English
Related papers

Related papers: Steady Prandtl Layer for Compressible Fluids

200 papers

In this work, a near-wall model, which couples the inverse of a recently developed compressible velocity transformation [Griffin, Fu, & Moin, PNAS, 118:34, 2021] and an algebraic temperature-velocity relation, is developed for high-speed…

Fluid Dynamics · Physics 2023-09-11 Kevin Patrick Griffin , Lin Fu , Parviz Moin

A thermodynamic framework that predicts the thermal conductivity $\lambda$ of simple fluids beyond the dilute-gas limit is introduced. By generalizing the transition-rate approach of particles on a lattice to conserved quantities in…

Statistical Mechanics · Physics 2025-12-03 Miguel Hoyuelos

In 1904, Prandtl introduced his famous boundary layer in order to describe the behavior of solutions of Navier Stokes equations near a boundary as the viscosity goes to $0$. His Ansatz has later been justified for analytic data by R.E.…

Analysis of PDEs · Mathematics 2024-03-05 Emmanuel Grenier , Toan T. Nguyen

The shape of velocity and temperature profiles near the horizontal conducting plates in turbulent Rayleigh-B\'{e}nard convection are studied numerically and experimentally over the Rayleigh number range $10^8\lesssim…

The unavailability of accurate boundary treatment methods for compressible Smoothed Particle Hydrodynamics (SPH) severely limits its ability to simulate flows in and around bodies. To this end, challenges specific to compressible flows with…

Fluid Dynamics · Physics 2024-08-27 Navaneet Villodi , Prabhu Ramachandran

This paper is concerned with the vanishing viscosity and magnetic resistivity limit for the two-dimensional steady incompressible MHD system on the half plane with no-slip boundary condition on velocity field and perfectly conducting wall…

Analysis of PDEs · Mathematics 2021-04-12 Cheng-Jie Liu , Tong Yang , Zhu Zhang

Despite the physical importance, there are limited mathematical theories for the compressible Navier-Stokes equations with strong boundary layers. This is mainly due to the absence of a stream function structure, unlike the extensively…

Analysis of PDEs · Mathematics 2025-02-12 Shengxin Li , Tong Yang , Zhu Zhang

In this paper, we obtain the global-in-$x$ Sobolev stability of Prandtl layer expansions for 2-D steady incompressible MHD flows with shear outer ideal MHD flows $(1,0,\sigma,0)$ ($\sigma\geq 0$) on a moving plate. It is worth noticing that…

Analysis of PDEs · Mathematics 2023-02-15 Shijin Ding , Zhijun Ji , Zhilin Lin

We provide an optimal Gevrey stability result for general boundary layer expansions, under a mild concavity condition on the boundary layer profile. Our result generalizes (and even improves in the non strictly concave case) the one…

Analysis of PDEs · Mathematics 2020-05-12 David Gerard-Varet , Yasunori Maekawa , Nader Masmoudi

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…

Fluid Dynamics · Physics 2019-11-19 David W. Weyburne

In this paper, we consider the zero-viscosity limit of the 2D steady Navier-Stokes equations in $(0,L)\times\mathbb{R}^+$ with non-slip boundary conditions. By estimating the stream-function of the remainder, we justify the validity of the…

Analysis of PDEs · Mathematics 2020-01-30 Chen Gao , Liqun Zhang

In this paper we establish the incompressible limit for the compressible free-boundary Euler equations with surface tension in the case of a liquid. Compared to the case without surface tension treated recently, the presence of surface…

Analysis of PDEs · Mathematics 2020-05-14 Marcelo M. Disconzi , Chenyun Luo

Statistical properties of turbulent Rayleigh-Benard convection at low Prandtl numbers (Pr), which are typical for liquid metals such as mercury, gallium or liquid sodium, are investigated in high-resolution three-dimensional spectral…

Fluid Dynamics · Physics 2016-09-13 Janet D. Scheel , Joerg Schumacher

We consider a steady, geophysical 2D fluid in a domain, and focus on its western boundary layer, which is formally governed by a variant of the Prandtl equation. By using the von Mises change of variables, we show that this equation is…

Analysis of PDEs · Mathematics 2016-03-17 Anne-Laure Dalibard , Matthew Paddick

We derive an improved rigorous bound on the space and time averaged temperature $<T>$ of an infinite Prandtl number Boussinesq fluid contained between isothermal no-slip boundaries thermally driven by uniform internal heating. A novel…

Fluid Dynamics · Physics 2015-05-27 Jared P. Whitehead , Charles R. Doering

We study the velocity field in a horizontal (x-y) plane 1.5 mm above the hot plate in turbulent natural convection using PIV at a Rayleigh number Raw=106 and Prandtl number Pr=5.2. The plane of measurement is inside the velocity boundary…

Fluid Dynamics · Physics 2014-04-07 Vipin Koothur , Baburaj A Puthenveettil

This work assesses several popular transformations for the velocity profile through their application to several types of non-canonical compressible wall-bounded turbulent flows. Specifically, this work explores DNS databases of…

Fluid Dynamics · Physics 2022-05-03 Tianyi Bai , Kevin P. Griffin , Lin Fu

We study penetrative convection of a fluid confined between two horizontal plates, the temperatures of which are such that a temperature of maximum density lies between them. The range of Rayleigh numbers studied is $Ra = \left[10^6, 10^8…

Fluid Dynamics · Physics 2019-09-10 Srikanth Toppaladoddi , J. S. Wettlaufer

This investigation deals with the analysis of stagnation point heat transfer and corresponding flow features of hydromagnetic viscous incompressible fluid over a vertical shrinking sheet. The considered sheet is assumed to be permeable and…

Fluid Dynamics · Physics 2015-11-20 Rakesh Kumar , Shilpa Sood

Anelastic convection at high Rayleigh number in a plane parallel layer with no slip boundaries is considered. Energy and entropy balance equations are derived, and they are used to develop scaling laws for the heat transport and the…

Fluid Dynamics · Physics 2023-06-22 Chris A. Jones , Krzysztof A. Mizerski , Mouloud Kessar