Corrections in doc

docs/nstrophy_doc/nstrophy_doc.tex

@@ -50,7 +50,7 @@ in terms of which, multiplying both sides of the equation by $\frac{k^\perp}{|k|
   \partial_t\hat \varphi_k=
   -4\pi^2\nu k^2\hat \varphi_k+\frac{k^\perp}{2i\pi|k|}\cdot\hat g_k
   +\frac{4\pi^2}{|k|}\sum_{\displaystyle\mathop{\scriptstyle p,q\in\mathbb Z^2}_{p+q=k}}
-  (q\cdot p^\perp)(k^\perp\cdot q^\perp)\hat\varphi_p\hat\varphi_q
+  \frac{(q\cdot p^\perp)(k^\perp\cdot q^\perp)}{|q||p|}\hat\varphi_p\hat\varphi_q
   .
   \label{ins_k}
 \end{equation}
@@ -88,7 +88,7 @@ using a fast Fourier transform, defined as
 \end{equation}
 where
 \begin{equation}
-  \mathcal N:=\{(n_1,n_2),\ 0\leqslant n_1\leqslant N_1,\ 0\leqslant n_2\leqslant N_2\}
+  \mathcal N:=\{(n_1,n_2),\ 0\leqslant n_1< N_1,\ 0\leqslant n_2< N_2\}
 \end{equation}
 for some fixed $N_1,N_2$. The transform is inverted by
 \begin{equation}
@@ -110,7 +110,8 @@ provided
 \begin{equation}
   N_i>4K_i.
 \end{equation}
-Indeed, $\sum_{n_i=0}^{N_i}e^{-\frac{2i\pi}{N_i}n_im_i}$ vanishes unless $m_i=0\%N_i$ (in which $\%N_i$ means `modulo $N_i$'), and, if $p,q\in\mathcal K$, then $|p_i+q_i|\leqslant2K_i$. Therefore,
+Indeed, $\sum_{n_i=0}^{N_i}e^{-\frac{2i\pi}{N_i}n_im_i}$ vanishes unless $m_i=0\%N_i$ (in which $\%N_i$ means `modulo $N_i$'), and, if $p,q\in\mathcal K$, then $|p_i+q_i|\leqslant2K_i$.
+Therefore,
 \begin{equation}
   T(\hat\varphi,k)
   =

src/main.c

@@ -77,10 +77,12 @@ int read_args(int argc, const char* argv[], ns_params* params, unsigned int* nst
   *nsteps=10000000;
   params->nu=1./1024/(2*params->K+1);
   */
-  params->K=3;
+  params->K=16;
   params->h=0.0001220703125;
+  params->h=0.001953125;
   *nsteps=10000000;
-  params->nu=0.00048828125;
+  //params->nu=0.00048828125;
+  params->nu=0.0078125;
 
   // loop over arguments
   for(i=1;i<argc;i++){
@@ -291,7 +293,7 @@ int enstrophy(ns_params params, unsigned int Nsteps){
       avg=avg-(avg-alpha)/t;
     }
 
-    if(t>0 && t%8192==0){
+    if(t>0 && t%1000==0){
       fprintf(stderr,"%8d % .8e % .8e % .8e % .8e\n",t, __real__ avg, __imag__ avg, __real__ alpha, __imag__ alpha);
       printf("%8d % .8e % .8e % .8e % .8e\n",t, __real__ avg, __imag__ avg, __real__ alpha, __imag__ alpha);
     }