Nonlinear motions induced by moving thermal waves

1972 ◽  
Vol 54 (1) ◽  
pp. 163-187 ◽  
Author(s):  
Richard E. Young ◽  
Gerald Schubert ◽  
Kenneth E. Torrance
Keyword(s):  
Thermal Wave ◽  
Fluid Layer ◽  
Lower Boundary ◽  
Phase Speed ◽  
Thermal Source ◽  
Nonlinear Interactions ◽  
Thermal Waves ◽  
Mean Flow ◽  
Mean Velocity ◽  
Boussinesq Fluid

The motion induced in a layer of Boussinesq fluid by moving periodic thermal waves is obtained by numerically solving the complete nonlinear two-dimensional momentum and temperature equations. Three sets of boundary conditions are treated: rigid upper and lower boundaries with symmetrical heating; free upper boundary and rigid lower boundary with heating only at the top; free upper and lower boundaries with symmetrical heating. The nonlinear streamline patterns show that, when the velocity fluctuations are larger than the phase speed of the thermal wave and the mean flow, the convection cells have shapes governed by fluctuating nonlinear interactions. Significant mean velocities can be created even without the characteristic tilt in the convection cells expected on the basis of linear theory. Nonlinear interactions can lead to a mean shear even in the absence of motion of the thermal source. When the viscous diffusion time across the fluid layer is less than or of the same order as the period of the thermal wave, the order of magnitude of the induced mean velocity does not exceed that of the phase speed of the wave, even for intense thermal forcing.

Strong streaming induced by a moving thermal wave

1971 ◽  
Vol 47 (2) ◽  
pp. 291-304 ◽  
Author(s):  
E. J. Hinch ◽  
Gerald Schubert
Keyword(s):  
Thermal Wave ◽  
Wave Speed ◽  
Nonlinear Boundary ◽  
Short Time Scale ◽  
Mean Flow ◽  
Mean Velocity ◽  
Weak Limits ◽  
The Mean ◽  
Boussinesq Fluid ◽  
Short Time

The motion induced in a layer of Boussinesq fluid by a moving thermal wave is studied in the case where the mean velocity could exceed the wave speed. A nonlinear boundary-layer theory shows that strong streaming is possible for small viscosity. Velocity fluctuations are limited in magnitude by their short time scale, while viscosity alone, assumed to be relatively weak, limits the mean flow.

On internal gravity waves in an accelerating shear flow

1978 ◽  
Vol 88 (4) ◽  
pp. 623-639 ◽  
Author(s):  
S. A. Thorpe
Keyword(s):  
Gravity Waves ◽  
Phase Distribution ◽  
Phase Speed ◽  
Internal Gravity Waves ◽  
Initial Energy ◽  
Constant Density ◽  
Mean Flow ◽  
Mean Velocity ◽  
The Mean ◽  
The Waves

The investigation of the effects which a changing mean flow has on a uniform train of internal gravity waves (Thorpe 1978a) is continued by considering waves in a uniformly accelerating stratified plane Couette flow with constant density gradient. Experiments reveal a change in the mode structure and phase distribution of the waves, and their eventual breaking near the boundary where the mean flow is greatest, the phase speed of the waves being positive. A linear numerical model is devised which accurately describes the waves up to the onset of their breaking, and this is used to investigate their energetics. The working of the Reynolds stress against the mean velocity gradient results in a very rapid transfer of energy from the waves to the mean flow, so that by the time breaking occurs only a small fraction of their initial energy remains for possible transfer into potential energy of the fluid.The consequences have important applications in oceanography and meteorology, to flow stability and flow generation, and explain some earlier laboratory observations.

Nonlinear interactions between convection, rotation and flows with vertical shear

1986 ◽  
Vol 164 ◽  
pp. 91-105 ◽  
Author(s):  
David H. Hathaway ◽  
Richard C. J. Somerville
Keyword(s):  
Kinetic Energy ◽  
Shear Flow ◽  
Fluid Layer ◽  
Three Dimensional ◽  
Rotation Vector ◽  
Vertical Shear ◽  
Nonlinear Interactions ◽  
Mean Flow ◽  
Rotation Vectors ◽  
Convective Motions

A three-dimensional and time-dependent numerical model is used to study the nonlinear interactions between thermal convective motions, rotation, and imposed flows with vertical shear. All cases have Rayleigh numbers of 104 and Prandtl numbers of 1.0. Rotating cases have Taylor numbers of 104.For the non-rotating cases, the effects of the shear on the convection produce longitudinal rolls aligned with the shear flow and a downgradient flux of momentum. The interaction between the convection and the shear flow decreases the shear in the interior of the fluid layer while adding kinetic energy to the convective motions. For unit Prandtl number the dimensionless flux of momentum is equal to the dimensionless flux of heat.For rotating cases with vertical rotation vectors, the shear flow favours rolls aligned with the shear and produces a downgradient flux of momentum. However, the Coriolis force turns the flow induced by the convection to produce a more complicated shear that changes direction with height. As in the non-rotating cases, the convective motions become more energetic by extracting energy from the mean flow. For Richardson numbers larger than about − 1.0, the dominant source of eddy kinetic energy is the shear flow rather than buoyancy.For rotating cases with tilted rotation vectors the results depend upon the direction of the shear. For weak shear, convective rolls aligned with the rotation vector are favoured. When the shear flow is directed to the east along the top, the rolls become broader and the convection weaker. For large shear in this direction, the convective motions are quenched by the competition between the shear flow and the tilted rotation vector. When the shear flow is directed to the west along the top, strong shear produces rolls aligned with the shear. The heat and momentum fluxes become large and can exceed those found in the absence of a tilted rotation vector. Countergradient fluxes of momentum can also be produced.

Nanofluids: Synthesis, Heat Conduction, and Extension

2009 ◽  
Vol 131 (3) ◽  
Author(s):  
Liqiu Wang ◽  
Xiaohao Wei
Keyword(s):  
Heat Conduction ◽  
Olive Oil ◽  
Thermal Wave ◽  
Thermal Waves ◽  
Water Conductivity ◽  
Conductivity Enhancement ◽  
Chemical Solution Method ◽  
New Type ◽  
Fourier Heat Conduction ◽  
Two Phases

We synthesize eight kinds of nanofluids with controllable microstructures by a chemical solution method (CSM) and develop a theory of macroscale heat conduction in nanofluids. By the CSM, we can easily vary and manipulate nanofluid microstructures through adjusting synthesis parameters. Our theory shows that heat conduction in nanofluids is of a dual-phase-lagging type instead of the postulated and commonly used Fourier heat conduction. Due to the coupled conduction of the two phases, thermal waves and possibly resonance may appear in nanofluid heat conduction. Such waves and resonance are responsible for the conductivity enhancement. Our theory also generalizes nanofluids into thermal-wave fluids in which heat conduction can support thermal waves. We emulsify olive oil into distilled water to form a new type of thermal-wave fluids that can support much stronger thermal waves and resonance than all reported nanofluids, and consequently extraordinary water conductivity enhancement (up to 153.3%) by adding some olive oil that has a much lower conductivity than water.

On resonant over-reflexion of internal gravity waves from a Helmholtz velocity profile

1979 ◽  
Vol 90 (1) ◽  
pp. 161-178 ◽  
Author(s):  
R. H. J. Grimshaw
Keyword(s):  
Velocity Profile ◽  
Gravity Waves ◽  
Second Harmonic ◽  
Phase Speed ◽  
Internal Gravity Waves ◽  
Finite Amplitude ◽  
Weakly Nonlinear ◽  
Velocity Discontinuity ◽  
Interface Displacement ◽  
Boussinesq Fluid

A Helmholtz velocity profile with velocity discontinuity 2U is embedded in an infinite continuously stratified Boussinesq fluid with constant Brunt—Väisälä frequency N. Linear theory shows that this system can support resonant over-reflexion, i.e. the existence of neutral modes consisting of outgoing internal gravity waves, whenever the horizontal wavenumber is less than N/2½U. This paper examines the weakly nonlinear theory of these modes. An equation governing the evolution of the amplitude of the interface displacement is derived. The time scale for this evolution is α−2, where α is a measure of the magnitude of the interface displacement, which is excited by an incident wave of magnitude O(α3). It is shown that the mode which is symmetrical with respect to the interface (and has a horizontal phase speed equal to the mean of the basic velocity discontinuity) remains neutral, with a finite amplitude wave on the interface. However, the other modes, which are not symmetrical with respect to the interface, become unstable owing to the self-interaction of the primary mode with its second harmonic. The interface displacement develops a singularity in a finite time.

The structure of a highly decelerated axisymmetric turbulent boundary layer

2021 ◽  
Vol 929 ◽  
Author(s):  
N. Agastya Balantrapu ◽  
Christopher Hickling ◽  
W. Nathan Alexander ◽  
William Devenport
Keyword(s):  
Boundary Layer ◽  
Pressure Gradient ◽  
Shear Layer ◽  
Layer Thickness ◽  
Boundary Layer Thickness ◽  
Large Scale ◽  
Convection Velocity ◽  
Mean Flow ◽  
Mean Velocity ◽  
The Mean

Experiments were performed over a body of revolution at a length-based Reynolds number of 1.9 million. While the lateral curvature parameters are moderate ( $\delta /r_s < 2, r_s^+>500$ , where $\delta$ is the boundary layer thickness and r s is the radius of curvature), the pressure gradient is increasingly adverse ( $\beta _{C} \in [5 \text {--} 18]$ where $\beta_{C}$ is Clauser’s pressure gradient parameter), representative of vehicle-relevant conditions. The mean flow in the outer regions of this fully attached boundary layer displays some properties of a free-shear layer, with the mean-velocity and turbulence intensity profiles attaining self-similarity with the ‘embedded shear layer’ scaling (Schatzman & Thomas, J. Fluid Mech., vol. 815, 2017, pp. 592–642). Spectral analysis of the streamwise turbulence revealed that, as the mean flow decelerates, the large-scale motions energize across the boundary layer, growing proportionally with the boundary layer thickness. When scaled with the shear layer parameters, the distribution of the energy in the low-frequency region is approximately self-similar, emphasizing the role of the embedded shear layer in the large-scale motions. The correlation structure of the boundary layer is discussed at length to supply information towards the development of turbulence and aeroacoustic models. One major finding is that the estimation of integral turbulence length scales from single-point measurements, via Taylor's hypothesis, requires significant corrections to the convection velocity in the inner 50 % of the boundary layer. The apparent convection velocity (estimated from the ratio of integral length scale to the time scale), is approximately 40 % greater than the local mean velocity, suggesting the turbulence is convected much faster than previously thought. Closer to the wall even higher corrections are required.

Control of Hemorrhage in Critical Femoral or Inguinal Penetrating Wounds—An Ultrasound Evaluation

2006 ◽  
Vol 21 (6) ◽  
pp. 379-382 ◽  
Author(s):  
Michael Blaivas ◽  
Stephen Shiver ◽  
Matthew Lyon ◽  
Srikar Adhikari
Keyword(s):  
Flow Velocity ◽  
Abdominal Aorta ◽  
Femoral Artery ◽  
Iliac Artery ◽  
Common Femoral Artery ◽  
Body Armor ◽  
Mean Flow ◽  
Mean Velocity ◽  
Flow Measurements ◽  
Ultrasound Evaluation

AbstractIntroduction:Exsanguination from a femoral artery wound can occur in sec-onds and may be encountered more often due to increased use of body armor. Some military physicians teach compression of the distal abdominal aorta (Abdominal Aorta) with a knee or a fist as a temporizing measure.Objective:The objective of this study was to evaluate if complete collapse of the Abdominal Aorta was feasible and with what weight it occurs.Methods:This was a prospective, interventional study at a Level-I, academ-ic, urban, emergency department with an annual census of 80,000 patients. Written, informed consent was obtained from nine male volunteers after Institutional Research Board approval. Any patient who presented with abdominal pain or had undergone previous abdominal surgery was excluded from the study. Subjects were placed supine on the floor to simulate an injured soldier. Various dumbbells of increasing weight were placed over the distal Abdominal Aorta, and pulsed-wave Doppler measurements were taken at the right common femoral artery (CFA). Dumbbells were placed on top of a tightly bundled towel roughly the surface area of an adult knee. Flow measurements at the CFA were taken at increments of 20 pounds. This was repeated with weight over the proximal right artery iliac and distal right iliac artery to eval- uate alternate sites. Descriptive statistics were utilized to evaluate the data.Results:The mean velocity through the CFA was 75.8 cm/ sec at 0 pounds. Compression of the Abdominal Aorta ranging 80 to 140 pounds resulted in no flow in the CFA. A steady decrease in mean flow velocity was seen starting with 20 pounds. Flow velocity decreased more rapidly with compression of the prox- imal right iliac artery, and stopped in all nine volunteers by 120 pounds of pressure. For all nine volunteers, up to 80 pounds of pressure over the distal iliac artery failed to decrease CFA flow velocity, and no subject was able to tolerate more weight at that location.Conclusion:Flow to the CFA can be stopped completely with pressure over the distal Abdominal Aorta or proximal iliac artery in catastrophic wounds. Compression over the proximal iliac artery worked best, but a first responder still may need to apply upward of 120 pounds of pressure to stop exsanguination.

Abstract WMP66: Cerebrovascular Hemodynamics of Mechanical Circulatory Support Device Patients

Stroke ◽  
2017 ◽  
Vol 48 (suppl_1) ◽  
Author(s):  
Kara R Melmed ◽  
Konrad H Shlick ◽  
Brenda Rinsky ◽  
Shlee S Song ◽  
Patrick D Lyden
Keyword(s):  
Continuous Flow ◽  
Mechanical Circulatory Support ◽  
Left Ventricular ◽  
Total Artificial Heart ◽  
Circulatory Support ◽  
Normative Values ◽  
Mean Flow ◽  
Mean Velocity ◽  
Ventricular Assist ◽  
Cerebrovascular Hemodynamics

Background: Multiple types of mechanical circulatory support (MCS) devices are commonly used in heart failure patients. These devices carry risk for neurologic complications, specifically cardioembolic stroke. Alterations in blood flow play a role in the pathophysiology, however there is limited data regarding cerebrovascular hemodynamics in MCS patients. We used transcranial Doppler (TCD) to define hemodynamics of commonly used MCS devices. Methods: We retrospectively examined charts from 2/2013 through 6/2016 for patients with MCS who underwent TCD, and obtained the following: peak systolic,end-diastolic velocities, mean flow velocities, pulsatility indices (PI) and number of high-intensity transient signals (HITS). Waveform morphologies were compared between devices. Results: Of 1,796 TCDs studies screened, 62 TCD studies were from 32 MCS patients. Of these, 21 were on extracorporeal membrane oxygenation (ECMO), 15 had a left ventricular assist device (LVAD), 18 had total artificial heart (TAH), and 2 had intra-aortic balloon pumps (IABP). Waveforms in patients supported by ECMO demonstrated continuous flow without clear systolic peaks. The averaged mean MCA velocity was 57.57 (SD= 21.00) cm/sec and mean PI is 0.35 (0.17). LVAD averaged mean MCA velocity was 57.57 (14.38) cm/sec and mean PI of 0.45 (0.28). PIs were low in patients with continuous-flow LVADs. Impella patients had morphologically distinct pulsatile waveforms compared to other types of VADs. IABP had averaged mean velocity of 56.21 (14.78) cm/sec and mean PI of 0.77 (0.15). These waveforms demonstrated pronounced diastolic upstrokes not present in other devices. In TAH patients, mean MCA velocity was 73.69 (33.00) cm/sec and PI of 0.86 (0.40). Emboli detection was performed in 46 studies, and HITS were detected in 29 (63%). Of these 15 (51%) were administered 100% oxygen which suppressed >50% HITS in 10 (67%) patients. Conclusion: Patients supported by MCS devices produce unique and characteristic waveforms on TCD studies. Further studies will describe normative values in this special population. HITS were not universally present and intermittently suppressible by oxygen, suggesting some may be gaseous in nature. Risk of stroke in patients with MCS and HITS is under study.

A Mean Flow Model for Polymer and Fiber Turbulent Drag Reduction

2005 ◽  
Vol 15 (6) ◽  
pp. 370-389 ◽  
Author(s):  
Anshuman Roy ◽  
Ronald G. Larson
Keyword(s):  
Drag Reduction ◽  
Weissenberg Number ◽  
Extensional Viscosity ◽  
Mean Flow ◽  
Dimensionless Numbers ◽  
Zero Shear Viscosity ◽  
Mean Velocity ◽  
Fiber Concentration ◽  
Turbulent Drag ◽  
The Mean

Abstract We present a one-parameter model that fits quantitatively the mean velocity profiles from experiments and numerical simulations of drag-reduced wall-bounded flows of dilute solutions of polymers and non-Brownian fibers in the low and modest drag reduction regime. The model is based on a viscous mechanism of drag reduction, in which either extended polymers or non-Brownian fibers increase the extensional viscosity of the fluid and thereby suppress both small and large turbulent eddies and reduce momentum transfer to the wall, resulting in drag reduction. Our model provides a rheological interpretation of the upward parallel shift S+ in the mean velocity profile upon addition of polymer, observed by Virk. We show that Virk’s correlations for the dependence on polymer molecular weight and concentration of the onset wall shear stress and slope increment on the Prandtl-Karman plot can be translated to two dimensionless numbers, namely an onset Weissenberg number and an asymptotic Trouton ratio of maximum extensional viscosity to zero-shear viscosity. We believe that our model, while simple, captures the essential features of drag reduction that are universal to flexible polymers and fibers, and, unlike the Virk phenomenology, can easily be extended to flows with inhomogeneous polymer or fiber concentration fields.

Sign in / Sign up

Export Citation Format

Share Document