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      F=1.
      G=9.8
      DO DD=-1,1,1.E-3
       SS=WNUMYOU(F,DD,G)
       WRITE (*,*) DD,SS
      ENDDO
      END
      

      FUNCTION WNUMYOU(F,DD,G) ! NG12022009 
CNG
CNG  APPROXIMATE SOLUTION OF WAVE DISPERSION EQUATION
CNG
CNG  F = FREQUENCY (HZ)
CNG  DD = DEPTH (M)
CNG  WNUMYOU = WAVENUMBER (1/M)
CNG
CNG Reference: Zai-Jin You, 2008
CNG "A close approximation of wave dispersion relation for
CNG direct calculation of wavelength in any coastal water depth."
CNG Equations 3 and 2 (or 3 and 4). 
CNG Applied Ocean Research
CNG Provides 0.01% (0.1%) maximum relative error.
CNG
CNG Note that the YOU (2) equation can be analytically rewritten BUT
CNG the resulting simpler expression becomes numerically indefinite
CNG because it involves ~inf/~inf expressions like cosh*sinh.
CNG
      DATA TPI/6.283185/
      HK0=DD*TPI*F*TPI*F/G
      X0=SQRT(HK0)*(1.+HK0/6.+HK0*HK0/30.) ! YOU (3)
      Y=X0*( (HK0+X0/COSH(X0)*X0/COSH(X0)) /
     +       (X0*TANH(X0)+X0/COSH(X0)*X0/COSH(X0)) ) ! YOU (2) NEWTON-RAPHSON
CNG   Y=HK0/TANH(X0) ! YOU (4), SOMEWHAT FASTER ~ HUNT IN ACCURACY AND SPEED
      WNUMYOU=Y/(DD+1.E-10)
      RETURN
      END