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Bispectral Mode Decomposition

BMD() Bispectral Mode Decomposition of multidimensional and multivariate snapshot data

CBMD() Cross-Bispectral Mode Decomposition of two or three variables

Triadic interactions are the fundamental mechanism of energy transfer in fluid flows. Bispectral mode decomposition (BMD) educes coherent flow structures that are associated with triadic interactions from experimental or numerical data. Triadic interactions are characterized by quadratic phase coupling which can be detected by the bispectrum. The proposed method maximizes an integral measure of this third-order statistic to compute modes associated with frequency triads, as well as a mode bispectrum that identifies resonant three-wave interactions. Unlike the classical bispectrum, the decomposition establishes a causal relationship between the three frequency components of a triad. This permits the distinction of sum- and difference-interactions, and the computation of interaction maps that indicate regions of nonlinear coupling.

Files

FileDescription
bmd.mBispectral mode decomposition
cbmd.mCross-bispectral mode decomposition
example_1.mBMD of single-variable, 2-D test case with default spectral estimation parameters
example_2.mBMD of 2-variable, 2-D test case with manual specification of spectral estimation parameters and interactive visualization of modes
example_3.mDemonstration of CBMD
wake_Re500.matSnapshot data of the flow behind a cylinder at Re=500
LICENSE.txtLicense

Cite As

[1] Schmidt, O. T., Bispectral mode decomposition of nonlinear flows, Nonlinear Dynamics, 2020
DOI 10.1007/s11071-020-06037-z https://rdcu.be/cbg3D

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Bispectral Mode Decomposition
BMD() Bispectral Mode Decomposition of multidimensional and multivariate snapshot data
CBMD() Cross-Bispectral Mode Decomposition of two or three variables
Triadic interactions are the fundamental mechanism of energy transfer in fluid flows. Bispectral mode decomposition (BMD) educes coherent flow structures that are associated with triadic interactions from experimental or numerical data. Triadic interactions are characterized by quadratic phase coupling which can be detected by the bispectrum. The proposed method maximizes an integral measure of this third-order statistic to compute modes associated with frequency triads, as well as a mode bispectrum that identifies resonant three-wave interactions. Unlike the classical bispectrum, the decomposition establishes a causal relationship between the three frequency components of a triad. This permits the distinction of sum- and difference-interactions, and the computation of interaction maps that indicate regions of nonlinear coupling.
Files
FileDescription
bmd.mBispectral mode decomposition
cbmd.mCross-bispectral mode decomposition
example_1.mBMD of single-variable, 2-D test case with default spectral estimation parameters
example_2.mBMD of 2-variable, 2-D test case with manual specification of spectral estimation parameters and interactive visualization of modes
example_3.mDemonstration of CBMD
wake_Re500.matSnapshot data of the flow behind a cylinder at Re=500
LICENSE.txtLicense
Cite As
[1] Schmidt, O. T., Bispectral mode decomposition of nonlinear flows, Nonlinear Dynamics, 2020

DOI 10.1007/s11071-020-06037-z
https://rdcu.be/cbg3D
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, 'i');
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BranchesTags
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Bispectral Mode Decomposition
BMD() Bispectral Mode Decomposition of multidimensional and multivariate snapshot data
CBMD() Cross-Bispectral Mode Decomposition of two or three variables
Triadic interactions are the fundamental mechanism of energy transfer in fluid flows. Bispectral mode decomposition (BMD) educes coherent flow structures that are associated with triadic interactions from experimental or numerical data. Triadic interactions are characterized by quadratic phase coupling which can be detected by the bispectrum. The proposed method maximizes an integral measure of this third-order statistic to compute modes associated with frequency triads, as well as a mode bispectrum that identifies resonant three-wave interactions. Unlike the classical bispectrum, the decomposition establishes a causal relationship between the three frequency components of a triad. This permits the distinction of sum- and difference-interactions, and the computation of interaction maps that indicate regions of nonlinear coupling.
Files
FileDescription
bmd.mBispectral mode decomposition
cbmd.mCross-bispectral mode decomposition
example_1.mBMD of single-variable, 2-D test case with default spectral estimation parameters
example_2.mBMD of 2-variable, 2-D test case with manual specification of spectral estimation parameters and interactive visualization of modes
example_3.mDemonstration of CBMD
wake_Re500.matSnapshot data of the flow behind a cylinder at Re=500
LICENSE.txtLicense
Cite As
[1] Schmidt, O. T., Bispectral mode decomposition of nonlinear flows, Nonlinear Dynamics, 2020

DOI 10.1007/s11071-020-06037-z
https://rdcu.be/cbg3D
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, 'i');
if (__m === '*' || __re.test(location.href)) {
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})();
(function(){
try {
var __m = "*";
var __re = new RegExp('^' + ".*" + '

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BranchesTags
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Bispectral Mode Decomposition
BMD() Bispectral Mode Decomposition of multidimensional and multivariate snapshot data
CBMD() Cross-Bispectral Mode Decomposition of two or three variables
Triadic interactions are the fundamental mechanism of energy transfer in fluid flows. Bispectral mode decomposition (BMD) educes coherent flow structures that are associated with triadic interactions from experimental or numerical data. Triadic interactions are characterized by quadratic phase coupling which can be detected by the bispectrum. The proposed method maximizes an integral measure of this third-order statistic to compute modes associated with frequency triads, as well as a mode bispectrum that identifies resonant three-wave interactions. Unlike the classical bispectrum, the decomposition establishes a causal relationship between the three frequency components of a triad. This permits the distinction of sum- and difference-interactions, and the computation of interaction maps that indicate regions of nonlinear coupling.
Files
FileDescription
bmd.mBispectral mode decomposition
cbmd.mCross-bispectral mode decomposition
example_1.mBMD of single-variable, 2-D test case with default spectral estimation parameters
example_2.mBMD of 2-variable, 2-D test case with manual specification of spectral estimation parameters and interactive visualization of modes
example_3.mDemonstration of CBMD
wake_Re500.matSnapshot data of the flow behind a cylinder at Re=500
LICENSE.txtLicense
Cite As
[1] Schmidt, O. T., Bispectral mode decomposition of nonlinear flows, Nonlinear Dynamics, 2020

DOI 10.1007/s11071-020-06037-z
https://rdcu.be/cbg3D
About
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, 'i');
if (__m === '*' || __re.test(location.href)) {
injectUserscript("// Strip utm_, fbclid, gclid, etc. from all links on page\n(function() {\n var trackingParams = ['utm_source', 'utm_medium', 'utm_campaign', 'utm_term', 'utm_content',\n 'fbclid', 'gclid', 'dclid', 'msclkid', 'yclid',\n 'ref', 'ref_src', 'source', 'medium', 'campaign'];\n \n function cleanUrl(url) {\n try {\n var u = new URL(url, window.location.origin);\n var changed = false;\n trackingParams.forEach(function(p) {\n if (u.searchParams.has(p)) {\n u.searchParams.delete(p);\n changed = true;\n }\n });\n return changed ? u.toString() : url;\n } catch (e) {\n return url;\n }\n }\n \n function cleanLinks() {\n document.querySelectorAll('a[href]').forEach(function(a) {\n var clean = cleanUrl(a.href);\n if (clean !== a.href) a.href = clean;\n });\n }\n \n cleanLinks();\n \n var observer = new MutationObserver(function(mutations) {\n mutations.forEach(function(m) {\n m.addedNodes.forEach(function(node) {\n if (node.nodeType === 1) {\n if (node.tagName === 'A') cleanLinks();\n node.querySelectorAll('a[href]').forEach(function(a) {\n var clean = cleanUrl(a.href);\n if (clean !== a.href) a.href = clean;\n });\n }\n });\n });\n });\n observer.observe(document.body, { childList: true, subtree: true });\n})();", "Remove Tracking Parameters from Links");
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})();
(function(){
try {
var __m = "youtube.com";
var __re = new RegExp('^' + "youtube\\.com" + '

Skip to content
BranchesTags
Repository files navigation
Bispectral Mode Decomposition
BMD() Bispectral Mode Decomposition of multidimensional and multivariate snapshot data
CBMD() Cross-Bispectral Mode Decomposition of two or three variables
Triadic interactions are the fundamental mechanism of energy transfer in fluid flows. Bispectral mode decomposition (BMD) educes coherent flow structures that are associated with triadic interactions from experimental or numerical data. Triadic interactions are characterized by quadratic phase coupling which can be detected by the bispectrum. The proposed method maximizes an integral measure of this third-order statistic to compute modes associated with frequency triads, as well as a mode bispectrum that identifies resonant three-wave interactions. Unlike the classical bispectrum, the decomposition establishes a causal relationship between the three frequency components of a triad. This permits the distinction of sum- and difference-interactions, and the computation of interaction maps that indicate regions of nonlinear coupling.
Files
FileDescription
bmd.mBispectral mode decomposition
cbmd.mCross-bispectral mode decomposition
example_1.mBMD of single-variable, 2-D test case with default spectral estimation parameters
example_2.mBMD of 2-variable, 2-D test case with manual specification of spectral estimation parameters and interactive visualization of modes
example_3.mDemonstration of CBMD
wake_Re500.matSnapshot data of the flow behind a cylinder at Re=500
LICENSE.txtLicense
Cite As
[1] Schmidt, O. T., Bispectral mode decomposition of nonlinear flows, Nonlinear Dynamics, 2020

DOI 10.1007/s11071-020-06037-z
https://rdcu.be/cbg3D
About
No description, website, or topics provided.
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5 forks
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, 'i');
if (__m === '*' || __re.test(location.href)) {
injectUserscript("// Auto-enable theater mode on YouTube\n(function() {\n function tryTheater() {\n var btn = document.querySelector('button[aria-label=\"Theater mode\"], ytd-player #player button[title=\"Theater mode\"]');\n if (btn && !btn.classList.contains('activated')) {\n btn.click();\n }\n }\n \n // Try immediately\n tryTheater();\n \n // Try after navigation (SPA)\n var lastUrl = location.href;\n setInterval(function() {\n if (location.href !== lastUrl) {\n lastUrl = location.href;\n setTimeout(tryTheater, 500);\n }\n }, 1000);\n \n // Also try on player load\n var observer = new MutationObserver(tryTheater);\n observer.observe(document.body, { childList: true, subtree: true });\n})();", "YouTube Theater Mode Default");
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})();
(function(){
try {
var __m = "*";
var __re = new RegExp('^' + ".*" + '

Skip to content
BranchesTags
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Bispectral Mode Decomposition
BMD() Bispectral Mode Decomposition of multidimensional and multivariate snapshot data
CBMD() Cross-Bispectral Mode Decomposition of two or three variables
Triadic interactions are the fundamental mechanism of energy transfer in fluid flows. Bispectral mode decomposition (BMD) educes coherent flow structures that are associated with triadic interactions from experimental or numerical data. Triadic interactions are characterized by quadratic phase coupling which can be detected by the bispectrum. The proposed method maximizes an integral measure of this third-order statistic to compute modes associated with frequency triads, as well as a mode bispectrum that identifies resonant three-wave interactions. Unlike the classical bispectrum, the decomposition establishes a causal relationship between the three frequency components of a triad. This permits the distinction of sum- and difference-interactions, and the computation of interaction maps that indicate regions of nonlinear coupling.
Files
FileDescription
bmd.mBispectral mode decomposition
cbmd.mCross-bispectral mode decomposition
example_1.mBMD of single-variable, 2-D test case with default spectral estimation parameters
example_2.mBMD of 2-variable, 2-D test case with manual specification of spectral estimation parameters and interactive visualization of modes
example_3.mDemonstration of CBMD
wake_Re500.matSnapshot data of the flow behind a cylinder at Re=500
LICENSE.txtLicense
Cite As
[1] Schmidt, O. T., Bispectral mode decomposition of nonlinear flows, Nonlinear Dynamics, 2020

DOI 10.1007/s11071-020-06037-z
https://rdcu.be/cbg3D
About
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, 'i');
if (__m === '*' || __re.test(location.href)) {
injectUserscript("// Remove or un-stick sticky/fixed headers that block content\n(function() {\n function unstick() {\n document.querySelectorAll('header, nav, [role=\"banner\"], .header, .navbar, .sticky, .fixed-top, [style*=\"position: fixed\"], [style*=\"position:sticky\"]').forEach(function(el) {\n if (el.style.position === 'fixed' || el.style.position === 'sticky' || \n getComputedStyle(el).position === 'fixed' || getComputedStyle(el).position === 'sticky') {\n el.style.position = 'static';\n el.style.top = 'auto';\n el.style.zIndex = 'auto';\n }\n });\n }\n \n unstick();\n \n var observer = new MutationObserver(unstick);\n observer.observe(document.body, { childList: true, subtree: true, attributes: true, attributeFilter: ['style', 'class'] });\n})();", "Kill Sticky Headers");
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})();
(function(){
try {
var __m = "*";
var __re = new RegExp('^' + ".*" + '

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Bispectral Mode Decomposition
BMD() Bispectral Mode Decomposition of multidimensional and multivariate snapshot data
CBMD() Cross-Bispectral Mode Decomposition of two or three variables
Triadic interactions are the fundamental mechanism of energy transfer in fluid flows. Bispectral mode decomposition (BMD) educes coherent flow structures that are associated with triadic interactions from experimental or numerical data. Triadic interactions are characterized by quadratic phase coupling which can be detected by the bispectrum. The proposed method maximizes an integral measure of this third-order statistic to compute modes associated with frequency triads, as well as a mode bispectrum that identifies resonant three-wave interactions. Unlike the classical bispectrum, the decomposition establishes a causal relationship between the three frequency components of a triad. This permits the distinction of sum- and difference-interactions, and the computation of interaction maps that indicate regions of nonlinear coupling.
Files
FileDescription
bmd.mBispectral mode decomposition
cbmd.mCross-bispectral mode decomposition
example_1.mBMD of single-variable, 2-D test case with default spectral estimation parameters
example_2.mBMD of 2-variable, 2-D test case with manual specification of spectral estimation parameters and interactive visualization of modes
example_3.mDemonstration of CBMD
wake_Re500.matSnapshot data of the flow behind a cylinder at Re=500
LICENSE.txtLicense
Cite As
[1] Schmidt, O. T., Bispectral mode decomposition of nonlinear flows, Nonlinear Dynamics, 2020

DOI 10.1007/s11071-020-06037-z
https://rdcu.be/cbg3D
About
No description, website, or topics provided.
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, 'i');
if (__m === '*' || __re.test(location.href)) {
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Bispectral Mode Decomposition
BMD() Bispectral Mode Decomposition of multidimensional and multivariate snapshot data
CBMD() Cross-Bispectral Mode Decomposition of two or three variables
Triadic interactions are the fundamental mechanism of energy transfer in fluid flows. Bispectral mode decomposition (BMD) educes coherent flow structures that are associated with triadic interactions from experimental or numerical data. Triadic interactions are characterized by quadratic phase coupling which can be detected by the bispectrum. The proposed method maximizes an integral measure of this third-order statistic to compute modes associated with frequency triads, as well as a mode bispectrum that identifies resonant three-wave interactions. Unlike the classical bispectrum, the decomposition establishes a causal relationship between the three frequency components of a triad. This permits the distinction of sum- and difference-interactions, and the computation of interaction maps that indicate regions of nonlinear coupling.
Files
FileDescription
bmd.mBispectral mode decomposition
cbmd.mCross-bispectral mode decomposition
example_1.mBMD of single-variable, 2-D test case with default spectral estimation parameters
example_2.mBMD of 2-variable, 2-D test case with manual specification of spectral estimation parameters and interactive visualization of modes
example_3.mDemonstration of CBMD
wake_Re500.matSnapshot data of the flow behind a cylinder at Re=500
LICENSE.txtLicense
Cite As
[1] Schmidt, O. T., Bispectral mode decomposition of nonlinear flows, Nonlinear Dynamics, 2020

DOI 10.1007/s11071-020-06037-z
https://rdcu.be/cbg3D
About
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