Questions tagged [turbulence]
A regime of nonlinear viscous flow characterized by random, rotational motion with a wide range of length scales. Its study is critical to many fields, such as aerospace, atmospheric science, chemical engineering, and astrophysics.
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Why don't they use golf ball dimples on cars? [duplicate]
Just watched an episode of mythbusters where they proved that a car got better fuel economy with golf ball dimples. So why don't they use that on cars?
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Drag coefficient of an oscillating film in a turbulent flow regime (stirred tank), experiment or theoretical?
I have been recently assigned to a new project and brushing up my fluid mechanics from years ago, so sorry if the question is too stupid to post here.
The goal is to quantitatively measure some form ...
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Questions regarding the derivation procedure of the Karman-Howarth-Monin relation
I was reading the book "Turbulence" written by Uriel Frisch (1995) and got stuck in following the proof of the Karman-Howarth-Monin relation. Although there is already a thread about it, I ...
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Value of the velocity at the largest correlation length in a turbulent medium
If a turbulent system is observed to follow a turbulent energy spectrum of the form $E(k)\propto k^{-p}$ for the range $k_{min}<k<k_{max}$, I was wondering if there is a way to have an order of ...
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Energy density at a given scale in terms of the Energy Spectrum
Background:
Let us have a turbulent fluid with a random velocity field $\mathbf{u}(\mathbf{x})$.
The volume averaged kinetic energy density $\mathscr{E}_K$ can be expressed as
$$\mathscr{E}_K=\frac{1}{...
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Relations of correlation function and structure function in fluid mechanics
This paper (LINDBORG, 2007, DOI:10.1175/JAS3864.1) involves 3 correlation functions and 1 structure function, as defined below:
$$
R_{ij}(\mathbf x, \mathbf r) =
\langle u_i(\mathbf x) u_j(\mathbf x +...
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Inverse Energy Cascade in 2D turbulence
If the production term in the Turbulent Kinetic Energy (TKE) budget equation is negative, it implies that energy is transferred from the turbulent flow field to the mean flow field. Does this imply an ...
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How to create an image of a velocity field representing Kolmogorov structure function?
I want to create a two-dimensional image where each pixel represents a velocity. The velocities are distributed in such a way that if you plot a function of separation between all unique pairs of ...
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Most general form of the velocity correlation tensor
The most general form of velocity correlation tensor for homogeneous and isotropic turbulence is given by:
$R_{ij}(r)=A(r)r_{i}r_{j}+B(r)\delta_{ij}$
How can this depend on $r_{i}r_{j}$ if it is ...
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Calculating the average of fluctuations of a given time series
I have a given data set, 4500 time data points approx, and the instantaneous velocity at each point. To calculate the time average of the velocity, I attempted to integrate the velocity function ...
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What causes drag crisis?
While reading the Wikipedia article on Drag Crisis, I found:
The drag crisis is associated with a transition from laminar to
turbulent boundary layer flow adjacent to the object.
While, the ...
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Calculating the Lyapunov exponents spectrum from particle trajectories
I am simulating a forced, compressible 2D flow, that is turbulent and statistically steady, but not stationary.
I want to calculate the Lyapunov exponents spectrum from the trajectories of Lagrangian ...
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Extract body force from non-Newtonian Reynolds number
To simulate turbulent non-Newtonian channel flow I intend to use the power law viscosity model given by
$$\mu = K\gamma^{n-1}$$
with $K$ the flow consistency index, n the flow behavioural index and $\...
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Change in the Form of the Equation of Continuity with an increase in Turbulence
Up until now, my learning has mostly been restricted to laminar (streamlined) flow, and its equations.
One such equation is the equation of continuity (A1V1=A2V2). I was wondering whether, with an ...
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A question in the book of Frisch&Kolmogorov at Chapter 4.5
in the book of Frisch’s Turbulence (http://users.uoa.gr/~pjioannou/mechgrad/Frisch_Turbulence.pdf), at chapter of 4.5 The spectrum of stationary random functions, as following picture shows, i have a ...
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Fluid dynamics: Euler equation and turbulence
I have a doubt, a sort of paradox. It is known that the classical Navier-Stokes equation in the limit of Reynolds number that goes to infinity - the high Reynolds regime - gives the classical Euler's ...
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Alfvenic Mach number and level of turbulence
I wanted to compute the level of turbulence $\delta B/B$ in MHD simulation.
In literature Alfvenic Mach number is considered to be a proxy for computing the turbulence level.
I wish to know why this ...
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What causes blood flow to become turbulent after a constriction?
If a blood vessel is narrowed from the middle, the blood flow turns turbulent (see image below).
Why does this happen? Does it have to do with Reynolds number becoming high because velocity has ...
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Would turbulence from flowing streams into a system be a form of work or heat loss?
Imagine a situation like this. If we consider the T-elbow to be our system, both the hot and cold streams are bringing energy into it (KE, flow energy, $u$).
However, in the middle where the streams ...
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Is there an easy explanation for this flow pattern? [closed]
I was just admiring the river formed after a storm and saw this flow pattern under the bridge. Is there an explanation for this flow pattern?
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What causes wind gusts?
A difference in temperature causes different pressures, air travel from high to low pressure, and that is wind.
We can even produce wind in an experiment like in this video. In this video, what is the ...
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Turbulence from a sphere spinning in an incompressible liquid
When I look online I can find plenty of simulations of Stokes flow: incompressible liquid flowing past a spherical object. What I'm interested in is the problem of a sphere (of given size) spinning (...
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Calculating an anisotropic or component Taylor microscale
The Taylor microscale in isotropic turbulence is given by:
$$\lambda = \sqrt{ 15 \frac{\nu \ v'^2}{\epsilon} }$$
where v' is the root mean square of the velocity fluctuations. In general, for ...
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At What Scales Turbulence Matters?
So from what I understand(like from this site: https://www.britannica.com/science/transport-phenomenon) is that turbulence is when the flow is almost unpredictable at different parts but on average ...
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Some questions in book of Frisch&Kolmogorov at Chapter 6
i'm not native speak, what does the above sentence meaning? —— whether the sentence “which are small compared to the integral scale” refers to increments $\ell$ only or refers to increments $\ell$ &...
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How to understand the Fourier transform of a stationary random function?
A stationary random function like $v(t;w)$ is not periodic and not squared integrable, why we can do a Fourier transform to it, which is a very common process to analyze turbulence. How will a ...
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Is it possible to convert separated flow back to attached?
Sometimes you cannot easily create ideal single streamlined shape...
Would it be possible to attach separated flow again somehow?
The point is - you have some base setup (average cyclist) and want to ...
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Turbulence, Euler equations and equipartition of energy
Recently the user CBBAM asked about the inviscid limit in turbulence and the relation between Navier-Stokes equations and Euler equations when $\nu \to 0$. There I pointed out that Onsager proposed ...
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What is the correct direction of turbulence energy cascade?
I have learned from a fluid mechanics textbook [1] that the turbulence energy is cascaded from the largest eddy to the smallest eddy and is then dissipated by the molecular viscous effect. But ...
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Can someone give a picture to visualize and elucidate the celebrated rhyme of Richardson about turbulence? [closed]
Richardson's celebrated rhyme is below:
Big whorls have little whorls,
which feed on their velocity,
and little whorls have lesser whorls,
and so on to viscosity.
(Lewis F. Richardson, 1920)
I read ...
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What does “eddy” mean in turbulence?
a newbie in turbulence study, very confused about the concept of eddy, I feel the word "eddy" having two meanings in fluid-mechanics maybe more and i'm not sure if i understand correctly.
a ...
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How to calculate the time it takes for an integral eddy to be reduced to the Kolmogorov microscale
I would like to calculate the time it takes for the largest eddies to be reduced to a specific size eddy (for example, the Kolmogorov length scale, but I would like a general equation if possible). I'...
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Vortex line, tube, sheet, and filament
In my study of fluid dynamics I have across these terms quite often and I am so far unable to create a physical picture in my head. Suppose we have a 3D velocity field $u$, and its corresponding ...
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Is turbulence more likely to form with the Euler equation as opposed to Navier-Stokes?
The Euler equation models perfectly inviscid fluids. Under this assumption, with $\nu = 0$, the Reynolds number should be infinite. I would guess that this implies the Euler equation is always ...
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Does the resolution of a timeseries affect the estimate of the power-spectrum?
I have been trying to estimate the power spectrum of a timeseries using fourier transform.
I noticed that by downsampling my timeseries I get a different spectrum as shown below
Here you can see ...
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What causes the formation of vortices in a separated flow?
Consider flow over a cylinder. At a high enough Reynold's Number, the strength of the adverse pressure gradient becomes too large for the boundary layer to be able to remain attached to the cylinder. ...
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What is the eponym associated with the relationship between phase variance and expected magnitude?
I'm looking for the eponym (e.g., Stigler's law) associated with the following relationship:
\begin{equation}
\left|\langle e^{-i\phi} \rangle\right| = e^{-\langle\phi^2\rangle/2}
\end{equation}
which ...
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Are all turbulent flows chaotic?
I have often read that all turbulent flows are chaotic. I have come across a few explanations on web forums, but are there any authoritative references/textbooks that explicitly cover this question?
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About the formula of the Taylor microscale
I am running simulations of a non-isotropic turbulent flow and I need to compute the Taylor microscale. The formula one can find in the book Turbulent flows (Stephen B. Pope) is :
$\lambda = \sqrt{10} ...
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Turbulent boundary layer: viscous sublayer definition
I have seen different definitions of the viscous sublayer within a turbulent boundary layer, through my searches. Ones say that the viscous sublayer area is for $y \leq 10 * \delta_v$ where $\delta_v$...
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The motion of a spring due to wind (Wind induced oscillations)
Consider a spring held in the direction of wind as shown in the image. the spring body is wrapped with paper so that the spring oscillates with the wind in a circular manner. Is there any mathematical ...
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2D Kolmogorov-Obukhov Developed Turbulent Flow
Are there any references to the derivation of the Kolmogorov-Obukhov theory for fully developed turbulent flow in 2-dimensions? That is, the derivation of the Kolmogorov power rules, but in 2D? I was ...
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Is the transition from laminar flow to turbulent flow a kind of phase transition like those in condensed matter?
From the laminar flow to turbulent flow, is it a kind of phase transition?
If so, what is the critical point? And what about the correlation length behaviours and fluctuation? Any critical exponents?
...
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Smoke and fluid mechanics
While lighting up a cigarette (I don't encourage smoking) I noticed that the flow of the smoke coming out of it, initially goes in a straight up direction, in a laminar flow, then about 10 cms above, ...
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How does turbulence arise from Navier-Stokes?
I would like to know how turbulence arises from the standard Navier-Stokes equations, both mathematically and also physically. At least I suspect this is the case as many of the "vanilla" ...
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Taylor's hypothesis in turbulence
Reading about Taylor's hypothesis for converting spatial to temporal scales and vice-versa, I understand that if $V$ is the bulk speed of the fluid then we could use:
$$\ell = V \cdot \tau$$
To ...
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Quasi-linear theory of plasma, some queries
I was studying about quasi linear theory of plasma turbulene and stuck at some questions (derivations),
I could able to derive upto Eq.14 of this paper, but not sure how proceed for deriving the ...
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Can we force turbulent transition of main flow despite unsufficient Reynolds number?
I was wondering something for awhile without finding what I was looking for :
let's consider a flow, for instance inside a pipe, with a Reynolds number $Re$ below a critical Reynolds number $Re_{cr}$ ...
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Why do mosquito coil smoke not rise in a linear manner even if there is no wind?
I observed that when a mosquito coil is lit and kept on the floor then the smoke raises almost linearly but after some distance covered vertically, their path of motion gets completely distorted. It ...
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Resultant particle distribution function for mixing of two particle species
I would like to know if there is any way to compute the resultant particle distribution for system where two kinds of particles are mixed. For me one kind is Maxwellian and another is non-thermal ...
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