# 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