{"id":97,"date":"2020-07-24T01:13:23","date_gmt":"2020-07-24T01:13:23","guid":{"rendered":"http:\/\/blogs.oregonstate.edu\/salty\/?page_id=97"},"modified":"2023-09-09T05:03:18","modified_gmt":"2023-09-09T05:03:18","slug":"matlab-tools-to-solve-the-viscous-taylor-goldstein-equation-for-both-instabilities-and-waves","status":"publish","type":"page","link":"https:\/\/blogs.oregonstate.edu\/salty\/matlab-tools-to-solve-the-viscous-taylor-goldstein-equation-for-both-instabilities-and-waves\/","title":{"rendered":"Matlab tools to solve the viscous Taylor Goldstein equation for both instabilities and waves"},"content":{"rendered":"\n

wave_analysis.m<\/a> : code to solve demonstration problem
nash_data.txt<\/a> : observational data for demonstration problem
SSF.m<\/a> : the main subroutine
ddz.m<\/a> , ddz2.m<\/a>, ddz4.m<\/a> : auxiliary subroutines<\/p>\n\n\n\n

Reference:<\/p>\n\n\n\n

Smyth, W.D., J.N. Moum and J.D. Nash, 2011: \u201cNarrowband, high-frequency oscillations at the equator. Part II: Properties of shear instabilities”, J. Phys. Oceanogr.<\/em> 41<\/strong>, <\/em>412-428. [PDF]<\/a><\/p>\n\n\n\n

A guide to the relevant theory:<\/p>\n\n\n\n

Smyth, W.D. and J.R. Carpenter, 2019, \u201cInstability in Geophysical Flows\u201d,<\/em> Cambridge University Press. https:\/\/www.amazon.com\/Instability-Geophysical-Flows-William-Smyth-ebook\/dp\/B07RP1MC8G\/ref=sr_1_1?keywords=smyth+instability&qid=1573683499&sr=8-1<\/a><\/p>\n\n\n\n

\n\n\n\n

NEW VERSION: Fourier-Galerkin method is faster and more accurate.wave_analysis_FG.m<\/a> : code to solve demonstration problem
nash_data.txt<\/a> : observational data for demonstration problem
vTG_FG.m<\/a> : the main subroutine
BaryL.m<\/a> : auxiliary subroutine
vTG_FGprep.m<\/a> : auxiliary subroutine (call first)<\/p>\n\n\n\n

Reference:<\/p>\n\n\n\n

Lian, Q., W. D. Smyth, and Z. Liu, 2020: “Numerical Computation of Instabilities and Internal Waves from In Situ Measurements via the Viscous Taylor\u2013Goldstein Problem”.\u00a0J. Atmos. Oceanic Technol.<\/em>,\u00a0\u00a037<\/strong>, 759\u2013776,\u00a0https:\/\/doi.org\/10.1175\/JTECH-D-19-0155.1<\/a>. <\/p>\n\n\n\n

\n\n\n\n

Watch this space for more efficient methods currently in the works.<\/p>\n","protected":false},"excerpt":{"rendered":"

wave_analysis.m : code to solve demonstration problemnash_data.txt : observational data for demonstration problemSSF.m : the main subroutineddz.m , ddz2.m, ddz4.m : auxiliary subroutines Reference: Smyth, W.D., J.N. Moum and J.D. Nash, 2011: \u201cNarrowband, high-frequency oscillations at the equator. Part II: Properties of shear instabilities”, J. Phys. Oceanogr. 41, 412-428. [PDF] A guide to the relevant theory: Smyth, W.D. and J.R. Carpenter, 2019, \u201cInstability in Geophysical Flows\u201d, Cambridge… Continue reading →<\/span><\/a><\/p>\n","protected":false},"author":1561,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":["post-97","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/blogs.oregonstate.edu\/salty\/wp-json\/wp\/v2\/pages\/97","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/blogs.oregonstate.edu\/salty\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/blogs.oregonstate.edu\/salty\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/blogs.oregonstate.edu\/salty\/wp-json\/wp\/v2\/users\/1561"}],"replies":[{"embeddable":true,"href":"https:\/\/blogs.oregonstate.edu\/salty\/wp-json\/wp\/v2\/comments?post=97"}],"version-history":[{"count":12,"href":"https:\/\/blogs.oregonstate.edu\/salty\/wp-json\/wp\/v2\/pages\/97\/revisions"}],"predecessor-version":[{"id":216,"href":"https:\/\/blogs.oregonstate.edu\/salty\/wp-json\/wp\/v2\/pages\/97\/revisions\/216"}],"wp:attachment":[{"href":"https:\/\/blogs.oregonstate.edu\/salty\/wp-json\/wp\/v2\/media?parent=97"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}