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Introduction Of Turbulence And Turbulent Flows

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MM4TTF: Introduction to Turbulence and Turbulent Flows
Case Study 1: Turbulent Boundary Layer Structure
Turbulent coherent structures are flow patterns that can be distinguished from each other, as opposed to motions such as eddies which are subject to the phenomenon of superpositioning. Several of these occur in the near-wall region:
‘Low speed streaks’ refer to the regions of relatively slow flow spaced out in a pronounced manner. They generally occur ‘between the legs of hairpin vortices, where flow is displaced upward from the surfaces so that it convects low momentum fluid away from the wall.’[2]. Streaks have been found to occur in the sublayer region by Kline and Runstandler (1959)[1] and have been shown to occur at a distance of y+
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Another type of coherent structure are ‘rolls’, which are ‘pairs of counter-rotating streamwise vortices that are the dominant vertical structures in the near-wall region defined by y+ < 100’[2]. They account for streak production also, as the fluid being pushed outwards between the rolls has reduced axial velocity, creating a velocity profile which is inviscidly unstable, and also associate with bursting and lift-up.
‘Bursting’ may be described as a characteristic behaviour of the low-speed streaks. It generally refers to the whole process of a streak undergoing lift-up from near the wall, beginning to oscillate, and subsequently undergoing break-up and ejection
Firstly the streaks slowly begin moving downstream and drifting outwards; this is the process known as ‘lift-up’. After the streak reaches a distance of around y+ = 8-12, it begins to rapidly oscillate, which increases in amplitude as outflow progresses. This ends in a sudden breakup, generally when y+ is between 10-30. After breakup, ‘the streak lifts away from the wall by a vigorous and chaotic motion. This process ‘ejects’ low-speed fluid into a region of the boundary layer with a faster streamwise velocity.’[3]. This process of bursting can be shown graphically, with a representation of a dye streak in a turbulent boundary layer; a typical example is shown below: The pressure gradient has been observed to have an effect on the bursting phenomenon; it has been observed that ‘a positive
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