"the so-called flank march across the Krasnaya Pakhra river"
After the loss of Moscow the Russian army were still locked in a defensive game of hide-and-seek with the French, who sought to engage them in a final, decisive battle. The Russian rear guard under General Miloradovich
were sent to fend off the French whilst the rest of the army withdrew in safety. Murat attacked Miloradovich's forcing, making him retreat to the Krasnaya Pakhra river, and nearly capturing the general in his headquarters. However, two days later Miloradovich counterattacked, enabling Kutuzov to withdraw the rest of the army still further.