A Modal One-Way Navier-Stokes Approach to Modelling Non-Modal Boundary Layer Instabilities

Fuente: arXiv
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Autori principali: Badcock, E. J., Mughal, S.
Natura: Preprint
Pubblicazione: 2025
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author Badcock, E. J.
Mughal, S.
author_facet Badcock, E. J.
Mughal, S.
contents This paper presents a method to solve the modal form of the linearised one-way Navier-Stokes (OWNS) equations for investigating disturbance development in developing subsonic and supersonic boundary layers. The modal framework offers significant advantages in robustness and computational efficiency over the conventional non-modal OWNS framework. Notably, we demonstrate that modal OWNS (M-OWNS) retains the capability to capture non-modal disturbance development. Our technique leverages the modal ansatz of parabolised stability equations (PSE) whilst employing the recursion-parameter parabolisation strategy of non-modal OWNS to stabilise the streamwise-marching modal algorithm. A key contribution is that we overcome the minimum streamwise step-size requirement that constrains conventional PSE in capturing short-scale disturbance evolution. We demonstrate through canonical test cases that fine-scale variations in the baseflow can be captured effectively. The M-OWNS procedure permits arbitrarily small streamwisemarching step-sizes whilst maintaining stability. Crucially, we find the algorithm to be more robust than conventional non-modal OWNS, whilst recovering identical modal and non-modal phenomena.
format Preprint
id arxiv_https___arxiv_org_abs_2511_12605
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle A Modal One-Way Navier-Stokes Approach to Modelling Non-Modal Boundary Layer Instabilities
Badcock, E. J.
Mughal, S.
Fluid Dynamics
Numerical Analysis
This paper presents a method to solve the modal form of the linearised one-way Navier-Stokes (OWNS) equations for investigating disturbance development in developing subsonic and supersonic boundary layers. The modal framework offers significant advantages in robustness and computational efficiency over the conventional non-modal OWNS framework. Notably, we demonstrate that modal OWNS (M-OWNS) retains the capability to capture non-modal disturbance development. Our technique leverages the modal ansatz of parabolised stability equations (PSE) whilst employing the recursion-parameter parabolisation strategy of non-modal OWNS to stabilise the streamwise-marching modal algorithm. A key contribution is that we overcome the minimum streamwise step-size requirement that constrains conventional PSE in capturing short-scale disturbance evolution. We demonstrate through canonical test cases that fine-scale variations in the baseflow can be captured effectively. The M-OWNS procedure permits arbitrarily small streamwisemarching step-sizes whilst maintaining stability. Crucially, we find the algorithm to be more robust than conventional non-modal OWNS, whilst recovering identical modal and non-modal phenomena.
title A Modal One-Way Navier-Stokes Approach to Modelling Non-Modal Boundary Layer Instabilities
topic Fluid Dynamics
Numerical Analysis
url https://arxiv.org/abs/2511.12605