{"product_id":"plumera-rayleigh-taylor-instability-physics-t-shirt","title":"Plumera – Rayleigh–Taylor Instability Physics T-Shirt","description":"\u003cp\u003ePlumera holds heavy fluid above light, and gravity pulls it into fingers: spikes fall, bubbles rise.\u003c\/p\u003e\u003ch3\u003eThe Physics\u003c\/h3\u003e\u003cp\u003eWhen a heavy fluid sits on top of a light one in gravity, any ripple on the interface grows. In the linear theory, a ripple of wavenumber k grows exponentially at rate σ, depending on the density contrast through the Atwood number. Spikes of heavy fluid fall and bubbles of light fluid rise.\u003c\/p\u003e\u003cp\u003e\u003cstrong\u003eσ = √(A g k),   A = (ρ_h − ρ_l)\/(ρ_h + ρ_l)\u003c\/strong\u003e\u003c\/p\u003e\u003cul\u003e\n\u003cli\u003eσ: growth rate (1\/s)\u003c\/li\u003e\n\u003cli\u003eA: Atwood number (dimensionless)\u003c\/li\u003e\n\u003cli\u003eg: gravitational acceleration (m\/s²)\u003c\/li\u003e\n\u003cli\u003ek: wavenumber (1\/m)\u003c\/li\u003e\n\u003cli\u003eρ_h, ρ_l: heavy and light densities (kg\/m³)\u003c\/li\u003e\n\u003c\/ul\u003e\u003cp\u003eLord Rayleigh analysed it in 1882, and G. I. Taylor followed in 1950.\u003c\/p\u003e\u003cp\u003e\u003cem\u003eHonest caveat:\u003c\/em\u003e The formula ignores viscosity and surface tension.\u003c\/p\u003e\u003ch3\u003eOn the shirt\u003c\/h3\u003e\u003cp\u003eFront: Plumera, the pixel-art character, with the title. Back: the growth rate, the Atwood number, spikes and bubbles and the 1882 and 1950 sources. Printed on a unisex tee.\u003c\/p\u003e","brand":"Printify","offers":[{"title":"S \/ White","offer_id":50936647254119,"sku":"12556819936159189451","price":29.99,"currency_code":"USD","in_stock":true},{"title":"S \/ Black","offer_id":50936647286887,"sku":"68434278301748014261","price":29.99,"currency_code":"USD","in_stock":true},{"title":"M \/ White","offer_id":50936647319655,"sku":"18347487420149129667","price":29.99,"currency_code":"USD","in_stock":true},{"title":"M \/ Black","offer_id":50936647352423,"sku":"21433786096457315733","price":29.99,"currency_code":"USD","in_stock":true},{"title":"L \/ White","offer_id":50936647385191,"sku":"23366511440776611967","price":29.99,"currency_code":"USD","in_stock":true},{"title":"L \/ Black","offer_id":50936647417959,"sku":"14462992562645910035","price":29.99,"currency_code":"USD","in_stock":true},{"title":"XL \/ White","offer_id":50936647450727,"sku":"51990240752371773115","price":29.99,"currency_code":"USD","in_stock":true},{"title":"XL \/ Black","offer_id":50936647483495,"sku":"47931742283414046142","price":29.99,"currency_code":"USD","in_stock":true},{"title":"2XL \/ White","offer_id":50936647516263,"sku":"27500835863138320361","price":29.99,"currency_code":"USD","in_stock":true},{"title":"2XL \/ Black","offer_id":50936647549031,"sku":"25997148241699704951","price":29.99,"currency_code":"USD","in_stock":true},{"title":"3XL \/ White","offer_id":50936647581799,"sku":"24219696439863930941","price":29.99,"currency_code":"USD","in_stock":true},{"title":"3XL \/ Black","offer_id":50936647614567,"sku":"25233760658490945086","price":29.99,"currency_code":"USD","in_stock":true},{"title":"4XL \/ White","offer_id":50936647647335,"sku":"32704363817077845688","price":29.99,"currency_code":"USD","in_stock":true},{"title":"4XL \/ Black","offer_id":50936647680103,"sku":"27533870588631415198","price":29.99,"currency_code":"USD","in_stock":true},{"title":"5XL \/ White","offer_id":50936647712871,"sku":"23915994768877657634","price":29.99,"currency_code":"USD","in_stock":true},{"title":"5XL \/ Black","offer_id":50936647745639,"sku":"14925357502583934414","price":29.99,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0596\/8746\/9159\/files\/rayleigh-taylor_front_02_white.png?v=1793595810","url":"https:\/\/pixelatedphysics.com\/zh-hant\/products\/plumera-rayleigh-taylor-instability-physics-t-shirt","provider":"Pixelated Physics","version":"1.0","type":"link"}