Preprint Article Version 4 Preserved in Portico This version is not peer-reviewed

Solitonlike Coherent Structure Is a Universal Motion Form of Viscous Fluid

Version 1 : Received: 10 October 2023 / Approved: 11 October 2023 / Online: 12 October 2023 (11:27:18 CEST)
Version 2 : Received: 15 October 2023 / Approved: 16 October 2023 / Online: 18 October 2023 (10:22:28 CEST)
Version 3 : Received: 22 October 2023 / Approved: 23 October 2023 / Online: 23 October 2023 (13:45:22 CEST)
Version 4 : Received: 25 October 2023 / Approved: 25 October 2023 / Online: 25 October 2023 (15:11:03 CEST)

How to cite: Sun, B. Solitonlike Coherent Structure Is a Universal Motion Form of Viscous Fluid. Preprints 2023, 2023100784. https://doi.org/10.20944/preprints202310.0784.v4 Sun, B. Solitonlike Coherent Structure Is a Universal Motion Form of Viscous Fluid. Preprints 2023, 2023100784. https://doi.org/10.20944/preprints202310.0784.v4

Abstract

The discovery of solitonlike coherent structure (SCS) in boundary layer flows is crucial for understanding turbulence origins and in particular for laminar-turbulence transition. However, the task of finding solutions for solitonlike coherent structure from the Navier-Stokes equations poses a significant challenge. In this paper, based on the author's previous work [B.H. Sun, Exact similarity solutions of unsteady laminar boundary layer flows, Preprints 2023, 2023092117], we are able to study convergent flow boundary layers, whose solution encompasses both shock wave and solitary wave solutions, and their superposition gives rise to solitary-like waves, namely solitonlike coherent structure. It is found that the solitonlike coherent structure can only be obtained by combining the Navier-Stokes equations and mass conservation, since the combined equations will have the third order derivatives respect to coordinate $x$, in other words, without the mass conservation condition, the Navier-Stokes equations does not contain solitonlike coherent structure by itself. Finally proved solitonlike coherent structure is a universal motion form of viscous fluid.

Keywords

solitonlike coherent structure; solitary wave; Navier-Stokes equation; 2D unsteady boundary layers; similar transformation; exact solution

Subject

Physical Sciences, Fluids and Plasmas Physics

Comments (1)

Comment 1
Received: 25 October 2023
Commenter: Bohua Sun
Commenter's Conflict of Interests: Author
Comment: somes changes have been made: a. abstract; b. some typo in Eqs. 4,5, 6, 7; c. added three more Refs. d. redraw  Fig 1 
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