{"id":3968,"date":"2013-03-14T10:17:00","date_gmt":"2013-03-14T10:17:00","guid":{"rendered":"http:\/\/thales.mit.edu\/bush\/?p=3968"},"modified":"2021-04-16T06:06:57","modified_gmt":"2021-04-16T06:06:57","slug":"the-hydraulic-bemp-no-not-bump","status":"publish","type":"post","link":"https:\/\/thales.mit.edu\/bush\/index.php\/2013\/03\/14\/the-hydraulic-bemp-no-not-bump\/","title":{"rendered":"The hydraulic bump and vortex instability"},"content":{"rendered":"\n<div class=\"wp-block-cover has-subtle-background-color has-background-dim\"><div class=\"wp-block-cover__inner-container is-layout-flow wp-block-cover-is-layout-flow\">\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"921\" height=\"242\" src=\"http:\/\/thales.mit.edu\/bush\/wp-content\/uploads\/2021\/03\/bemp.jpg\" alt=\"\" class=\"wp-image-3998\"\/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">When a falling jet of fluid strikes a horizontal fluid layer, a hydraulic jump arises&nbsp;downstream of the point of impact, provided a critical flow rate is exceeded.We here&nbsp;examine a phenomenon that arises below this jump threshold, a circular deflection of&nbsp;relatively small amplitude on the free surface that we call the hydraulic bump. The&nbsp;form of the circular bump can be simply understood in terms of the underlying vortex&nbsp;structure and its height simply deduced with Bernoulli arguments. As the incoming&nbsp;flux increases, a breaking of axial symmetry leads to polygonal hydraulic bumps.&nbsp;The relation between this polygonal instability and that arising in the hydraulic jump&nbsp;is discussed. The coexistence of hydraulic jumps and bumps can give rise to striking&nbsp;nested structures with polygonal jumps bound within polygonal bumps. The absence&nbsp;of a pronounced surface signature on the hydraulic bump indicates the dominant&nbsp;influence of the subsurface vorticity on its instability.  See paper: &nbsp;<a href=\"http:\/\/math.mit.edu\/~bush\/wordpress\/wp-content\/uploads\/2013\/10\/Bump-2013.pdf\">Labousse &amp; Bush (2013)<\/a><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">This study prompted a theoretical description of the polygonal instability of toroidal vortices presented in the subsequent paper:  <a href=\"http:\/\/thales.mit.edu\/bush\/wp-content\/uploads\/2021\/04\/Labousse-epje-2015.pdf\">Labousse &amp; Bush (2015)<\/a><\/p>\n<\/div><\/div>\n","protected":false},"excerpt":{"rendered":"","protected":false},"author":1,"featured_media":6440,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[6],"tags":[],"class_list":["post-3968","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-interfacial-flows","entry"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v16.3 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>The hydraulic bump and vortex instability - John W. M. Bush<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/thales.mit.edu\/bush\/index.php\/2013\/03\/14\/the-hydraulic-bemp-no-not-bump\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"The hydraulic bump and vortex instability - John W. M. Bush\" \/>\n<meta property=\"og:url\" content=\"https:\/\/thales.mit.edu\/bush\/index.php\/2013\/03\/14\/the-hydraulic-bemp-no-not-bump\/\" \/>\n<meta property=\"og:site_name\" content=\"John W. M. 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