(*********************************************************************** Mathematica-Compatible Notebook This notebook can be used on any computer system with Mathematica 3.0, MathReader 3.0, or any compatible application. The data for the notebook starts with the line of stars above. To get the notebook into a Mathematica-compatible application, do one of the following: * Save the data starting with the line of stars above into a file with a name ending in .nb, then open the file inside the application; * Copy the data starting with the line of stars above to the clipboard, then use the Paste menu command inside the application. Data for notebooks contains only printable 7-bit ASCII and can be sent directly in email or through ftp in text mode. Newlines can be CR, LF or CRLF (Unix, Macintosh or MS-DOS style). 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The data consists of the horizontal and \ vertical velocity components", StyleBox[" u", FontSlant->"Italic"], " and ", StyleBox["w", FontSlant->"Italic"], " stored in (jn,in) arrays, and read in as a nested list, stored as rows \ j=1,2,3 ...The ", StyleBox["u", FontSlant->"Italic"], " fields are stored in ", StyleBox["ustbu000.dat, ustbu001.dat, ... ustabu005.dat", FontFamily->"Courier"], " for times t=0,5,10,13,15,20. Similarly for ", StyleBox["w", FontSlant->"Italic"], ".\n\nAn extra data point has been given to you: i=in is the same as i=1and \ should not be used in computing horizontal averages. (The reason the data \ was stored this way was to make it easier to make a contour plot an entire \ wavelength.)\n\n" }], "Text"], Cell[TextData[{ "Your tasks:\n", StyleBox[" \[HappySmiley] ", FontSize->24], "Make cool plots of ", Cell[BoxData[ \(TraditionalForm\`u\&_\)]], StyleBox["(z), ", FontSlant->"Italic"], Cell[BoxData[ \(TraditionalForm\`uw\&_\)], FontSlant->"Italic"], StyleBox["(z), ", FontSlant->"Italic"], Cell[BoxData[ \(TraditionalForm\`d\/dz\)], FontSlant->"Italic"], Cell[BoxData[ \(TraditionalForm\`uw\&_\)], FontSlant->"Italic"], StyleBox["(z)", FontSlant->"Italic"], " , etc. that show how these fields change with time.\n ", StyleBox["\[HappySmiley] ", FontSize->24], "Plot the value of the total energy , momentum and enstrophy in the domain, \ at the data sampling times. If the model were perfect all those quantities \ would be invariant. Note that j=0 and j=jn correspond to the rigid boundary \ at ", StyleBox["z", FontSlant->"Italic"], "=-1 and ", StyleBox["z", FontSlant->"Italic"], "=1. The volumes surrounding the grid points on the boundaries are only \ half the size of the volumes surrounding the interior points. This fact \ should be recognized when computing the volume sums (or \"integrals\").\n ", StyleBox["\[HappySmiley] ", FontSize->24], "Using the time series stored in ", StyleBox["woftime.dat, ", FontFamily->"Courier"], "find the growth rate of the instability by fitting a curve (use ", StyleBox["Fit ", FontWeight->"Bold"], ", see page 859) to the\n appropriate portion of the time series.\n ", StyleBox["\[HappySmiley] ", FontSize->24], "Or do something else creative..." }], "Text"], Cell[CellGroupData[{ Cell["Initialization", "Section"], Cell[BoxData[ \(\(in = 65; \)\)], "Input"], Cell[BoxData[ \(\(jn = 65; \)\)], "Input"], Cell[CellGroupData[{ Cell[BoxData[ \(dx = Pi/\((in - 1)\) // N\)], "Input"], Cell[BoxData[ \(0.0490873852123405196`\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(dz = 2/\((jn - 1)\) // N\)], "Input"], Cell[BoxData[ \(0.03125`\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(z = Table[\(-1\) + 2*\((j - 1)\)/\((jn - 1)\) // N, {j, 1, jn}]\)], "Input"], Cell[BoxData[ \({\(-1.`\), \(-0.96875`\), \(-0.9375`\), \(-0.90625`\), \(-0.875`\), \(-0.84375`\), \(-0.8125`\), \(-0.78125`\), \(-0.75`\), \(-0.71875`\), \(-0.6875`\), \(-0.65625`\), \(-0.625`\), \(-0.59375`\), \(-0.5625`\), \(-0.53125`\), \(-0.5`\), \(-0.46875`\), \(-0.4375`\), \(-0.40625`\), \(-0.375`\), \(-0.34375`\), \(-0.3125`\), \(-0.28125`\), \(-0.25`\), \(-0.21875`\), \(-0.1875`\), \(-0.15625`\), \(-0.125`\), \(-0.09375`\), \(-0.0625`\), \(-0.03125`\), 0, 0.03125`, 0.0625`, 0.09375`, 0.125`, 0.15625`, 0.1875`, 0.21875`, 0.25`, 0.28125`, 0.3125`, 0.34375`, 0.375`, 0.40625`, 0.4375`, 0.46875`, 0.5`, 0.53125`, 0.5625`, 0.59375`, 0.625`, 0.65625`, 0.6875`, 0.71875`, 0.75`, 0.78125`, 0.8125`, 0.84375`, 0.875`, 0.90625`, 0.9375`, 0.96875`, 1.`}\)], "Output"] }, Open ]], Cell["\<\ Your path to the data files. Probaby \"ezm/\", unless you are \ Brian Fiedler, in which case it is \"Power HD:5123 notebooks:ezm:\"\ \>", "Text"], Cell[BoxData[ \(\( (*path = "\"\ *) \npath = "\"\ \)\)], "Input"], Cell["\<\ mean[q_] calculates the horizontal mean of a quantity q(x,z) as a \ function of z.\ \>", "Text"], Cell[BoxData[ \(\(mean[q_] := Table[\n\t\t\t\tSum[q[\([j, i]\)], {i, 1, in - 1}]/\((in - 1)\)\n \t\t\t\t, {j, 1, jn}]; \)\)], "Input"], Cell["\<\ covar[q_,r_] calculates the horizontal mean of a quantity \ q(x,z)r(x,z) as a function of z.\ \>", "Text"], Cell[BoxData[ \(\(covar[q_, r_] := Table[\n\t\t\t\t Sum[q[\([j, i]\)]*r[\([j, i]\)], {i, 1, in - 1}]/\((in - 1)\)\n \t\t\t\t, {j, 1, jn}]; \)\)], "Input"] }, Closed]], Cell[CellGroupData[{ Cell["Analyze some data", "Section"], Cell[CellGroupData[{ Cell[BoxData[ \(ufile = "\"\)], "Input"], Cell[BoxData[ \("ustbu003.dat"\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(wfile = "\"\)], "Input"], Cell[BoxData[ \("ustbw003.dat"\)], 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