@proceedings {willis2022reduced,
	title = {Reduced-order models of coalescing Mach waves},
	publisher = {AIAA Scitech 2022 Forum, AIAA Paper 2022-1792},
    year = {2022},
	address = {San Diego, California, USA},
	author = {Willis, W. A., Tinney, C. E., Hamilton, M. F., Cormack, J. M.},
	abstract = {<p>Prior measurements of the sound field produced by a laboratory-scale, Mach 3 jet flow (Baars et al. 2013; Fiévet et al. 2016) suggest that acoustic waves steepen early on in their development. This explained the discrepancy between the theoretical prediction, based on expressions for effective Gol’dberg numbers, that shocks should not form in most laboratory scale facilities, and the apparent observation of steepened Mach waves close to laboratory-scale jets. The present work serves to continue our understanding of this phenomenon by exploring the coalescence process that occurs when neighboring waveforms intersect to form large amplitude waveforms capable of undergoing cumulative nonlinear distortion. A numerical model based on the Khokhlov–Zabolotskaya–Kuznetsov equation is first developed to show that coalescence-induced steepening is most sensitive to the intersection angle between adjacent waveforms, while increasing waveform duration decreases steepening overall. The model is expanded to include cylindrical spreading effects, which are pronounced within the peripheries of axisymmetric jets. High frame-rate schlieren images of sound waves propagating from the post potential core region of a laboratory scale Mach 3 jet are then captured along an angle following the ridge of most intense noise in order to study the development and evolution of coalescence. A new shock detection algorithm isolates shock-like features in the images at both upstream and downstream points along the propagation path. The isolated events are tracked using a translating coordinate system and decomposed using a Lagrangian form of the proper orthogonal decomposition. Reduced-order reconstructions of both the schlieren images and the KZK model identify common patterns that characterize the shock coalescence process as it leads to cumulative nonlinear waveform distortions.</p>},
	doi = {10.2514/6.2022-1792},
	url = {https://arc.aiaa.org/doi/pdf/10.2514/6.2022-1792},
}

{"_id":"wx9bRvi29YB6QSkZN","bibbaseid":"willis-tinney-hamilton-cormack-reducedordermodelsofcoalescingmachwaves-2022","author_short":["Willis, W. A.","Tinney, C. E.","Hamilton, M. F.","Cormack, J. M."],"bibdata":{"bibtype":"proceedings","type":"proceedings","title":"Reduced-order models of coalescing Mach waves","publisher":"AIAA Scitech 2022 Forum, AIAA Paper 2022-1792","year":"2022","address":"San Diego, California, USA","author":[{"propositions":[],"lastnames":["Willis"],"firstnames":["W.","A."],"suffixes":[]},{"propositions":[],"lastnames":["Tinney"],"firstnames":["C.","E."],"suffixes":[]},{"propositions":[],"lastnames":["Hamilton"],"firstnames":["M.","F."],"suffixes":[]},{"propositions":[],"lastnames":["Cormack"],"firstnames":["J.","M."],"suffixes":[]}],"abstract":"<p>Prior measurements of the sound field produced by a laboratory-scale, Mach 3 jet flow (Baars et al. 2013; Fiévet et al. 2016) suggest that acoustic waves steepen early on in their development. This explained the discrepancy between the theoretical prediction, based on expressions for effective Gol’dberg numbers, that shocks should not form in most laboratory scale facilities, and the apparent observation of steepened Mach waves close to laboratory-scale jets. The present work serves to continue our understanding of this phenomenon by exploring the coalescence process that occurs when neighboring waveforms intersect to form large amplitude waveforms capable of undergoing cumulative nonlinear distortion. A numerical model based on the Khokhlov–Zabolotskaya–Kuznetsov equation is first developed to show that coalescence-induced steepening is most sensitive to the intersection angle between adjacent waveforms, while increasing waveform duration decreases steepening overall. The model is expanded to include cylindrical spreading effects, which are pronounced within the peripheries of axisymmetric jets. High frame-rate schlieren images of sound waves propagating from the post potential core region of a laboratory scale Mach 3 jet are then captured along an angle following the ridge of most intense noise in order to study the development and evolution of coalescence. A new shock detection algorithm isolates shock-like features in the images at both upstream and downstream points along the propagation path. The isolated events are tracked using a translating coordinate system and decomposed using a Lagrangian form of the proper orthogonal decomposition. Reduced-order reconstructions of both the schlieren images and the KZK model identify common patterns that characterize the shock coalescence process as it leads to cumulative nonlinear waveform distortions.</p>","doi":"10.2514/6.2022-1792","url":"https://arc.aiaa.org/doi/pdf/10.2514/6.2022-1792","bibtex":"@proceedings {willis2022reduced,\r\n\ttitle = {Reduced-order models of coalescing Mach waves},\r\n\tpublisher = {AIAA Scitech 2022 Forum, AIAA Paper 2022-1792},\r\n year = {2022},\r\n\taddress = {San Diego, California, USA},\r\n\tauthor = {Willis, W. A., Tinney, C. E., Hamilton, M. F., Cormack, J. M.},\r\n\tabstract = {<p>Prior measurements of the sound field produced by a laboratory-scale, Mach 3 jet flow (Baars et al. 2013; Fiévet et al. 2016) suggest that acoustic waves steepen early on in their development. This explained the discrepancy between the theoretical prediction, based on expressions for effective Gol’dberg numbers, that shocks should not form in most laboratory scale facilities, and the apparent observation of steepened Mach waves close to laboratory-scale jets. The present work serves to continue our understanding of this phenomenon by exploring the coalescence process that occurs when neighboring waveforms intersect to form large amplitude waveforms capable of undergoing cumulative nonlinear distortion. A numerical model based on the Khokhlov–Zabolotskaya–Kuznetsov equation is first developed to show that coalescence-induced steepening is most sensitive to the intersection angle between adjacent waveforms, while increasing waveform duration decreases steepening overall. The model is expanded to include cylindrical spreading effects, which are pronounced within the peripheries of axisymmetric jets. High frame-rate schlieren images of sound waves propagating from the post potential core region of a laboratory scale Mach 3 jet are then captured along an angle following the ridge of most intense noise in order to study the development and evolution of coalescence. A new shock detection algorithm isolates shock-like features in the images at both upstream and downstream points along the propagation path. The isolated events are tracked using a translating coordinate system and decomposed using a Lagrangian form of the proper orthogonal decomposition. Reduced-order reconstructions of both the schlieren images and the KZK model identify common patterns that characterize the shock coalescence process as it leads to cumulative nonlinear waveform distortions.</p>},\r\n\tdoi = {10.2514/6.2022-1792},\r\n\turl = {https://arc.aiaa.org/doi/pdf/10.2514/6.2022-1792},\r\n}\r\n","author_short":["Willis, W. A.","Tinney, C. E.","Hamilton, M. F.","Cormack, J. 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