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-#======================================================================
-# L I B G M . P L
-# doc: Sun Feb 20 14:43:47 2011
-# dlm: Tue Nov 18 12:42:30 2014
-# (c) 2011 A.M. Thurnherr
-# uE-Info: 22 53 NIL 0 0 70 2 2 4 NIL ofnI
-#======================================================================
-
-# HISTORY:
-# Feb 20, 2011: - created
-# Feb 28, 2011: - cosmetics
-# Mar 28, 2012: - BUG: N had been ignored (but only affects vertical
-# wavelengths > 1000m in any was significantly
-# - changed from Munk eqn 9.23b to 9.23a, which also
-# affects only long wavelengths
-# - return nan for omega outside internal-wave band
-# Mar 29, 2012: - re-wrote using definition of B(omega) from Munk (1981)
-# Aug 23, 2012: - cosmetics?
-# Sep 7, 2012: - made N0, E0, b, jstar global
-# Dec 28, 2012: - added allowance for small roundoff error to Sw()
-# Oct 6, 2014: - made omega optional in Sw()
-# Nov 18, 2014: - made b & jstar mandatory for Sw()
-
-require "$ANTS/libEOS83.pl";
-
-my($pi) = 3.14159265358979;
-
-#======================================================================
-# Global Constants
-#======================================================================
-
-$GM_N0 = 5.24e-3; # rad/s # reference stratification (from Gregg + Kunze, 1991)
-$GM_E0 = 6.3e-5; # dimensionless # spectral level (Munk 1981)
-$GM_b = 1300; # m # pycnocline e-folding scale
-$GM_jstar = 3; # dimless # peak mode number
-
-#======================================================================
-# Vertical velocity spectral density
-#
-# Units: K.E. per frequency per wavenumber [m^2/s^2*1/s*1/m = m^3/s]
-# Version: GM79?
-#
-# E. Kunze (email, Feb 2011): The GM vertical velocity w spectrum is described by
-#
-# S[w](omega, k_z) = PI*E_0*b*{f*sqrt(omega^2-f^2)/omega}*{j*/(k_z + k_z*)^2}
-#
-# where E_0 = 6.3 x 10^-5 is the dimensionless spectral level, b = 1300 m is
-# the pycnocline lengthscale, j* = 3 the peak mode number and k_z* the
-# corresponding vertical wavenumber. The flat log-log spectrum implies w is
-# dominated by near-N frequencies (where we know very little though Yves
-# Desaubies wrote some papers back in the late 70's/early 80's about the
-# near-N peak) and low modes. The rms w = 0.6 cm/s, right near your noise
-# level. Interestingly, the only N dependence is in m and m*. As far
-# as I know, little is known about its intermittency compared to horizontal
-# velocity. Since w WKB-scales inversely with N, the largest signals should
-# be in the abyss where you therefore likely have the best chance of
-# measuring it.
-#
-# E. Kunze (email, Sep 19, 2013):
-#
-# S[w](omega, m) = PI*E0*b*[f*sqrt(omega^2-f^2)/omega]*[jstar/(m+mstar)^2] with
-#
-# S[w](m) = PI*E0*b*N*f*[jstar/(m+mstar)^2]
-#
-# where the nondimensional spectral energy level E0 = 6.3e-5, stratification
-# lengthscale b = 1500 m, jstar = 3, mstar = jstar*PI*N/b/N0, and N0 =
-# 5.3e-3 rad/s.
-#
-# NOTES:
-# - b=1500m is a likely typo, as Gregg & Kunze (1991) have b=1300m
-# - k_z == m
-#
-#======================================================================
-
-sub m($$) # vertical wavenumber as a function of mode number & stratification params
-{
- my($j,$N,$omega) = @_;
-
- return defined($omega) && ($omega <= $GM_N0)
- ? $pi / $GM_b * sqrt(($N**2 - $omega**2) / ($GM_N0**2 - $omega**2)) * $j
- : $pi * $j * $N / ($GM_b * $GM_N0); # valid, except in vicinity of buoyancy turning frequency (Munk 1981, p.285)
-}
-
-sub B($) # structure function (omega dependence)
-{ # NB: f must be defined
- my($omega) = @_;
- croak("coriolis parameter not defined\n")
- unless defined($f);
- return 2 / $pi * $f / $omega / sqrt($omega**2 - $f**2);
-}
-
-
-sub Sw(@)
-{
- my($omega,$m,$lat,$b,$jstar,$N) =
- &antsFunUsage(-5,'fff','[frequency[1/s]] <vertical wavenumber[rad/m]> <lat[deg]> <N[rad/s]> <b[m]> <j*>',@_);
-
- if (defined($N)) { # Sw(omega,m)
- local($f) = abs(&f($lat));
- $omega += $PRACTICALLY_ZERO if ($omega < $f);
- $omega -= $PRACTICALLY_ZERO if ($omega > $N);
- return nan if ($omega < $f || $omega > $N);
- my($mstar) = &m($jstar,$N,$omega);
- return $GM_E0 * $b * 2 * $f**2/$omega**2/B($omega) * $jstar / ($m+$mstar)**2;
- } else { # Sw(m)
- $N = $lat; # shift arguments to account for missing omega
- $lat = $m;
- local($f) = abs(&f($lat));
- $m = $omega;
- undef($omega);
- my($mstar) = &m($jstar,$N);
- return $pi * $GM_E0 * $b * $N * $f * $jstar / ($m+$mstar)**2;
- }
-}
-
-#----------------------------------------------------------------------
-# GM76, as per Gregg and Kunze (JGR 1991)
-# - beta is vertical wavenumber (m above)
-#----------------------------------------------------------------------
-
-sub Su($$)
-{
- my($beta,$N) = @_;
-
- my($beta_star) = &m($GM_jstar,$N); # A3
- return 3*$GM_E0*$GM_b**3*$GM_N0**2 / (2*$GM_jstar*$pi) / (1+$beta/$beta_star)**2; # A2
-}
-
-sub Su_z($$)
-{
- my($beta,$N) = &antsFunUsage(2,'ff','<vertical wavenumber[rad/m]> <N[rad/s]>',@_);
- return $beta**2 * &Su($beta,$N);
-}
-
-1;