Related papers: The Prandtl Plus Scaling Failure and its Remedy
Using the flow governing equation approach to similarity, Weyburne (D. Weyburne, arXiv:1701.02364, 2016) recently showed that for 2-D turbulent boundary layer flows, the Prandtl Plus scalings are NOT, in general, the proper similarity…
A second derivative-based moment method is proposed for describing the thickness and shape of the region where viscous forces are dominant in turbulent boundary layer flows. Rather than the fixed location sublayer model presently employed,…
Recent theoretical results together with established theory have identified the displacement thickness and the velocity at the boundary layer edge as similarity scaling parameter candidates for the wall-bounded turbulent boundary layer. In…
This paper deals with the two-dimensional incompressible, laminar, steady-state boundary layer equations.First, we determine a family of velocity distributions outside the boundary layer such that these problems may have similarity…
Wang and Castillo have developed empirical parameters for scaling the temperature profile of the turbulent boundary layer flowing over a heated wall in the paper X. Wang and L. Castillo, J. Turbul., 4, 1(2003). They presented experimental…
Hydrodynamic stability of compressible boundary layers is strongly influenced by Mach number ($M$), Prandtl number ($Pr$) and thermal wall boundary condition. These effects manifest on the flow stability via the flow-thermodynamic…
Many environmental flows arise due to natural convection at a vertical surface, from flows in buildings to dissolving ice faces at marine-terminating glaciers. We use three-dimensional direct numerical simulations of a vertical channel with…
A systematic search for the Lie point symmetries admitted by the steady hydromagnetic two-dimensional incompressible viscous flow boundary layer equation and associated boundary conditions is performed. Unlike previous works, the specific…
The transitional boundary layer flow over a flat plate is investigated. The boundary layer flow is known to develop unstable Tollmien-Schlichting waves above a critical value of the Reynolds number. However, it is also known that this…
Passive scalar dynamics in wall-bounded turbulence is studied via Direct Numerical Simulations of plane channel flow, for a friction Reynolds number $Re_* = 160$ and a Schmidt number $Sc=1$. Peculiar to the present research is that the…
This paper deals with the optimal streaky perturbations (which maximize the perturbed energy growth) in a wedge flow boundary layer. These three dimensional perturbations are governed by a system of linearized boundary layer equations…
In this paper we present a mathematical analysis for a steady-state laminar boundary layer flow, governed by the Ostwald-de Wael power-law model of an incompressible non- Newtonian fluid past a semi-infinite power-law stretched flat plate…
In wall-bounded flows, the laminar regime remain linearly stable up to large values of the Reynolds number while competing with nonlinear turbulent solutions issued from finite amplitude perturbations. The transition to turbulence of plane…
We demonstrate that the asymptotic approximant applied to the Blasius boundary layer flow over a flat plat (Barlow et al., 2017 Q. J. Mech. Appl. Math., 70(1): 21-48) yields accurate analytic closed-form solutions to the Falkner-Skan…
The problem of discerning key features of steady turbulent flow adjacent to a wall has drawn the attention of some of the most noted fluid dynamicists of all time. Standard examples of such features are found in the mean velocity profiles…
New scaling relations for the mean velocity and Reynolds shear stress in viscous sublayer were proposed based on the application of matched asymptotic expansion method to the mean momentum balance. It was shown that the new parameter…
Wall-bounded flows experience a transition to turbulence characterized by the coexistence of laminar and turbulent domains in some range of Reynolds number R, the natural control parameter. This transitional regime takes place between an…
Castillo and George (Castillo, L. and George, W., AIAA J. 39, 41(2001)) developed a flow governing equation approach for describing the turbulent outer boundary layer region. The approach was used to develop similarity criteria for the mean…
A new slow growth formulation for DNS of wall-bounded turbulent flow is developed and demonstrated to enable extension of slow growth modeling concepts to complex boundary layer flows. As in previous slow growth approaches, the formulation…
The (favorable) Falkner-Skan boundary layer profiles are a one parameter ($\beta \in [0,2]$) family of self-similar solutions to the stationary Prandtl system which describes the flow over a wedge with angle $\beta \frac{\pi}{2}$. The most…