Merge branch 'bugfix/average-Uint' into 'develop'

Compute Uint from time-averaged energy

See merge request !68

TurTLE/DNS.py

@@ -415,16 +415,28 @@ class DNS(_code):
             R_{\\lambda} = \\frac{U_{\\textrm{int}} \\lambda}{\\nu}
 
             D = \\frac{\\varepsilon L_{\\textrm{int}}}{U_{\\textrm{int}}^3}
+
+
+        Note: the "time-averaged" integral-scale velocity is obtained from the
+        time-averaged energy. This is nominally different from time-averaging
+        the time-dependent integral-scale velocity, but in practice the
+        differences are not very large for data we've looked at so far.
+        For future reference, it seems advisable to compute energy and
+        dissipation as "primary" quantities (nice because they are L2 norms),
+        to which temporal averaging can be applied; other "time-averaged"
+        derived quantities (Rlambda, Taylor micro-scale itself, etc) should be
+        computed from the time-averaged energy and dissipation.
+        This is consistent with the integral length-scale, which is computed
+        from the time-averaged energy spectrum.
         """
-        self.statistics['Uint(t)'] = np.sqrt(2*self.statistics['energy(t)'] / 3)
         for key in ['energy',
                     'enstrophy',
-                    'mean_trS2',
-                    'Uint']:
+                    'mean_trS2']:
             if key + '(t)' in self.statistics.keys():
                 self.statistics[key] = np.average(self.statistics[key + '(t)'], axis = 0)
         self.statistics['vel_max'] = np.max(self.statistics['vel_max(t)'])
         for suffix in ['', '(t)']:
+            self.statistics['Uint'    + suffix] = np.sqrt(2*self.statistics['energy' + suffix] / 3)
             self.statistics['diss'    + suffix] = (self.parameters['nu'] *
                                                    self.statistics['enstrophy' + suffix]*2)
             self.statistics['etaK'    + suffix] = (self.parameters['nu']**3 /