How to run a bash script using threads/parallel

I think a nice way for parallel commands might be ... GNU parallel. Define your block as function as glenn jackmann suggested and then run them with parallel, where -j allows defining the maximal parallel runs. The advantage over glenn's approach is that if any block is done, a new one will be started so you always have 10 running at once. Note that you will have to export the function for parallel to be able to see it.

#!/bin/bash
g++ -std=c++11 shrink_files.cpp -o _shrink

block() {
  prefetch "$1"
  fastq-dump --fasta 0 "$1"
  ...
}

export -f block

parallel -j 10 block ::: id1 id2 id3 id4 ....

Replace idi with your ids. Alternatively if you have the IDs (SRR837459 and so on) in a file like

id1
id2
id3

then use this line instead (GNU Parallel reads from standard input if there is no other input source):

parallel -j 10 block

and run the script via

bash script < idlist.txt

You can group commands to run in the background

untested

#!/bin/bash
g++ -std=c++11 shrink_files.cpp -o _shrink

block() {
    local id=$1
    prefetch "$id"
    fastq-dump --fasta 0 "$id"
    rm ../../sra_sequences/sra/"$id".sra
    ./_shrink "$id"
    rm "$id".fasta
    echo "$id" >> list_of_done.txt
}

# run first 10 blocks in the background
block SRR837459 &
block SRR805782 &
...
block 10th_id &

# and wait for them to complete
wait

# now start up on the next 10 ...
block 11th_id &
...

Or the following is a bit more programmatic:

# all the ids to fetch
ids=( SRR837459 SRR805782 ... )

while (( ${#ids[@]} > 0 )); do
    # copy the first 10 as positional parameters
    set -- "${ids[@]:0:10}"
    # launch the blocks
    for id; do
        block "$id" &
    done
    # wait until done
    wait
    # remove the first 10 from the list
    ids=( "${ids[@]:10}" )
done