---
title: "Nature of turbulence and energy cascade"
subject: "Applied Computational Fluid Dynamics"
chapter: 5
key: "semester_7/applied_computational_fluid_dynamics:turbulence-energy-cascade-nature"
source: https://www.bctengineer.com/q/semester_7/applied_computational_fluid_dynamics/turbulence-energy-cascade-nature
site: BCT Engineering
---

# Nature of turbulence and energy cascade

Applied Computational Fluid Dynamics · Chapter 5: Turbulence Modeling

- Asked in: year not given, 5 marks
- Video: [Understanding Laminar and Turbulent Flow](https://www.youtube.com/watch?v=9A-uUG0WR0w) — The Efficient Engineer
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_7/applied_computational_fluid_dynamics/turbulence-energy-cascade-nature
- Whole chapter: https://www.bctengineer.com/md/semester_7/applied_computational_fluid_dynamics/chapter-5

## Question

Describe the physical nature of turbulent flow. Explain the energy cascade and the scales of turbulence (Kolmogorov), and state the engineering implications of turbulence.

## Short answer

Turbulence is unsteady, three-dimensional, chaotic flow with random fluctuations, enhanced mixing, and viscous dissipation. Energy cascades from large eddies (size of geometry) through inertial breakup to the smallest Kolmogorov scales where viscosity dissipates it as heat. Engineering implications include increased drag and heat transfer, improved mixing, delayed separation, and the need for turbulence modelling due to prohibitive DNS cost.

## Answer

#### Nature of turbulence
Turbulence is an unsteady, three-dimensional, chaotic flow in which velocity and pressure fluctuate randomly around a mean value. Its main features:
- **Irregularity:** random fluctuations that cannot be predicted in detail; treated statistically.
- **Diffusivity:** rapid mixing of momentum, heat and mass, much faster than molecular diffusion.
- **Rotationality and 3D vortex stretching:** it is made of eddies of many sizes.
- **Dissipation:** viscous action turns kinetic energy into heat, so turbulence needs a continuous energy supply.
- **High Reynolds number:** it appears when $Re$ exceeds a critical value.
- It is a property of the flow, not of the fluid.

#### Energy cascade (Richardson, Kolmogorov)
```text
 mean flow
    | energy input
    v
 [ large eddies  L ]   (size of the geometry)
    |  vortex stretching, breakup
    v
 [ medium eddies   ]   inertial range
    |  no dissipation here
    v
 [ small eddies eta ]  viscous dissipation
    |
    v
   heat
```
- Large eddies, of size comparable to the flow geometry ($\ell_0$), extract energy from the mean flow.
- They are unstable and break up into smaller eddies, passing energy down the scales (the inertial range) with little loss.
- At the smallest scales, the **Kolmogorov scales**, viscosity dissipates the energy as heat:
$$
\eta=\left(\frac{\nu^3}{\varepsilon}\right)^{1/4},\qquad \tau_\eta=\left(\frac\nu\varepsilon\right)^{1/2},\qquad u_\eta=(\nu\varepsilon)^{1/4}
$$
where $\varepsilon$ is the dissipation rate per unit mass. The ratio of the largest to the smallest scale grows as $\ell_0/\eta\sim Re^{3/4}$.

#### Engineering implications
- Increases drag, pressure losses, wall friction and heat transfer coefficients (useful in heat exchangers, harmful in pipelines).
- Improves mixing (combustors, reactors) and delays flow separation (golf ball dimples).
- Causes noise and vibration.
- For CFD: direct simulation (DNS) needs about $Re^{9/4}$ grid points, which is impractical, so modelling (RANS, LES) is used.

## Check yourself

The answer's key points as multiple-choice questions, with the correct option and why.

1. Which feature belongs to turbulence?
   A. It is regular, steady and two-dimensional
   B. It mixes momentum, heat and mass much faster than molecular diffusion
   C. It needs no energy supply because dissipation is zero
   D. It is a property of the fluid, not of the flow
   Answer: B. Turbulence is irregular, 3D and diffusive, dissipates energy (so needs supply), and is a property of the flow. (Key point: Nature of turbulence)

2. In the energy cascade, where is the energy dissipated into heat?
   A. By the large eddies
   B. In the inertial range
   C. At the smallest (Kolmogorov) scales by viscosity
   D. In the mean flow
   Answer: C. Large eddies extract energy, pass it down through the inertial range with little loss, and viscosity dissipates it at the smallest scales. (Key point: Energy cascade)

3. Which is the Kolmogorov length scale, and how does the scale ratio vary with Re?
   A. eta = (nu^3/epsilon)^(1/4); l0/eta ~ Re^(3/4)
   B. eta = (nu/epsilon)^(1/2); l0/eta ~ Re
   C. eta = (nu epsilon)^(1/4); l0/eta ~ Re^(3/4)
   D. eta = (nu^3/epsilon)^(1/4); l0/eta ~ Re^(9/4)
   Answer: A. eta = (nu^3/epsilon)^(1/4), and the range of scales grows as Re^(3/4); Re^(9/4) is the DNS grid-point count. (Key point: Kolmogorov scale)

## Related in Applied Computational Fluid Dynamics

- [Turbulence intensity and inlet k, epsilon](https://www.bctengineer.com/question.md?key=semester_7%2Fapplied_computational_fluid_dynamics%3Aturbulence-intensity-inlet-numerical) — Applied Computational Fluid Dynamics, chapter 5
- [Reynolds number and flow regime in pipes](https://www.bctengineer.com/question.md?key=semester_7%2Fapplied_computational_fluid_dynamics%3Areynolds-number-flow-regime) — Applied Computational Fluid Dynamics, chapter 1

## Related in other subjects

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- [Velocity for fully turbulent flow in rough pipe](https://www.bctengineer.com/question.md?key=semester_4%2Fhydraulics%3Afully-turbulent-velocity-1200mm-pipe) — Hydraulics, chapter 1
- [Implications of settlement on structures](https://www.bctengineer.com/question.md?key=semester_5%2Ffoundation_engineering%3Asettlement-implications) — Foundation Engineering, chapter 6
- [Sound energy flow per square cm](https://www.bctengineer.com/question.md?key=semester_1%2Fengineering_physics%3Asound-energy-flow-frequency-amplitude) — Engineering Physics, chapter 3