VMT_Vorticity

PURPOSE ^

Not currently implemented

SYNOPSIS ^

function [V] = VMT_Vorticity(V)

DESCRIPTION ^

 Not currently implemented

 Computes normalized STREAMWISE vorticity for the averaged cross-section
 based 3 different measures of secondary flow (Transverse (v), Secondary
 (zsd), Secondary (Roz)). This function uses the smoothed values of each
 component, and thus is called with each REPLOT.
 
 Vorticity (\omega) is normalized by the channel top width &
 average streamwise velocity:
       \omega = \tilde{\omega} frac{B}{U} 
 
 FROM WIKIPEDIA: In fluid dynamics, the vorticity is a vector that
 describes the local spinning motion of a fluid near some point, as would
 be seen by an observer located at that point and traveling along with the
 fluid. Conceptually, the vorticity could be determined by marking the
 particles of the fluid in a small neighborhood of the point in question,
 and watching their relative displacements as they move along the flow.
 The vorticity vector would be twice the mean angular velocity vector of
 those particles relative to their center of mass, oriented according to
 the right-hand rule. This quantity must not be confused with the angular
 velocity of the particles relative to some other point. More precisely,
 the vorticity of a flow is a vector field (\omega), equal to the CURL
 (rotational) of its velocity field (v,w).
 
 Written by Frank L. Engel, USGS
 Last modified: F.L. Engel, USGS, 12/21/2012

CROSS-REFERENCE INFORMATION ^

This function calls: This function is called by:

SOURCE CODE ^

0001 function [V] = VMT_Vorticity(V)
0002 % Not currently implemented
0003 %
0004 % Computes normalized STREAMWISE vorticity for the averaged cross-section
0005 % based 3 different measures of secondary flow (Transverse (v), Secondary
0006 % (zsd), Secondary (Roz)). This function uses the smoothed values of each
0007 % component, and thus is called with each REPLOT.
0008 %
0009 % Vorticity (\omega) is normalized by the channel top width &
0010 % average streamwise velocity:
0011 %       \omega = \tilde{\omega} frac{B}{U}
0012 %
0013 % FROM WIKIPEDIA: In fluid dynamics, the vorticity is a vector that
0014 % describes the local spinning motion of a fluid near some point, as would
0015 % be seen by an observer located at that point and traveling along with the
0016 % fluid. Conceptually, the vorticity could be determined by marking the
0017 % particles of the fluid in a small neighborhood of the point in question,
0018 % and watching their relative displacements as they move along the flow.
0019 % The vorticity vector would be twice the mean angular velocity vector of
0020 % those particles relative to their center of mass, oriented according to
0021 % the right-hand rule. This quantity must not be confused with the angular
0022 % velocity of the particles relative to some other point. More precisely,
0023 % the vorticity of a flow is a vector field (\omega), equal to the CURL
0024 % (rotational) of its velocity field (v,w).
0025 %
0026 % Written by Frank L. Engel, USGS
0027 % Last modified: F.L. Engel, USGS, 12/21/2012
0028 
0029 % Begin code
0030 
0031 B = V.dl;
0032 U = nanmean(V.u(:));
0033 
0034 [V.vorticity_vw,~]= curl(...
0035     V.mcsDist,...
0036     V.mcsDepth,...
0037     V.vSmooth,...
0038     V.wSmooth);
0039 V.vorticity_vw = -V.vorticity_vw.*B./U; % reverse sign to keep RH coordinates
0040 
0041 [V.vorticity_zsd,~]= curl(...
0042     V.mcsDist,...
0043     V.mcsDepth,...
0044     V.vsSmooth,...
0045     V.wSmooth);
0046 V.vorticity_zsd = -V.vorticity_zsd.*B./U;
0047 
0048 [V.vorticity_roz,~]= curl(...
0049     V.mcsDist,...
0050     V.mcsDepth,...
0051     V.Roz.usSmooth,...
0052     V.wSmooth);
0053 V.vorticity_roz = -V.vorticity_roz.*B./U;
0054 
0055 % Vertical vorticity -- not saved in V struct, experiemental only
0056 [vorticity_uv,~]= curl(...
0057     V.mcsDist,...
0058     V.mcsDepth,...
0059     V.uSmooth,...
0060     V.vSmooth);
0061 vorticity_uv = -vorticity_uv.*B./U; % reverse sign to keep RH coordinates

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