{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,24]],"date-time":"2026-08-24T16:31:26Z","timestamp":1787589086562,"version":"build-2736575974"},"reference-count":41,"publisher":"Acoustical Society of America (ASA)","issue":"2","funder":[{"DOI":"10.13039\/501100001665","name":"Agence Nationale de la Recherche","doi-asserted-by":"publisher","award":["ANR-24-CE51-3544-01"],"award-info":[{"award-number":["ANR-24-CE51-3544-01"]}],"id":[{"id":"10.13039\/501100001665","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["pubs.aip.org"],"crossmark-restriction":true},"short-container-title":[],"published-print":{"date-parts":[[2026,8,1]]},"abstract":"<jats:p>The interaction of a weak shock wave in a fluid with an incident sound wave is investigated, either in the counter- or co-propagating cases. This last situation is possible because the shock wave moves supersonically and overcomes the sonic sound wave. For a sustained shock, the problem can be solved analytically by introducing a transmitted sound wave, a vorticity mode and an entropy mode in the post-shock region, and a perturbation of the shock front. Due to the relative motions of the shock and the incident wave, a Doppler effect occurs. The analysis of the eight possible regimes of interaction outlines the influence of the shock strength. For an intermediate range of angles, transmitted waves are observed. For the highest incidence angles in the co-propagating case, the transmitted wave is propagative again but exhibits meta-like properties similar to those searched for in artificial meta-materials. These properties are negative transmission, or reversal of the direction of the transmitted wave along the shock front, and anomalous Doppler effect (Doppler ratio smaller than unity).<\/jats:p>","DOI":"10.1121\/10.0044525","type":"journal-article","created":{"date-parts":[[2026,8,24]],"date-time":"2026-08-24T15:53:15Z","timestamp":1787586795000},"page":"1761-1774","update-policy":"https:\/\/doi.org\/10.1063\/aip-crossmark-policy-page","source":"Crossref","is-referenced-by-count":0,"title":["Giant and anomalous Doppler effect, negative transmission and meta-like interaction between an acoustical wave and a weak shock"],"prefix":"10.1121","volume":"160","author":[{"given":"Ronan","family":"Delalande","sequence":"first","affiliation":[{"name":"Sorbonne Universit\u00e9, Centre National de la Recherche Scientifique, Institut Jean Le Rond d'Alembert 1 , F-75005 Paris,","place":["France"]},{"name":"Proc\u00e9d\u00e9s et Ing\u00e9nierie en M\u00e9canique et Mat\u00e9riaux Laboratory, Unit\u00e9 Mixte de Recherche 8006, Arts et Metiers Institute of Technology 2 , \u00c9cole Nationale Sup\u00e9rieure d'Arts et M\u00e9tiers, Centre National de la Recherche Scientifique, Conservatoire National des Arts et M\u00e9tiers, 151 Boulevard de l'H\u00f4pital, 75013 Paris,","place":["France"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4014-6747","authenticated-orcid":false,"given":"Mathieu","family":"Ducousso","sequence":"additional","affiliation":[{"name":"Proc\u00e9d\u00e9s et Ing\u00e9nierie en M\u00e9canique et Mat\u00e9riaux Laboratory, Unit\u00e9 Mixte de Recherche 8006, Arts et Metiers Institute of Technology 2 , \u00c9cole Nationale Sup\u00e9rieure d'Arts et M\u00e9tiers, Centre National de la Recherche Scientifique, Conservatoire National des Arts et M\u00e9tiers, 151 Boulevard de l'H\u00f4pital, 75013 Paris,","place":["France"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Guillaume","family":"Musy","sequence":"additional","affiliation":[{"name":"Sorbonne Universit\u00e9, Centre National de la Recherche Scientifique, Institut Jean Le Rond d'Alembert 1 , F-75005 Paris,","place":["France"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7395-0088","authenticated-orcid":false,"given":"Fran\u00e7ois","family":"Coulouvrat","sequence":"additional","affiliation":[{"name":"Sorbonne Universit\u00e9, Centre National de la Recherche Scientifique, Institut Jean Le Rond d'Alembert 1 , F-75005 Paris,","place":["France"]}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"231","published-online":{"date-parts":[[2026,8,24]]},"reference":[{"issue":"2","key":"2026082411531027500_c1","first-page":"465","article-title":"\u00dcber das farbige Licht der Doppelsterne und einiger anderer Gestirne des Himmels\u201d (\u201cOn the coloured light of the binary stars and some other stars of the heavens\u201d)","volume":"5","year":"1843","journal-title":"Abh. K\u00f6nigl. B\u00f6hm. Ges. Wiss."},{"key":"2026082411531027500_c2","doi-asserted-by":"publisher","first-page":"321","DOI":"10.1002\/andp.18451421102","article-title":"Akustische Versuche auf der Niederlandische Eisenbahn, nebst gelegentliche Bemerkungen zur Theorie des Herrn Prof. Doppler\u201d (\u201cAcoustic experiments on the Dutch railways, along with occasional remarks on the theory of Prof. Doppler\u201d)","volume":"142","year":"1845","journal-title":"Ann. Phys. Chem."},{"issue":"16","key":"2026082411531027500_c3","doi-asserted-by":"publisher","first-page":"241","DOI":"10.1002\/asna.18710781602","article-title":"Resultate spectralanalytischer Beobachtungen, angestellt auf der Sternwarte zu Bothkamp\u201d (\u201cResults of spectral analyses conducted at the Bothkamp observatory\u201d)","volume":"78","year":"1872","journal-title":"Astron. Nachr."},{"issue":"6555","key":"2026082411531027500_c4","doi-asserted-by":"publisher","first-page":"355","DOI":"10.1038\/378355a0","article-title":"A Jupiter-mass companion to a solar-type star","volume":"378","year":"1995","journal-title":"Nature"},{"issue":"3","key":"2026082411531027500_c5","doi-asserted-by":"publisher","first-page":"30","DOI":"10.1063\/PT.3.4429","article-title":"The fall and rise of the Doppler effect","volume":"73","year":"2020","journal-title":"Phys. Today"},{"issue":"11","key":"2026082411531027500_c6","doi-asserted-by":"publisher","first-page":"1181","DOI":"10.1121\/1.1908737","article-title":"Ultrasonic Doppler method for the inspection of cardiac functions","volume":"29","year":"1957","journal-title":"J. Acoust. Soc. Am."},{"key":"2026082411531027500_c7","doi-asserted-by":"publisher","first-page":"151","DOI":"10.20697\/jasj.15.3_151","article-title":"Study of the flow patterns in peripheral arteries by ultrasonics","volume":"15","year":"1959","journal-title":"J. Acoust. Soc. Jpn."},{"issue":"1","key":"2026082411531027500_c8","doi-asserted-by":"publisher","first-page":"11","DOI":"10.1016\/0301-5629(75)90036-8","article-title":"Development of the ultrasonic flowmeter","volume":"2","year":"1975","journal-title":"Ultrasound Med. Biol."},{"issue":"2","key":"2026082411531027500_c9","doi-asserted-by":"publisher","first-page":"179","DOI":"10.1016\/S0039-6109(05)70308-X","article-title":"The history of ultrasound","volume":"78","year":"1998","journal-title":"Surg. Clin. North Am."},{"key":"2026082411531027500_c10","doi-asserted-by":"publisher","first-page":"48(1\u20133)","DOI":"10.1186\/s12947-015-0042-3","article-title":"Shigeo Satomura: 60 years of Doppler ultrasound in medicine","volume":"13","year":"2015","journal-title":"Cardiovasc. Ultrasound"},{"issue":"4","key":"2026082411531027500_c11","doi-asserted-by":"publisher","first-page":"509","DOI":"10.1070\/PU1968v010n04ABEH003699","article-title":"The electrodynamics of substances with simultaneously negative values of \u03b5 and","volume":"10","year":"1968","journal-title":"Phys. Usp."},{"issue":"1","key":"2026082411531027500_c12","doi-asserted-by":"publisher","first-page":"015602","DOI":"10.1103\/PhysRevE.73.015602","article-title":"Anomalous Doppler effects in phononic band gaps","volume":"73","year":"2006","journal-title":"Phys. Rev. E"},{"key":"2026082411531027500_c13","doi-asserted-by":"publisher","first-page":"32388(1\u201310)","DOI":"10.1038\/srep32388","article-title":"Inverse Doppler effects in broadband acoustic metamaterials","volume":"6","year":"2016","journal-title":"Sci. Rep."},{"key":"2026082411531027500_c14","doi-asserted-by":"publisher","first-page":"1519(1\u20137)","DOI":"10.1038\/s41598-020-58370-3","article-title":"Reversed Doppler effect based on hybridized acoustic Mie resonances","volume":"10","year":"2020","journal-title":"Sci. Rep."},{"key":"2026082411531027500_c15","first-page":"1","article-title":"Fundamentals of duct acoustics","volume":"598","year":"2015","journal-title":"VKI Lect. Notes"},{"issue":"9","key":"2026082411531027500_c16","doi-asserted-by":"publisher","first-page":"667","DOI":"10.1038\/s41578-020-0206-0","article-title":"Nonreciprocity in acoustic and elastic materials","volume":"5","year":"2020","journal-title":"Nat. Rev. Mater."},{"issue":"1","key":"2026082411531027500_c17","doi-asserted-by":"publisher","first-page":"016602","DOI":"10.1103\/PhysRevE.64.016602","article-title":"Breaking of time reversal invariance in nonlinear acoustics","volume":"64","year":"2001","journal-title":"Phys. Rev. E"},{"issue":"5","key":"2026082411531027500_c18","doi-asserted-by":"publisher","first-page":"055602","DOI":"10.1103\/PhysRevE.70.055602","article-title":"Double-negative acoustic metamaterial","volume":"70","year":"2004","journal-title":"Phys. Rev. E"},{"issue":"18","key":"2026082411531027500_c19","doi-asserted-by":"publisher","first-page":"3966","DOI":"10.1103\/PhysRevLett.85.3966","article-title":"Negative refraction makes a perfect lens","volume":"85","year":"2000","journal-title":"Phys. Rev. Lett."},{"issue":"5514","key":"2026082411531027500_c20","doi-asserted-by":"publisher","first-page":"77","DOI":"10.1126\/science.1058847","article-title":"Experimental verification of a negative index of refraction","volume":"292","year":"2001","journal-title":"Science"},{"issue":"11","key":"2026082411531027500_c21","doi-asserted-by":"publisher","first-page":"399(1\u201318)","DOI":"10.1088\/1367-2630\/9\/11\/399","article-title":"Acoustic metamaterials for sound focusing and confinement","volume":"9","year":"2007","journal-title":"New J. Phys."},{"issue":"5485","key":"2026082411531027500_c22","doi-asserted-by":"publisher","first-page":"1734","DOI":"10.1126\/science.289.5485.1734","article-title":"Locally resonant sonic materials","volume":"289","year":"2000","journal-title":"Science"},{"issue":"19","key":"2026082411531027500_c23","doi-asserted-by":"publisher","first-page":"194301(1\u20134)","DOI":"10.1103\/PhysRevLett.102.194301","article-title":"Focusing ultrasound with an acoustic metamaterial network","volume":"102","year":"2009","journal-title":"Phys. Rev. Lett."},{"issue":"4","key":"2026082411531027500_c24","doi-asserted-by":"publisher","first-page":"384","DOI":"10.1038\/nmat4164","article-title":"Soft 3D acoustic metamaterial with negative index","volume":"14","year":"2015","journal-title":"Nat. Mater."},{"issue":"2","key":"2026082411531027500_c25","doi-asserted-by":"publisher","first-page":"2000988","DOI":"10.1002\/adem.202000988","article-title":"Fabricating and assembling acoustic metamaterials and phononic crystals","volume":"23","year":"2021","journal-title":"Adv. Eng. Mater."},{"key":"2026082411531027500_c26","volume-title":"\u00dcber Den Einflu\u00df Der Bewegung Des Fortpflanzungsmittels Auf Die Erscheinung Der \u00c4ther-, Luft-Und Wasserwellen: ein Weiterer Beitrag Zur Allgemeinen Wellenlehre","year":"1847"},{"issue":"10","key":"2026082411531027500_c27","doi-asserted-by":"publisher","first-page":"277","DOI":"10.1002\/andp.18872681008","article-title":"Photographische Fixirung der durch Projectile in der Luft eingeleiteten Vorg\u00e4nge\u201d (\u201cPhotographic capture of the processes initiated by projectiles in flight\u201d)","volume":"268","year":"1887","journal-title":"Ann. Phys."},{"issue":"3","key":"2026082411531027500_c28","doi-asserted-by":"publisher","first-page":"301","DOI":"10.1002\/cpa.3160050305","article-title":"The flow pattern of a supersonic projectile","volume":"5","year":"1952","journal-title":"Commun. Pure Appl. Math."},{"key":"2026082411531027500_c29","first-page":"273","article-title":"On the transmission of sound waves through a shock wave","volume":"XLIX","year":"1946","journal-title":"Kon. Ned. Akad. Wetensch."},{"key":"2026082411531027500_c30","doi-asserted-by":"crossref","first-page":"478","DOI":"10.1007\/978-94-011-0195-0","article-title":"On the transmission of sound waves through a shock wave","volume-title":"Selected Papers of J. M. Burgers","author":"Nieuwstadt","year":"1995"},{"issue":"21","key":"2026082411531027500_c31","doi-asserted-by":"publisher","first-page":"1351","DOI":"10.1103\/PhysRevLett.46.1351","article-title":"Experimental black-hole evaporation?","volume":"46","year":"1981","journal-title":"Phys. Rev. Lett."},{"key":"2026082411531027500_c32","unstructured":"F. K.\n            Moore\n          , \u201cUnsteady oblique interaction of a shock wave with a plane disturbance,\u201d Technical Report No. 2879, NACA, Cleveland, OH (1953)."},{"key":"2026082411531027500_c33","doi-asserted-by":"publisher","first-page":"2350","DOI":"10.1063\/1.1691825","article-title":"Interaction of linear waves with oblique shock waves","volume":"11","year":"1968","journal-title":"Phys. Fluids"},{"issue":"6","key":"2026082411531027500_c34","doi-asserted-by":"publisher","first-page":"4085","DOI":"10.1121\/10.0034623","article-title":"Nonlinear interaction of an acoustical wave with a counter-propagating weak shock","volume":"156","year":"2024","journal-title":"J. Acoust. Soc. Am."},{"issue":"2","key":"2026082411531027500_c35","doi-asserted-by":"publisher","first-page":"1302","DOI":"10.1121\/10.0035846","article-title":"Erratum: Nonlinear interaction of an acoustical wave with a counter-propagating weak shock [J. Acoust. Soc. Am. 156, 4085\u20134098 (2024)]","volume":"157","year":"2025","journal-title":"J. Acoust. Soc. Am."},{"issue":"5","key":"2026082411531027500_c36","doi-asserted-by":"publisher","first-page":"L051002","DOI":"10.1103\/PhysRevApplied.15.L051002","article-title":"Bulk probing of shock wave spatial distribution in opaque solids by ultrasonic interaction","volume":"15","year":"2021","journal-title":"Phys. Rev. Appl."},{"key":"2026082411531027500_c37","volume-title":"Nonlinear Acoustics","year":"1998"},{"key":"2026082411531027500_c38","first-page":"527","article-title":"Physics of shock-wave lithotripsy","volume-title":"Smith's Textbook of Endourology","year":"2012"},{"issue":"24","key":"2026082411531027500_c39","doi-asserted-by":"publisher","first-page":"244903","DOI":"10.1063\/5.0021131","article-title":"Propagation of laser-generated shock waves in metals: 3D axisymmetric simulations compared to experiments","volume":"128","year":"2020","journal-title":"J. Appl. Phys."},{"key":"2026082411531027500_c40","volume-title":"Elastic-Plastic Response of Solids under Shock-Wave Loading","year":"2004"},{"issue":"4","key":"2026082411531027500_c41","first-page":"A314","article-title":"Negative Doppler effect and negative transmission of an acoustical wave overtaken by a finite-size weak shock","volume":"159","year":"2026","journal-title":"J. Acoust. Soc. Am."}],"container-title":["The Journal of the Acoustical Society of America"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/pubs.aip.org\/asa\/jasa\/article-pdf\/160\/2\/1761\/21117175\/1761_1_10.0044525.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"syndication"},{"URL":"https:\/\/pubs.aip.org\/asa\/jasa\/article-pdf\/160\/2\/1761\/21117175\/1761_1_10.0044525.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,24]],"date-time":"2026-08-24T15:53:18Z","timestamp":1787586798000},"score":1,"resource":{"primary":{"URL":"https:\/\/pubs.aip.org\/jasa\/article\/160\/2\/1761\/3402979\/Giant-and-anomalous-Doppler-effect-negative"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,8,1]]},"references-count":41,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2026,8,1]]}},"URL":"https:\/\/doi.org\/10.1121\/10.0044525","relation":{},"ISSN":["1520-8524"],"issn-type":[{"value":"1520-8524","type":"electronic"}],"subject":[],"published-other":{"date-parts":[[2026,8]]},"published":{"date-parts":[[2026,8,1]]}}}