scholarly journals An exact solution of the convective Couette flow under the parabolic heating condition at the lower boundary of a fluid layer

2020 ◽  
Author(s):  
V. V. Privalova ◽  
E. Yu. Prosviryakov
Keyword(s):  
Exact Solution ◽  
Couette Flow ◽  
Fluid Layer ◽  
Lower Boundary ◽  
Heating Condition

An exact solution in the stability of m. h. d. Couette flow

1972 ◽  
Vol 327 (1569) ◽  
pp. 269-278 ◽  
Keyword(s):  
Magnetic Field ◽  
Exact Solution ◽  
Couette Flow ◽  
Stability Problem ◽  
Axial Magnetic Field ◽  
Narrow Gap ◽  
Mhd Stability ◽  
Arbitrary Magnetic Field ◽  
The Stability ◽  
Conducting Cylinders

The MHD stability problem for dissipative Couette flow in a narrow gap between corotating, conducting cylinders with an axial magnetic field is solved exactly. Results are presented for an arbitrary magnetic field; in particular, previous results on the zero and infinite magnetic field limits are verified.

Stability of plane Poiseuille–Couette flow in a fluid layer overlying a porous layer

2017 ◽  
Vol 826 ◽  
pp. 376-395 ◽  
Author(s):  
Ting-Yueh Chang ◽  
Falin Chen ◽  
Min-Hsing Chang
Keyword(s):  
Couette Flow ◽  
Porous Layer ◽  
Poiseuille Flow ◽  
Fluid Layer ◽  
Maximum Velocity ◽  
Stability Characteristic ◽  
Layer System ◽  
Neutral Curves ◽  
Layer Mode ◽  
The Stability

This paper performs a linear stability analysis to investigate the stability of plane Poiseuille–Couette flow in a fluid layer overlying a porous medium saturated with the same fluid. The effect of superimposed Couette flow on the associated Poiseuille flow in such a two-layer system is explored carefully. The result shows that the presence of Couette flow may destabilize the Poiseuille flow at small depth ratio $\hat{d}$, defined by the ratio of the depth of the fluid layer to the depth of the porous layer, and induce a tri-modal structure to the neutral curves. At moderate $\hat{d}$, the Couette component generally produces a stabilization effect on the flow. When the velocity of the upper moving wall is large enough, a bi-modal behaviour of the neutral curves appears and a shift of instability mode occurs from the long-wave fluid-layer mode to the porous-layer mode with higher wavenumber. These stability characteristics are remarkably different from those of the plane Poiseuille–Couette flow in a single fluid layer in that the flow becomes absolutely stable when the wall velocity is over 70 % of the maximum velocity of the Poiseuille component of flow. The stability of pure Couette flow in such a two-layer system is also studied. It is found that the flow is still absolutely stable with respect to infinitesimal disturbances, which is the same as the stability characteristic of a single-layer plane Couette flow.

scholarly journals A note on “Taylor–Couette flow of a generalized second grade fluid due to a constant couple”

2010 ◽  
Vol 15 (2) ◽  
pp. 155-158 ◽  
Author(s):  
C. Fetecau ◽  
A. U. Awan ◽  
M. Athar
Keyword(s):  
Exact Solution ◽  
Steady State ◽  
Unsteady Flow ◽  
Couette Flow ◽  
Second Grade ◽  
Second Grade Fluid ◽  
Grade Fluid ◽  
Generalized Second Grade Fluid ◽  
New Form ◽  
Second Grade Fluids

In this brief note, we show that the unsteady flow of a generalized second grade fluid due to a constant couple, as well as the similar flow of Newtonian and ordinary second grade fluids, ultimately becomes steady. For this, a new form of the exact solution for velocity is established. This solution is presented as a sum of the steady and transient components. The required time to reach the steady-state is obtained by graphical illustrations.

The Galerkin method applied to convective instability problems

1968 ◽  
Vol 33 (1) ◽  
pp. 201-208 ◽  
Author(s):  
Bruce A. Finlayson
Keyword(s):  
Exact Solution ◽  
Time Dependence ◽  
Galerkin Method ◽  
Convective Instability ◽  
Fluid Layer ◽  
Oscillatory Instability ◽  
Rotating Fluid ◽  
Exponential Time ◽  
The Stability ◽  
The Galerkin Method

The Galerkin method is applied in a new way to problems of stationary and oscillatory convective instability. By retaining the time derivatives in the equations rather than assuming an exponential time-dependence, the exact solution is approximated by the solution to a set of ordinary differential equations in time. Computations are simplified because the stability of this set of equations can be determined without finding the detailed solution. Furthermore, both stationary and oscillatory instability can be studied by means of the same trial functions. Previous studies which have treated only stationary instability by the Galerkin method can now be extended easily to include oscillatory instability. The method is illustrated for convective instability of a rotating fluid layer transferring heat.

Impacts of Soil Heating Condition on Precipitation Simulations in the Weather Research and Forecasting Model

2009 ◽  
Vol 137 (7) ◽  
pp. 2263-2285 ◽  
Author(s):  
Xingang Fan
Keyword(s):  
Soil Temperature ◽  
Air Temperature ◽  
Land Surface ◽  
Lower Boundary ◽  
Land Surface Model ◽  
Surface Model ◽  
Heating Condition ◽  
Near Surface ◽  
Thermal Fields ◽  
Soil Temperatures

Soil temperature is a major variable in land surface models, representing soil energy status, storage, and transfer. It serves as an important factor indicating the underlying surface heating condition for weather and climate forecasts. This study utilizes the Weather Research and Forecasting (WRF) model to study the impacts of changes to the surface heating condition, derived from soil temperature observations, on regional weather simulations. Large cold biases are found in the 40-yr European Centre for Medium-Range Weather Forecasts (ECMWF) Re-Analysis project (ERA-40) soil temperatures as compared to observations. At the same time, a warm bias is found in the lower boundary assumption adopted by the Noah land surface model. In six heavy rain cases studied herein, observed soil temperatures are used to initialize the land surface model and to provide a lower boundary condition at the bottom of the model soil layer. By analyzing the impacts from the incorporation of observed soil temperatures, the following major conclusions are drawn: 1) A consistent increase in the ground heat flux is found during the day, when the observed soil temperatures are used to correct the cold bias present in ERA-40. Soil temperature changes introduced at the initial time maintain positive values but gradually decrease in magnitude with time. Sensible and latent heat fluxes and the moisture flux experience an increase during the first 6 h. 2) An increase in soil temperature impacts the air temperature through surface exchange, and near-surface moisture through evaporation. During the first two days, an increase in air temperature is seen across the region from the surface up to about 800 hPa (∼1450 m). The maximum near-surface air temperature increase is found to be, averaged over all cases, 0.5 K on the first day and 0.3 K on the second day. 3) The strength of the low-level jet is affected by the changes described above and also by the consequent changes in horizontal gradients of pressure and thermal fields. Thus, the three-dimensional circulation is affected, in addition to changes seen in the humidity and thermal fields and the locations and intensities of precipitating systems. 4) Overall results indicate that the incorporation of observed soil temperatures introduces a persistent soil heating condition that is favorable to convective development and, consequently, improves the simulation of precipitation.

scholarly journals Finite amplitude thermal convection with spatially modulated boundary temperatures

1995 ◽  
Vol 449 (1937) ◽  
pp. 459-478 ◽  
Keyword(s):  
Stability Analysis ◽  
Thermal Convection ◽  
Fluid Layer ◽  
Perturbation Technique ◽  
Lower Boundary ◽  
Finite Amplitude ◽  
Resonant Wavelength ◽  
Two Dimensional ◽  
Dimensional Solution ◽  
One Dimensional

Finite amplitude thermal convection in a fluid layer between two horizontal walls with different fixed mean temperatures is considered when spatially modulated temperatures with amplitudes L 1 * and L u * are prescribed at the lower and upper walls, respectively. The nonlinear steady problem is solved by a perturbation technique, and the preferred mode of convection is determined by a stability analysis. In the case of a resonant wavelength excitation, regular or non-regular multi-modal pattern convection can be preferred for some ranges of L 1 * and L u *, provided the wave vectors for such patterns are contained in a certain subset of the wave vectors representing a linear combination of modulated upper and lower boundary temperatures. In the case of non-resonant wavelength excitation, a three (two) dimensional solution in the form of multi-modal (rolls) pattern convection can be preferred, even if the boundary modulations are one (two) or two (one) dimensional, provided the wavelengths of the modulations are not too small. Heat transported by convection can be enhanced by boundary modulations in some ranges of L 1 * and L u *.

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