Revised Prandtl mixing length model applied to the two-dimensional turbulent classical wake

Hutchinson, A.J.; Mason, D. P.

doi:10.1016/j.ijnonlinmec.2015.08.006

Cited by 10 publications

(7 citation statements)

References 19 publications

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“…Introducing the dimensionless variables x∗=xL,1emy∗=ReTLy,1emu¯∗=ufalse¯U,1emv¯∗=v¯ReTU1emand1empfalse¯∗=pρU2, the boundary layer equations for the two-dimensional turbulent classical wake in terms of the dimensionless mean velocity components are [23] normal∂u¯∗normal∂x∗+normal∂v¯∗normal∂y∗=0 and u¯∗normal∂u¯∗normal∂x∗+v¯∗normal∂u¯∗normal∂y∗…”

Section: Mathematical Model For a Two-dimensional Turbulent Classical Far Wakementioning

confidence: 99%

“…This condition comes from a conserved quantity, which for the classical wake is the drag force [16]. The conserved quantity imposes the constraint [23] ∫0ybfalse(xfalse)wfalse¯false(x,yfalse) dy=D2, where the dimensionless drag force per unit breadth D is independent of x .…”

Section: Mathematical Model For a Two-dimensional Turbulent Classical Far Wakementioning

confidence: 99%

“…Previous work investigates the class of models that can be described by a kinematic eddy viscosity of the form νT=νTfalse(x,y,normal∂ufalse¯/normal∂yfalse) [23,32,34,35]. In this paper, we extend the work conducted in [23] by considering effective kinematic viscosities of the form E=E(x,∂u¯∂y,normal∂2u¯∂y2). This form is convenient not only in that it extends the range of closure models that can be applied, but it also incorporates the CEV model, the PML model, the EPML model, and any variations thereof, as special cases, allowing for a unified derivation and a direct comparison.…”

Section: Derivation Of the Eddy Viscosity For The Extended Prandtl Mixing Length Modelmentioning

confidence: 99%

“…Prandtl’s original model was recently modified to include the kinematic viscosity [23]. It was shown that the mixing length can be derived without imposing any additional hypotheses and that the wake boundary predicted from this model lies outside of the underestimated boundary obtained from the original PML model where the kinematic viscosity is neglected.…”

Section: Introductionmentioning

confidence: 99%

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Prandtl’s extended mixing length model applied to the two-dimensional turbulent classical far wake

et al. 2021

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Despite its limitations, Prandtl’s mixing length model is widely applied in modelling turbulent free shear flows. Prandtl’s extended model addresses many of the shortfalls of the original model, but is not so widely used, in part due to additional mathematical complexities that arise in its derivation and implementation. Furthermore, in both models, Prandtl neglects the kinematic viscosity on the basis that it is much smaller in magnitude than the turbulent viscosity. Recent work has shown that including the kinematic viscosity in the original model has both mathematical and physical advantages. In the present work, a novel derivation of the extended model is provided, and it is demonstrated that similar advantages are again obtained when the kinematic viscosity is included. Additionally, through the use of scaling techniques, similarity mean velocity profiles of the extended model are derived, resulting in a single nonlinear ordinary differential equation that is solved numerically with a Hermite spectral method. The computed profiles for the normalized similarity mean velocity and shear stress are compared with experimental observations and shown to be in excellent agreement.

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Section: Mathematical Model For a Two-dimensional Turbulent Classical Far Wakementioning

confidence: 99%

Section: Mathematical Model For a Two-dimensional Turbulent Classical Far Wakementioning

confidence: 99%

Section: Derivation Of the Eddy Viscosity For The Extended Prandtl Mixing Length Modelmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Prandtl’s extended mixing length model applied to the two-dimensional turbulent classical far wake

et al. 2021

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“…the boundary layer equations for the two-dimensional turbulent classical wake in terms of the dimensionless mean velocity components are [23]…”

Section: (A) Governing Equationsmentioning

confidence: 99%

Prandtl's extended mixing length model applied to the two-dimensional turbulent classical far wake

Hutchinson,

Hale,

Born

et al. 2021

Preprint

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Despite its limitations, Prandtl's mixing length model is widely applied in modelling turbulent free shear flows. Prandtl's extended model addresses many of the shortfalls of the original model, but is not so widely used, in part due to additional mathematical complexities that arise in its derivation and implementation. Furthermore, in both models Prandtl neglects the kinematic viscosity on the basis that it is much smaller in magnitude than the turbulent viscosity. Recent work has shown that including the kinematic viscosity in the original model has both mathematical and physical advantages. In the present work, a novel derivation of the extended model is provided, and it is demonstrated that similar advantages are again obtained when the kinematic viscosity is included. Additionally, through the use of scaling techniques, similarity mean velocity profiles of the extended model are derived, resulting in a single nonlinear ordinary differential equation that is solved numerically with a Hermite spectral method. The computed profiles for the normalised similarity mean velocity and shear stress are compared to experimental observations and shown to be in excellent agreement.

show abstract

The extended Prandtl closure model applied to the two-dimensional turbulent classical far wake

Hutchinson¹

2021

2019-20 MATRIX Annals

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Revised Prandtl mixing length model applied to the two-dimensional turbulent classical wake

Cited by 10 publications

References 19 publications

Prandtl’s extended mixing length model applied to the two-dimensional turbulent classical far wake

Prandtl’s extended mixing length model applied to the two-dimensional turbulent classical far wake

Prandtl's extended mixing length model applied to the two-dimensional turbulent classical far wake

The extended Prandtl closure model applied to the two-dimensional turbulent classical far wake

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