

Intermittency corrections (sic) and the perversity of group think. In The Times of 11 January this year, there was a report by their Science Editor which had the title Expert’s lonely 30-year quest for Alzheimer’s cure offers new hope. Senile dementia is the curse of the age (even if temporarily eclipsed by the Corona virus)Continue reading Intermittency corrections (sic) and the perversity of group think

The infinite-Reynolds number limit: a first look

The infinite-Reynolds number limit: a first look. I notice that MSRI at Berkeley have a programme next year on math problems in fluid dynamics. The primary component seems to be an examination of the relationship between the Euler and Navier-Stokes equations, `in the zero-viscosity limit’. The latter is, of course, the same as the limitContinue reading The infinite-Reynolds number limit: a first look

The energy balance equation: or what’s in a name?

The energy balance equations: or what’s in a name?  Over the last few years I have noticed that the Karman-Howarth equation is sometimes referred to nowadays as the `scale-by-scale energy budget equation’. Having thought about it carefully, I have concluded that I understand that description; but I think the mere fact that one has toContinue reading The energy balance equation: or what’s in a name?

Wavenumber Murder and other grisly tales

Wavenumber Murder and other grisly tales. When I was first at Edinburgh, I worked on developing a theory of turbulent drag reduction by additives. But, instead of considering polymers, I studied the much less well-known phenomenon involving macroscopic fibres. This was because it seemed to me that the fibres were probably of a length whichContinue reading Wavenumber Murder and other grisly tales

HIT: Do three-letter acronyms always win out?

HIT: Do three-letter acronyms always win out? In 1997, I visited Delft Technical University and while I was there gave a course of lectures on turbulence theory. During these lectures, I mentioned that nowadays people seemed to refer to homogeneous, isotropic turbulence; whereas, when I started out, it was commonplace to simply say isotropic turbulence.Continue reading HIT: Do three-letter acronyms always win out?