Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed

Are There Solitonlike Coherent Structure in Boundary Layers ?

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. Are There Solitonlike Coherent Structure in Boundary Layers ?. Preprints 2023, 2023100784. https://doi.org/10.20944/preprints202310.0784.v1 Sun, B. Are There Solitonlike Coherent Structure in Boundary Layers ?. Preprints 2023, 2023100784. https://doi.org/10.20944/preprints202310.0784.v1

Abstract

The identification 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 [Sun (2023) in Ref.31], 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 do exit in all kind of flows.

Keywords

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

Subject

Physical Sciences, Fluids and Plasmas Physics

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