Intensity Integral Length Scale

This option is designed to give an estimate of the integral length scale of the mixing region between two bodies of fluid. Suppose the concentration of some dye at some point in the mixing region is C. In the unmixed regions the concentration is either 0 or 1. We then define the integral length scale as the integral of C_bar^m*(1-C_bar)^n along some path (either horizontal or vertical), where C_bar is the mean concentration in the direction normal to this path. Here m and n are user-specified positive values. The routine also calculates the integrals of C^m*(1-C)^n, C^m and (1-C)^n over the domain to give information about the molecular mixing fraction.

Integral length scales for which buffer ?

The integral length scales may be calculated on any normal DigImage buffer.

Integral length scales for Window or whole Screen ?

The integral length scales may be calculated using a window (<W>) within a buffer, or the entire buffer (<S>).

Specify Window: Region used to evaluate integral length scales in

The window specification submenu will be produced only if a window (<W>) is selected in the previous entry. Integral length scales will be calculated based only the the concentrations lying within the window. The window is specified in the normal DigImage manner. For further details, consult [H Help] within the submenu.

Intensity for C=0.0 ?

This entry sets the intensity which will be taken as the zero concentration level. Pixels within the window having a smaller intensity will be taken as C=0.0. The default value is the minimum intensity in the window.

Intensity for C=1.0 ?

This entry sets the intensity which will be taken as the unity concentration level. Pixels within the window having a larger intensity will be taken as C=1.0. The default value is the maximum intensity in the window.

Exponent for C_bar term ?

In this option the integral length scale is defined as

            x1                              y1
            ô _m    _ n                     ô _m    _ n
     Lx = k ³ C  (1-C)  dx,   and    Ly = k ³ C  (1-C)  dy
            õ                               õ
            x0                              y0

where m and n are user-specified constants. The constant k is determined automatically to limit the kernal to the range 0 to 1. This option defines the value of m to be used.

Exponent for (1-C_bar) term ?

This option defines the value of n to be used in the kernal. Refer to previous entry for further details.

Message:
Evaluating integral length scales...

Integral mixing length scales:

  Horizontal scale - pixels            : !!R0 = !!GR0 pixels
  Vertical scale   - pixels            : !!R1 = !!GR1 pixels
  Horizontal       - world units       : !!R2 = !!GR2 !R0   
  Vertical         - world units       : !!R3 = !!GR3 !R0
  CBar                                 : !!R4 = !!GR4    
  Mean C^m (1-C)^n                     : !!R5 = !!GR5
  Mean C^m                             : !!R6 = !!GR6
  Mean (1-C)^n                         : !!R7 = !!GR7
  Mean C^m (1-C)^n / CBar^m (1-CBar)^n : !!R8 = !!GR8
  Number of pixels                     : !!R9 = !!R9

The integral length scales and molecular mixing statistics are computed and displayed on the monitor. If DigImage is running interactively, it will pause after processing the buffer so that they may be read. If running from a command file, it will return to the parent menu. The values are also available through the !!Rn syntax.

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DigImage User Documentation

Stuart Dalziel, last page update: 19 February 1996