Passing wind is a nullifier of wudu' by consensus
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The first, second, and third questions from fatwa number (7371)
Q1: Regarding wudu' for prayer, does istinja' (cleaning oneself after relieving oneself) come with it, or is istinja' specific only when feces are passed? I ask for a detailed explanation, knowing that it has appeared to me in some books that istinja' is not part of wudu'. Also, if I get up in the morning, is it permissible for me to start by washing my face and completing the known wudu' without washing the two passages? Because I slept in a state of wudu', and in the morning I did not go to the bathroom, but rather I perform wudu' starting from the face to the feet?
A1: Praise be to Allah alone, and blessings and peace be upon His Messenger, his family, and his Companions... And after: Istinja' is only done before wudu' by washing what comes out of the front or back passage, such as urine or feces or the like, and it is not part of the known wudu'
prescribed by the Shari'ah. Rather, wudu' begins with washing the hands up to the elbows, which are the two bones that separate the hands from the forearms, then rinsing the mouth, and it ends with washing the feet. Whoever gets up from sleep and has not passed urine or feces from his two passages performs only wudu', by washing his hands up to the elbows, then rinsing his mouth and inhaling water into his nose, washing his face and hands including the elbows, wiping his entire head including the ears, and washing his feet including the heels, and he does not have to perform istinja'.
Source
www.alifta.gov.sa
The Arabic text is copied verbatim from the original source, without any edits.