{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

lecture36 - ME 563 Intermediate Fluid Dynamics Su Lecture...

Info icon This preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon
ME 563 - Intermediate Fluid Dynamics - Su Lecture 36 - Turbulence: more on scaling, and the Reynolds stress In the last class we looked at the Kolmogorov similarity hypotheses, which expressed the idea that the smaller scales of turbulence approach a universal state for high enough Reynolds number. (The Reynolds number we’re interested in is Re = u 0 l 0 , where u 0 is a characteristic velocity of the flow large scale, and l 0 is a characteristic large-scale flow dimension.) That is, while the large scales will obviously be different, being set by the different flow boundary conditions, etc., the statistics of the small scales of the flow will be the same between flows if the Reynolds numbers are high enough. Also, if you look at the smallest turbulent scales, the turbulence at those scales will be isotropic, meaning that all of the spatial directions will look the same. Based on Kolmogorov’s hypotheses, we can also extimate the size of the smallest turbulence length, time and velocity scales. From Kolmogorov’s first similarity hypothesis, the universal form of the smallest turbulence scales is dependent only on the viscosity, ν and the rate of energy dissipation, ε . The units of these terms are ν = length 2 time , ε = velocity 2 time = length 2 time 3 (1) where we’ll note that ε is really the specific rate of energy dissipation, i.e. the rate per unit mass. From these, we can form a unique length scale, η , time scale, τ η , and velocity scale, u η , as: η = ν 3 ε 1 / 4 τ = ν ε 1 / 2 u η = ( εν ) 1 / 4 . (2) These are collective called the
Image of page 1

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Image of page 2
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern