{"product_id":"9781470472252-dynamics-near-the-subcritical-trans","title":"Dynamics Near the Subcritical Transition of the 3D Couette Flow II: Above Threshold Case","description":"\u003cmeta content=\"text\/html; charset=utf-8\" http-equiv=\"Content-Type\"\u003e\u003cp\u003e\u003cspan\u003eThe second in a pair of works which study small disturbances to the plane, periodic 3D Couette flow in the incompressible Navier-Stokes equations at high Reynolds number Re.\u003cbr\u003eThis is the second in a pair of works which study small disturbances to the plane, periodic 3D Couette flow in the incompressible Navier-Stokes equations at high Reynolds number Re. In this work, we show that there is constant 0 0 exist at least until t = c0???1 and in general evolve to be O(c0) due to the lift-up e?ect. Further, after times t Re1\/3, the streamwise dependence of the solution is rapidly diminished by a mixing-enhanced dissipation e?ect and the solution is attracted back to the class of \"2.5 dimensional\" streamwise-independent solutions (sometimes referred to as \"streaks\"). The largest of these streaks are expected to eventually undergo a secondary instability at t ? ???1. Hence, our work strongly suggests, for all (sufficiently regular) initial data, the genericity of the \"lift-up e?ect streak growth streak breakdown\" scenario for turbulent transition of the 3D Couette flow near the threshold of stability forwarded in the applied mathematics and physics literature.\u003cbr\u003e\u003cbr\u003e\u003c\/span\u003e\u003c\/p\u003e","brand":"Rarewaves","offers":[{"title":"Default Title","offer_id":54845445177718,"sku":"9781470472252","price":69.09,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0092\/7504\/8033\/files\/orig_36017219_dffec737-de4a-46dc-a044-d90f905057f9.jpg?v=1757557742","url":"https:\/\/www.rarewaves.com\/products\/9781470472252-dynamics-near-the-subcritical-trans","provider":"Rarewaves.com","version":"1.0","type":"link"}