# Reynolds averaging

Reynolds averaging refers to the process of averaging a variable or an equation in time. Let $\Phi$ be any dependent variable that varies in time. This variable can be decomposed into a fluctuating part, $\Phi'$ and an average part $\overline{\Phi}$ in the following way:
 $\overline{\Phi} \equiv \frac{1}{T} \int_T \Phi(t) dt$ (1) $\Phi' \equiv \Phi - \overline{\Phi}$
Where $T$ is a long enough time to average out the fluctuations in $\Phi$.
{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 7, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.951891303062439, "perplexity": 204.92934946475998}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2015-22/segments/1432207929418.92/warc/CC-MAIN-20150521113209-00091-ip-10-180-206-219.ec2.internal.warc.gz"}