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, 12/21/20120001 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