TL;DR
Get-ChildItem | Sort-Object { [regex]::Replace($_.Name, '\d+', { $args[0].Value.PadLeft(20) }) }
Here is some very short code (just the $ToNatural script block) that does the trick with a regular expression and a match evaluator in order to pad the numbers with spaces. Then we sort the input with padded numbers as usual and actually get natural order as a result.
$ToNatural = { [regex]::Replace($_, '\d+', { $args[0].Value.PadLeft(20) }) }
'----- test 1 ASCIIbetical order'
Get-Content list.txt | Sort-Object
'----- test 2 input with padded numbers'
Get-Content list.txt | %{ . $ToNatural }
'----- test 3 Natural order: sorted with padded numbers'
Get-Content list.txt | Sort-Object $ToNatural
Output:
----- test 1 ASCIIbetical order
1.txt
10.txt
3.txt
a10b1.txt
a1b1.txt
a2b1.txt
a2b11.txt
a2b2.txt
b1.txt
b10.txt
b2.txt
----- test 2 input with padded numbers
1.txt
10.txt
3.txt
a 10b 1.txt
a 1b 1.txt
a 2b 1.txt
a 2b 11.txt
a 2b 2.txt
b 1.txt
b 10.txt
b 2.txt
----- test 3 Natural order: sorted with padded numbers
1.txt
3.txt
10.txt
a1b1.txt
a2b1.txt
a2b2.txt
a2b11.txt
a10b1.txt
b1.txt
b2.txt
b10.txt
And finally we use this one-liner to sort files by names in natural order:
Get-ChildItem | Sort-Object { [regex]::Replace($_.Name, '\d+', { $args[0].Value.PadLeft(20) }) }
Output:
Directory: C:\TEMP\_110325_063356
Mode LastWriteTime Length Name
---- ------------- ------ ----
-a--- 2011-03-25 06:34 8 1.txt
-a--- 2011-03-25 06:34 8 3.txt
-a--- 2011-03-25 06:34 8 10.txt
-a--- 2011-03-25 06:34 8 a1b1.txt
-a--- 2011-03-25 06:34 8 a2b1.txt
-a--- 2011-03-25 06:34 8 a2b2.txt
-a--- 2011-03-25 06:34 8 a2b11.txt
-a--- 2011-03-25 06:34 8 a10b1.txt
-a--- 2011-03-25 06:34 8 b1.txt
-a--- 2011-03-25 06:34 8 b2.txt
-a--- 2011-03-25 06:34 8 b10.txt
-a--- 2011-03-25 04:54 99 list.txt
-a--- 2011-03-25 06:05 346 sort-natural.ps1
-a--- 2011-03-25 06:35 96 test.ps1