In principle, transition to turbulence can be studied using direct numerical simulation (DNS) and large eddy simulation (LES), but these approaches are limited by their large computational cost. The Nonlinear One-Way Navier-Stokes (NOWNS) equations have recently been developed and applied to study the early stages of boundary layer transition, and it was demonstrated that they can accurately replicate DNS results with similar accuracy to the nonlinear parabolized stability equations (NPSE) [15]. While having greater computational cost than NPSE, NOWNS is a more robust, convergent parabolization of the governing equations and succeeds for stronger nonlinearity where NPSE fails. In this work, we use NOWNS to reproduce (to the extent possible) the H- and K-type transition scenarios simulated using DNS by Sayadi et al.
",
"doi": "10.1007/978-981-96-9829-5_19",
"issn": "1875-3507",
"isbn": "9789819698288",
"publisher": "Springer Nature Singapore",
"place_of_publication": "Singapore",
"publication_date": "2026",
"pages": "143-149"
},
{
"id": "authors:jsmfb-ecf46",
"collection": "authors",
"collection_id": "jsmfb-ecf46",
"cite_using_url": "https://authors.library.caltech.edu/records/jsmfb-ecf46",
"type": "article",
"title": "Boundary-Layer Stability Analysis Using the Nonlinear One-Way Navier\u2013Stokes Approach",
"author": [
{
"family_name": "Sleeman",
"given_name": "Michael K.",
"orcid": "0000-0001-5949-9289",
"clpid": "Sleeman-Michael-K"
},
{
"family_name": "Colonius",
"given_name": "Tim",
"orcid": "0000-0003-0326-3909",
"clpid": "Colonius-T"
},
{
"family_name": "Lakebrink",
"given_name": "Matthew T."
}
],
"abstract": "We extend the one-way Navier Stokes (OWNS) approach to support nonlinear interactions between waves of different frequencies, which will enable nonlinear analysis of instability and transition. In OWNS, the linearized Navier\u2013Stokes equations are parabolized and solved in the frequency domain as a spatial initial-value (marching) problem. OWNS yields a reduced computational cost compared to global solvers while also conferring numerous advantages over the parabolized stability equations (PSEs), despite its higher computational cost relative to PSE, that we seek to extend to nonlinear analysis. We validate the nonlinear OWNS (NOWNS) method by examining the nonlinear evolution of two- and three-dimensional disturbances in a low-speed Blasius boundary layer compared to nonlinear PSE (NPSE) and direct numerical simulation (DNS) results from the literature. We demonstrate that NOWNS can be used to simulate flows involving blowing/suction strips, is more robust to numerical noise, and converges for stronger nonlinearities, as compared to NPSE.",
"doi": "10.2514/1.j064909",
"issn": "0001-1452",
"publisher": "AIAA",
"publication": "AIAA Journal",
"publication_date": "2025-08",
"series_number": "8",
"volume": "63",
"issue": "8",
"pages": "3145\u20133159"
},
{
"id": "authors:rdt9a-tra90",
"collection": "authors",
"collection_id": "rdt9a-tra90",
"cite_using_url": "https://authors.library.caltech.edu/records/rdt9a-tra90",
"type": "conference_item",
"title": "Nonlinear stability of wall-bounded flows using the One-Way Navier-Stokes (OWNS) Equations",
"book_title": "AIAA AVIATION 2023 Forum",
"author": [
{
"family_name": "Sleeman",
"given_name": "Michael K.",
"orcid": "0000-0001-5949-9289",
"clpid": "Sleeman-Michael-K"
},
{
"family_name": "Lakebrink",
"given_name": "Matthew T.",
"clpid": "Lakebrink-Matthew-T"
},
{
"family_name": "Colonius",
"given_name": "Tim",
"orcid": "0000-0003-0326-3909",
"clpid": "Colonius-T"
}
],
"abstract": "\n
\n
We extend the One-Way Navier Stokes (OWNS) approach to support nonlinear interactions between waves of different frequencies, which will enable nonlinear analysis of instability and transition. In linear OWNS, the linearized Navier-Stokes equations are modified such that upstream propagating modes are removed, so that they can be solved efficiently in the frequency domain as a spatial initial-value (marching) problem. Linear OWNS confers numerous advantages over the parabolized stability equations (PSE) that we seek to extend to nonlinear analysis. In the proposed method, the fully nonlinear Navier-Stokes equations are marched in the downstream direction. At each step of the march, the projection operator from the linear OWNS procedure is applied to (approximately) remove modes with upstream group velocity. We validate the method by examining the nonlinear evolution of two- and three-dimensional disturbances in a low-speed Blasius boundary layer by comparing with PSE and DNS results from the literature.
\n
\n