# Essentials of Turbulence

- Institution: IIT Bombay
- Department: Mechanical Engineering
- Teacher: Prof. Abhilash J. Chandy
- Level: Undergraduate
- Language: English
- Subjects: Engineering
- Source: [NPTEL](https://nptel.ac.in/courses/112101906)
- Licence: [CC BY-NC-SA](https://nptel.ac.in/faq) (Non-commercial use only.)
- Syllabus: [at the source](https://nptel.ac.in/courses/112101906)
- Who can watch: Tweens profiles and older (sources give no ratings; placed by Invisible Network from the source's own words)

## Lectures

1. [Lecture 1 : The “despair” in turbulence](https://invisiblenetwork.ai/learn/nptel/112101906/ac8ea1681417) (Video)
2. [Lecture 2 : Why Study Turbulence?](https://invisiblenetwork.ai/learn/nptel/112101906/5325125ace6b) (Video)
3. [Lecture 3 : Some descriptions of turbulence](https://invisiblenetwork.ai/learn/nptel/112101906/f55210545855) (Video)
4. [Lecture 4 : How to define turbulence?](https://invisiblenetwork.ai/learn/nptel/112101906/3058dbd0bbc1) (Video)
5. [Lecture 5 : A brief history of turbulence](https://invisiblenetwork.ai/learn/nptel/112101906/b5176db8fe2d) (Video)
6. [Lecture 6 : Characteristics of turbulent flow](https://invisiblenetwork.ai/learn/nptel/112101906/42dfba315adf) (Video)
7. [Lecture 7 : Methods of analysis](https://invisiblenetwork.ai/learn/nptel/112101906/e1f8bc2d7573) (Video)
8. [Lecture 8 : Origin of turbulence](https://invisiblenetwork.ai/learn/nptel/112101906/1b11f0a78974) (Video)
9. [Lecture 9 : Diffusivity of turbulence](https://invisiblenetwork.ai/learn/nptel/112101906/a5b3508a2477) (Video)
10. [Lecture 10 : Length scales in turbulent flows - Part A](https://invisiblenetwork.ai/learn/nptel/112101906/8940fe22520b) (Video)
11. [Lecture 11 : Length scales in turbulent flows - Part B](https://invisiblenetwork.ai/learn/nptel/112101906/1a6048c94398) (Video)
12. [Lecture 12 : Length scales in turbulent flows - Part C](https://invisiblenetwork.ai/learn/nptel/112101906/ed2e7f04b390) (Video)
13. [Lecture 13 : Length scales in turbulent flows - Part D](https://invisiblenetwork.ai/learn/nptel/112101906/3d4fbc8aa9b8) (Video)
14. [Lecture 14 : Nature of turbulent flows and Continuity equation](https://invisiblenetwork.ai/learn/nptel/112101906/8ff578c0465d) (Video)
15. [Lecture 15 : Momentum equations, Pressure and Conserved scalars](https://invisiblenetwork.ai/learn/nptel/112101906/fd26d762ee63) (Video)
16. [Lecture 16 : Vorticity equation, Rates of strain and rotation](https://invisiblenetwork.ai/learn/nptel/112101906/c8f9538e39da) (Video)
17. [Lecture 17 : Random nature of turbulence](https://invisiblenetwork.ai/learn/nptel/112101906/208ac733e31b) (Video)
18. [Lecture 18 : Characterization of random variables and examples of PDF](https://invisiblenetwork.ai/learn/nptel/112101906/8fbbe21446f4) (Video)
19. [Lecture 19 : Joint random variables, Joint PDFs and Conditional PDFs](https://invisiblenetwork.ai/learn/nptel/112101906/d6c4becd4821) (Video)
20. [Lecture 20 : Random processes](https://invisiblenetwork.ai/learn/nptel/112101906/c88bcf847000) (Video)
21. [Lecture 21 : Frequency spectrum and Gaussian process](https://invisiblenetwork.ai/learn/nptel/112101906/bd69165244ae) (Video)
22. [Lecture 22 : Random fields and Wavenumber spectra](https://invisiblenetwork.ai/learn/nptel/112101906/c102b44486b6) (Video)
23. [Lecture 23 : Reynolds equations](https://invisiblenetwork.ai/learn/nptel/112101906/8edab87a65e1) (Video)
24. [Lecture 24 : Closure problem in turbulence](https://invisiblenetwork.ai/learn/nptel/112101906/3c4a85e7ae8b) (Video)
25. [Lecture 25 : Gradient diffusion and Turbulent viscosity hypotheses](https://invisiblenetwork.ai/learn/nptel/112101906/88e59f71fbc2) (Video)
26. [Lecture 26 : Energy cascade](https://invisiblenetwork.ai/learn/nptel/112101906/ec9b2b89c97c) (Video)
27. [Lecture 27 : Kolmogorov hypotheses Part 1](https://invisiblenetwork.ai/learn/nptel/112101906/c19bb52666d0) (Video)
28. [Lecture 28 : Kolmogorov hypotheses Part 2](https://invisiblenetwork.ai/learn/nptel/112101906/1a0563c62425) (Video)
29. [Lecture 29 : Energy spectrum Part 1](https://invisiblenetwork.ai/learn/nptel/112101906/561ad6246ba3) (Video)
30. [Lecture 30 : Energy spectrum Part 2](https://invisiblenetwork.ai/learn/nptel/112101906/822b473166d1) (Video)
31. [Lecture 31 : Fourier modes and Fourier series representation](https://invisiblenetwork.ai/learn/nptel/112101906/dd2bcc817e2d) (Video)
32. [Lecture 32 : The evolution of Fourier modes Part 1](https://invisiblenetwork.ai/learn/nptel/112101906/7ab1b2c324c0) (Video)
33. [Lecture 33 : The evolution of Fourier modes Part 2](https://invisiblenetwork.ai/learn/nptel/112101906/0f3afa0b1550) (Video)
34. [Lecture 34 : The kinetic energy of Fourier modes](https://invisiblenetwork.ai/learn/nptel/112101906/a53bf7b03d95) (Video)
35. [Lecture 35 : Velocity spectrum tensor and Energy spectrum function](https://invisiblenetwork.ai/learn/nptel/112101906/f9898f949d93) (Video)
36. [Lecture 36 : One-dimensional spectra and comparison of spectra](https://invisiblenetwork.ai/learn/nptel/112101906/bf91071bf731) (Video)
37. [Lecture 37 : Kolmogorov spectra](https://invisiblenetwork.ai/learn/nptel/112101906/5b0530b76c11) (Video)
38. [Lecture 38 : Model spectra](https://invisiblenetwork.ai/learn/nptel/112101906/d7b422392c0d) (Video)
39. [Lecture 39 : Dissipation spectra](https://invisiblenetwork.ai/learn/nptel/112101906/b51d690e13ed) (Video)
40. [Lecture 40 : Inertial subrange and Energy-containing range](https://invisiblenetwork.ai/learn/nptel/112101906/19a327fb30f9) (Video)
41. [Lecture 41 : Effects of Reynolds number](https://invisiblenetwork.ai/learn/nptel/112101906/759fd0b442be) (Video)
42. [Lecture 42 : Energy-spectrum balance](https://invisiblenetwork.ai/learn/nptel/112101906/82b31260efe7) (Video)
43. [Lecture 43 : Challenges and modeling approaches](https://invisiblenetwork.ai/learn/nptel/112101906/4006d747c9f3) (Video)
44. [Lecture 44 : Criteria for appraising models Part 1](https://invisiblenetwork.ai/learn/nptel/112101906/e2f44e53620b) (Video)
45. [Lecture 45 : Criteria for appraising models Part 2](https://invisiblenetwork.ai/learn/nptel/112101906/baa8125b455a) (Video)
46. [Lecture 46 : Pseudo-spectral methods for DNS](https://invisiblenetwork.ai/learn/nptel/112101906/bd883145596e) (Video)
47. [Lecture 47 : Computational cost of DNS Part 1](https://invisiblenetwork.ai/learn/nptel/112101906/14033ef2da1d) (Video)
48. [Lecture 48 : Computational cost of DNS Part 2](https://invisiblenetwork.ai/learn/nptel/112101906/4cca8a1d1855) (Video)
49. [Lecture 49 : Turbulent Viscosity Models](https://invisiblenetwork.ai/learn/nptel/112101906/57f3ff3eb8ab) (Video)
50. [Lecture 50 : Four conceptual steps in LES](https://invisiblenetwork.ai/learn/nptel/112101906/4f82a56d090b) (Video)
51. [Lecture 51 : Filtering in one-dimension](https://invisiblenetwork.ai/learn/nptel/112101906/7d6ce40d11ab) (Video)
52. [Lecture 52 : Spectral representation of LES filter](https://invisiblenetwork.ai/learn/nptel/112101906/85bbebeae505) (Video)
53. [Lecture 53 : Filtering in three-dimension](https://invisiblenetwork.ai/learn/nptel/112101906/01ebd08a73cf) (Video)
54. [Lecture 54 : Filtered conservation equations](https://invisiblenetwork.ai/learn/nptel/112101906/2ad5d19c2917) (Video)
55. [Lecture 55 : Smagorinsky model](https://invisiblenetwork.ai/learn/nptel/112101906/5e65508f8a28) (Video)
56. [Lecture 56 : LES in wavenumber space](https://invisiblenetwork.ai/learn/nptel/112101906/9c940fdb6ac2) (Video)
57. [Lecture 57 : Practice Problems Part 1](https://invisiblenetwork.ai/learn/nptel/112101906/ae4ff696271e) (Video)
58. [Lecture 58 : Practice Problems Part 2](https://invisiblenetwork.ai/learn/nptel/112101906/21e6ca5ab262) (Video)
59. [Lecture 59 : Practice Problems Part 3](https://invisiblenetwork.ai/learn/nptel/112101906/c4556c2ff00d) (Video)
60. [Lecture 60 : Practice Problems Part 4](https://invisiblenetwork.ai/learn/nptel/112101906/dd300ae45c9a) (Video)
61. [Tutorial 1 - Practice Problem](https://invisiblenetwork.ai/learn/nptel/112101906/e26c642cf08b) (Video)