scholarly journals Energy budget in internal wave attractor experiments

2019 ◽  
Vol 880 ◽  
pp. 743-763 ◽  
Author(s):  
Géraldine Davis ◽  
Thierry Dauxois ◽  
Timothée Jamin ◽  
Sylvain Joubaud
Keyword(s):  
Velocity Field ◽  
Internal Wave ◽  
Boundary Layers ◽  
Energy Budget ◽  
Dissipation Rate ◽  
Theoretical Expression ◽  
Two Dimensional ◽  
Energy Sink ◽  
Set Up ◽  
Different Sources

The current paper presents an experimental study of the energy budget of a two-dimensional internal wave attractor in a trapezoidal domain filled with uniformly stratified fluid. The injected energy flux and the dissipation rate are simultaneously measured from a two-dimensional, two-component, experimental velocity field. The pressure perturbation field needed to quantify the injected energy is determined from the linear inviscid theory. The dissipation rate in the bulk of the domain is directly computed from the measurements, while the energy sink occurring in the boundary layers is estimated using the theoretical expression for the velocity field in the boundary layers, derived recently by Beckebanze et al. (J. Fluid Mech., vol. 841, 2018, pp. 614–635). In the linear regime, we show that the energy budget is closed, in the steady state and also in the transient regime, by taking into account the bulk dissipation and, more importantly, the dissipation in the boundary layers, without any adjustable parameters. The dependence of the different sources on the thickness of the experimental set-up is also discussed. In the nonlinear regime, the analysis is extended by estimating the dissipation due to the secondary waves generated by triadic resonant instabilities, showing the importance of the energy transfer from large scales to small scales. The method tested here on internal wave attractors can be generalized straightforwardly to any quasi-two-dimensional stratified flow.

How the Raleigh Flow Transits to Blasius Numerically

1998 ◽  
Vol 65 (2) ◽  
pp. 445-453
Author(s):  
G. N. Sarma
Keyword(s):  
Boundary Layer ◽  
Velocity Field ◽  
Flat Plate ◽  
Boundary Layers ◽  
Boundary Layer Theory ◽  
Two Dimensional ◽  
Blasius Flow ◽  
Weighted Residuals ◽  
Uniform Velocity ◽  
Method Of Weighted Residuals

This paper answers the question numerically how a two-dimensional incompressible Rayleigh boundary layer started impulsively past a semi-infinite flat plate with uniform velocity in the mainstream transits to steady Blasius flow. It is shown that the transition is a convective transition and smooth with no discontinuities. It is effected by the parameters called the convective and angular parameters. The velocity field gets disintegrated into discrete dissimilar diffusive layers of different convective orders. This is an example based on modified boundary layer theory of Sarma. Polynomial solutions are found using the theory of definite thickness boundary layers and the method of weighted residuals. This modifies the numerical works of Hall and Dennis, which are based on Stewartson’s theory of propagation of disturbances.

On the method for solution of unsteady thermal boundary-layers in case of two-dimensional low-speed flows

1968 ◽  
Vol 64 (3) ◽  
pp. 849-870
Author(s):  
Milan Ð. Ðurić
Keyword(s):  
Velocity Field ◽  
Boundary Layers ◽  
The Body ◽  
Main Stream ◽  
Two Dimensional ◽  
Low Speed ◽  
Velocity Boundary Layer ◽  
The Difference ◽  
Image Position ◽  
Thermal Boundary Layers

AbstractThis paper is dedicated to the question of solving unsteady thermal boundary-layers in the case of two-dimensional low-speed flows, provided that the difference between the temperature of the stream and that of the wall is not too great (so that the density is sensibly constant) and that the change in the wall temperature Tw (x, t) takes place at the same instant as the body is set into motion. The velocity boundary-layer is uncoupled from the thermal one and can be considered separately. In paper (2) is given the method for obtaining the velocity field (u, v). The temperature field T depends on the velocity field and can be obtained only after this one. The method (2) being available for this purpose assuming the difference between the temperature of the wall Tw (x, t) and that of the main-stream T∞ in the form ofwhere S(x) and θ(t) are arbitrary functions of x respectively t, satisfying certain conditions required by the method.

The background flow method. Part 2. Asymptotic theory of dissipation bounds

1998 ◽  
Vol 363 ◽  
pp. 301-323 ◽  
Author(s):  
ROLF NICODEMUS ◽  
S. GROSSMANN ◽  
M. HOLTHAUS
Keyword(s):  
Reynolds Number ◽  
Boundary Layers ◽  
Variational Approach ◽  
Dissipation Rate ◽  
Asymptotic Theory ◽  
Two Dimensional ◽  
Plane Couette Flow ◽  
Shape Functions ◽  
Background Flow ◽  
Asymptotic Parameter

We study analytically the asymptotics of the upper bound on energy dissipation for the two-dimensional plane Couette flow considered numerically in Part 1 of this work, in order to identify the mechanisms underlying the variational approach. With the help of shape functions that specify the variational profiles either in the interior or in the boundary layers, it becomes possible to quantitatively explain all numerically observed features, from the occurrence of two branches of minimizing wavenumbers to the asymptotic parameter scaling with the Reynolds number. In addition, we derive a new variational principle for the asymptotic bound on the dissipation rate. The analysis of this principle reveals that the best possible bound can only be attained if the variational profiles allow the shape of the boundary layers to change with increasing Reynolds number.

The Departure from Equilibrium of Turbulent Boundary Layers

1968 ◽  
Vol 19 (1) ◽  
pp. 1-19 ◽  
Author(s):  
H. McDonald
Keyword(s):  
Boundary Layer ◽  
Shear Stress ◽  
Kinetic Energy ◽  
Stress Distribution ◽  
Boundary Layers ◽  
Turbulent Boundary Layers ◽  
Two Dimensional ◽  
Pressure Distributions ◽  
Momentum Integral ◽  
State Examination

SummaryRecently two authors, Nash and Goldberg, have suggested, intuitively, that the rate at which the shear stress distribution in an incompressible, two-dimensional, turbulent boundary layer would return to its equilibrium value is directly proportional to the extent of the departure from the equilibrium state. Examination of the behaviour of the integral properties of the boundary layer supports this hypothesis. In the present paper a relationship similar to the suggestion of Nash and Goldberg is derived from the local balance of the kinetic energy of the turbulence. Coupling this simple derived relationship to the boundary layer momentum and moment-of-momentum integral equations results in quite accurate predictions of the behaviour of non-equilibrium turbulent boundary layers in arbitrary adverse (given) pressure distributions.

Restoration of the velocity field of the heart from two-dimensional echocardiograms

1989 ◽  
Vol 8 (2) ◽  
pp. 143-153 ◽  
Author(s):  
G.E. Mailloux ◽  
F. Langlois ◽  
P.Y. Simard ◽  
M. Bertrand
Keyword(s):  
Velocity Field ◽  
Two Dimensional

Effects of plane progressive irrotational waves on thermal boundary layers

1971 ◽  
Vol 50 (2) ◽  
pp. 321-334 ◽  
Author(s):  
James Witting
Keyword(s):  
Boundary Layers ◽  
Deep Water ◽  
Maximum Amplitude ◽  
Capillary Waves ◽  
Temperature Gradients ◽  
Two Dimensional ◽  
Inviscid Incompressible Fluid ◽  
Mean Temperature ◽  
The Waves ◽  
Thermal Boundary Layers

The average changes in the structure of thermal boundary layers at the surface of bodies of water produced by various types of surface waves are computed. the waves are two-dimensional plane progressive irrotational waves of unchanging shape. they include deep-water linear waves, deep-water capillary waves of arbitrary amplitude, stokes waves, and the deep-water gravity wave of maximum amplitude.The results indicate that capillary waves can decrease mean temperature gradients by factors of as much as 9·0, if the average heat flux at the air-water interface is independent of the presence of the waves. Irrotational gravity waves can decrease the mean temperature gradients by factors no more than 1·381.Of possible pedagogical interest is the simplicity of the heat conduction equation for two-dimensional steady irrotational flows in an inviscid incompressible fluid if the velocity potential and the stream function are taken to be the independent variables.

Comparative studies of the set up of two-dimensional pneumatic arm systems by muscle and rotational actuators

2007 ◽  
Vol 221 (5) ◽  
pp. 743-748 ◽  
Author(s):  
Y-T Wang ◽  
R-H Wong ◽  
J-T Lu
Keyword(s):  
Control Systems ◽  
Fuzzy Controller ◽  
Control Algorithms ◽  
Two Dimensional ◽  
Pneumatic Control ◽  
Learning Mechanism ◽  
Set Up ◽  
And Control ◽  
Self Learning ◽  
System Characteristics

As opposed to traditional pneumatic linear actuators, muscle and rotational actuators are newly developed actuators in rotational and specified applications. In the current paper, these actuators are used to set up two-dimensional pneumatic arms, which are used mainly to simulate the excavator's motion. Fuzzy control algorithms are typically applied in pneumatic control systems owing to their non-linearities and ill-defined mathematical model. The self-organizing fuzzy controller, which includes a self-learning mechanism to modify fuzzy rules, is applied in these two-dimensional pneumatic arm control systems. Via a variety of trajectory tracking experiments, the present paper provides comparisons of system characteristics and control performances.

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