scholarly journals Fully developed anelastic convection with no-slip boundaries

2021 ◽  
Vol 930 ◽  
Author(s):  
Chris A. Jones ◽  
Krzysztof A. Mizerski ◽  
Mouloud Kessar
Keyword(s):  
Rayleigh Number ◽  
Prandtl Number ◽  
Boundary Layers ◽  
Scaling Laws ◽  
Thin Layers ◽  
Parallel Layer ◽  
Theoretical Predictions ◽  
Bottom Boundary Layers ◽  
Bottom To Top ◽  
Crucial Part

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 Reynolds number. The appearance of an entropy structure consisting of a well-mixed uniform interior, bounded by thin layers with entropy jumps across them, makes it possible to derive explicit forms for these scaling laws. These are given in terms of the Rayleigh number, the Prandtl number and the bottom to top temperature ratio, which also measures how much the density varies across the layer. The top and bottom boundary layers are examined and they are found to be very different, unlike in the Boussinesq case. Elucidating the structure of these boundary layers plays a crucial part in determining the scaling laws. Physical arguments governing these boundary layers are presented, concentrating on the case in which the boundary layers are so thin that temperature and density vary little across them, even though there may be substantial temperature and density variations across the whole layer. Different scaling laws are found, depending on whether the viscous dissipation is primarily in the boundary layers or in the bulk. The cases of both high and low Prandtl number are considered. Numerical simulations of no-slip anelastic convection up to a Rayleigh number of $10^7$ have been performed and our theoretical predictions are compared with the numerical results.

Plume formation and resonant bifurcations in porous-media convection

1994 ◽  
Vol 272 ◽  
pp. 67-90 ◽  
Author(s):  
Michael D. Graham ◽  
Paul H. Steen
Keyword(s):  
Boundary Layer ◽  
Porous Media ◽  
Rayleigh Number ◽  
Scaling Laws ◽  
Thermal Plumes ◽  
Scaling Behaviour ◽  
Parametric Resonances ◽  
Classical Boundary ◽  
Rayleigh Benard Convection ◽  
Rayleigh Benard

The classical boundary-layer scaling laws proposed by Howard for Rayleigh–Bénard convection at high Rayleigh number extend to the analogous case of convection in saturated porous media. We computationally study two-dimensional porous-media convection near the onset of this scaling behaviour. The main result of the paper is the observation and study of instabilities that lead to deviations from the scaling relations.At Rayleigh numbers below the scaling regime, boundary-layer fluctuations born at a Hopf bifurcation strengthen and eventually develop into thermal plumes. The appearance of plumes corresponds to the onset of the boundary-layer scaling behaviour of the oscillation frequency and mean Nusselt number, in agreement with the classical theory. As the Rayleigh number increases further, the flow undergoes instabilities that lead to ‘bubbles’ in parameter space of quasi-periodic flow, and eventually to weakly chaotic flow. The instabilities disturb the plume formation process, effectively leading to a phase modulation of the process and to deviations from the scaling laws. We argue that these instabilities correspond to parametric resonances between the timescale for plume formation and the characteristic convection timescale of the flow.

scholarly journals The breakdown of the anelastic approximation in rotating compressible convection: implications for astrophysical systems

2015 ◽  
Vol 471 (2175) ◽  
pp. 20140689 ◽  
Author(s):  
Michael A. Calkins ◽  
Keith Julien ◽  
Philippe Marti
Keyword(s):  
Prandtl Number ◽  
Scaling Laws ◽  
Fluid Layer ◽  
Time Derivative ◽  
Density Perturbation ◽  
Plane Layer ◽  
Relative Magnitude ◽  
Critical Parameters ◽  
Anelastic Equations ◽  
Prandtl Numbers

The linear theory for rotating compressible convection in a plane layer geometry is presented for the astrophysically relevant case of low Prandtl number gases. When the rotation rate of the system is large, the flow remains geostrophically balanced for all stratification levels investigated and the classical (i.e. incompressible) asymptotic scaling laws for the critical parameters are recovered. For sufficiently small Prandtl numbers, increasing stratification tends to further destabilize the fluid layer, decrease the critical wavenumber and increase the oscillation frequency of the convective instability. In combination, these effects increase the relative magnitude of the time derivative of the density perturbation contained in the conservation of mass equation to non-negligible levels; the resulting convective instabilities occur in the form of compressional quasi-geostrophic oscillations. We find that the anelastic equations, which neglect this term, cannot capture these instabilities and possess spuriously growing eigenmodes in the rapidly rotating, low Prandtl number regime. It is shown that the Mach number for rapidly rotating compressible convection is intrinsically small for all background states, regardless of the departure from adiabaticity.

Bottom Boundary Layers

2021 ◽  
Author(s):  
Stephen M. Henderson ◽  
Jeffrey R. Nielson
Keyword(s):  
Boundary Layers ◽  
Bottom Boundary ◽  
Bottom Boundary Layers

scholarly journals NUMERICAL MODELING OF A TURBULENT BOTTOM BOUNDARY LAYER UNDER SOLITARY WAVES ON A SMOOTH SURFACE

2018 ◽  
pp. 26
Author(s):  
Ahmad Sana ◽  
Hitoshi Tanaka
Keyword(s):  
Boundary Layer ◽  
Boundary Layers ◽  
Solitary Waves ◽  
Bottom Boundary Layer ◽  
Stream Velocity ◽  
Bottom Boundary ◽  
Sediment Movement ◽  
Bottom Boundary Layers ◽  
Turbulent Models

A number of studies on bottom boundary layers under sinusoidal and cnoidal waves were carried out in the past owing to the role of bottom shear stress on coastal sediment movement. In recent years, the bottom boundary layers under long waves have attracted considerable attention due to the occurrence of huge tsunamis and corresponding sediment movement. In the present study two-equation turbulent models proposed by Menter(1994) have been applied to a bottom boundary layer under solitary waves. A comparison has been made for cross-stream velocity profile and other turbulence properties in x-direction.

Scale Analysis of Thermocapillary Weld Pool Shape With High Prandtl Number

2011 ◽  
Author(s):  
P. S. Wei ◽  
C. L. Lin ◽  
H. J. Liu
Keyword(s):  
Prandtl Number ◽  
Boundary Layers ◽  
Molten Pool ◽  
Surface Flow ◽  
Transport Processes ◽  
Surface Boundary ◽  
Scale Analysis ◽  
Melting Front ◽  
Pool Shape ◽  
High Prandtl Number

The molten pool shape and thermocapillary convection during melting or welding of metals or alloys are self-consistently predicted from parametric scale analysis for the first time. Determination of the molten pool shape is crucial due to its close relationship with the strength and properties of the fusion zone. In this work, surface tension coefficient is considered to be negative values, indicating an outward surface flow, whereas high Prandtl number represents the thermal boundary layer thickness to be less than that of momentum. Since Marangoni number is usually very high, the scaling of transport processes is divided into the hot, intermediate and cold corner regions on the flat free surface, boundary layers on the solid-liquid interface and ahead of the melting front. Coupling among distinct regions and thermal and momentum boundary layers, the results find that the width and depth of the pool can be determined as functions of Marangoni, Prandtl, Peclet, Stefan, and beam power numbers. The predictions agree with numerical computations and available experimental data.

scholarly journals On the streamwise evolution of turbulent boundary layers in arbitrary pressure gradients

2002 ◽  
Vol 461 ◽  
pp. 61-91 ◽  
Author(s):  
A. E. PERRY ◽  
IVAN MARUSIC ◽  
M. B. JONES
Keyword(s):  
Boundary Layers ◽  
Scaling Laws ◽  
Power Spectra ◽  
Adverse Pressure Gradient ◽  
Turbulent Boundary Layers ◽  
Stream Velocity ◽  
Mean Flow ◽  
Mean Velocity ◽  
Law Of The Wall ◽  
The Mean

A new approach to the classic closure problem for turbulent boundary layers is presented. This involves, first, using the well-known mean-flow scaling laws such as the log law of the wall and the law of the wake of Coles (1956) together with the mean continuity and the mean momentum differential and integral equations. The important parameters governing the flow in the general non-equilibrium case are identified and are used for establishing a framework for closure. Initially closure is achieved here empirically and the potential for achieving closure in the future using the wall-wake attached eddy model of Perry & Marusic (1995) is outlined. Comparisons are made with experiments covering adverse-pressure-gradient flows in relaxing and developing states and flows approaching equilibrium sink flow. Mean velocity profiles, total shear stress and Reynolds stress profiles can be computed for different streamwise stations, given an initial upstream mean velocity profile and the streamwise variation of free-stream velocity. The attached eddy model of Perry & Marusic (1995) can then be utilized, with some refinement, to compute the remaining unknown quantities such as Reynolds normal stresses and associated spectra and cross-power spectra in the fully turbulent part of the flow.

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