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Air pressure, fronts and temperature

I have spent hours on this topic and I seem unable to make sense of it. If air moves from high pressure toward low pressure, and wind is the movement of air due to differences in pressure, how can, for example, a warm front occur? What can bring a warm air mass to overtake a cold air mass? Shouldn't just the cold air mass move toward the warm air mass, as the warm air mass has lower pressure and winds will be blowing in that direction?

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    $\begingroup$ @BaroclinicCplusplus winds move parallel to the pressure gradient in geostrophic balance or perpendicular ? They move parallel to the isobars $\endgroup$
    –gansub
    Oct 21, 2022 at 8:37
  • 1
    $\begingroup$ @gansub The pressure gradient is perpendicular to the isobars. So my original statement is true. That is, the pressure gradient is perpendicular (really orthogonal) to the isobars. Air parcels move along the isobars in geostrophic balance. Therefore air parcels in geostrophic balance move perpendicular to the pressure gradient. $\endgroup$
    –BarocliniCplusplus
    Oct 22, 2022 at 15:35
  • $\begingroup$ @BaroclinicCplusplus But you have written winds will move parallel to the pressure gradient ? $\endgroup$
    –gansub
    Oct 23, 2022 at 2:14
  • 1
    $\begingroup$ @gansub fixed♂️ $\endgroup$
    –BarocliniCplusplus
    Oct 24, 2022 at 3:39

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