High-mode stationary waves in stratified flow over large obstacles

2010 ◽  
Vol 644 ◽  
pp. 321-336 ◽  
Author(s):  
JODY M. KLYMAK ◽  
SONYA M. LEGG ◽  
ROBERT PINKEL
Keyword(s):  
Steady State ◽  
Aspect Ratio ◽  
Vertical Component ◽  
Phase Speed ◽  
Stratified Flow ◽  
Buoyancy Frequency ◽  
Stationary Waves ◽  
Vertical Wavelength ◽  
Mean Velocity ◽  
Lee Wave

Simulations of steady two-dimensional stratified flow over an isolated obstacle are presented where the obstacle is tall enough so that the topographic Froude number, Nhm/Uo ≫ 1. N is the buoyancy frequency, hm the height of the topography from the channel floor and Uo the flow speed infinitely far from the obstacle. As for moderate Nhm/Uo (~1), a columnar response propagates far up- and downstream, and an arrested lee wave forms at the topography. Upstream, most of the water beneath the crest is blocked, while the moving layer above the crest has a mean velocity Um = UoH/(H−hm). The vertical wavelength implied by this velocity scale, λo = 2πUm/N, predicts dominant vertical scales in the flow. Upstream of the crest there is an accelerated region of fluid approximately λo thick, above which there is a weakly oscillatory flow. Downstream the accelerated region is thicker and has less intense velocities. Similarly, the upstream lift of isopycnals is greatest in the first wavelength near the crest, and weaker above and below. Form drag on the obstacle is dominated by the blocked response, and not on the details of the lee wave, unlike flows with moderate Nhm/Uo.Directly downstream, the lee wave that forms has a vertical wavelength given by λo, except for the deepest lobe which tends to be thicker. This wavelength is small relative to the fluid depth and topographic height, and has a horizontal phase speed cpx = −Um, corresponding to an arrested lee wave. When considering the spin-up to steady state, the speed of vertical propagation scales with the vertical component of group velocity cgz = αUm, where α is the aspect ratio of the topography. This implies a time scale = tNα/2π for the growth of the lee waves, and that steady state is attained more rapidly with steep topography than shallow, in contrast with linear theory, which does not depend on the aspect ratio.

scholarly journals Equatorial Waves in Opposite QBO Phases

2011 ◽  
Vol 68 (4) ◽  
pp. 839-862 ◽  
Author(s):  
Gui-Ying Yang ◽  
Brian J. Hoskins ◽  
Julia M. Slingo
Keyword(s):  
Group Velocity ◽  
Lower Stratosphere ◽  
Phase Speed ◽  
Kelvin Waves ◽  
Western Hemisphere ◽  
Equatorial Waves ◽  
Vertical Wavelength ◽  
Quasi Biennial Oscillation ◽  
Zonal Wavenumber ◽  
The Waves

Abstract A methodology for identifying equatorial waves is used to analyze the multilevel 40-yr ECMWF Re-Analysis (ERA-40) data for two different years (1992 and 1993) to investigate the behavior of the equatorial waves under opposite phases of the quasi-biennial oscillation (QBO). A comprehensive view of 3D structures and of zonal and vertical propagation of equatorial Kelvin, westward-moving mixed Rossby–gravity (WMRG), and n = 1 Rossby (R1) waves in different QBO phases is presented. Consistent with expectation based on theory, upward-propagating Kelvin waves occur more frequently during the easterly QBO phase than during the westerly QBO phase. However, the westward-moving WMRG and R1 waves show the opposite behavior. The presence of vertically propagating equatorial waves in the stratosphere also depends on the upper tropospheric winds and tropospheric forcing. Typical propagation parameters such as the zonal wavenumber, zonal phase speed, period, vertical wavelength, and vertical group velocity are found. In general, waves in the lower stratosphere have a smaller zonal wavenumber, shorter period, faster phase speed, and shorter vertical wavelength than those in the upper troposphere. All of the waves in the lower stratosphere show an upward group velocity and downward phase speed. When the phase of the QBO is not favorable for waves to propagate, their phase speed in the lower stratosphere is larger and their period is shorter than in the favorable phase, suggesting Doppler shifting by the ambient flow and a filtering of the slow waves. Tropospheric WMRG and R1 waves in the Western Hemisphere also show upward phase speed and downward group velocity, with an indication of their forcing from middle latitudes. Although the waves observed in the lower stratosphere are dominated by “free” waves, there is evidence of some connection with previous tropical convection in the favorable year for the Kelvin waves in the warm water hemisphere and WMRG and R1 waves in the Western Hemisphere, which is suggestive of the importance of convective forcing for the existence of propagating coupled Kelvin waves and midlatitude forcing for the existence of coupled WMRG and R1 waves.

A mathematical analysis of the steady response of floating ice to the uniform motion of a rectangular load

1995 ◽  
Vol 287 ◽  
pp. 173-197 ◽  
Author(s):  
F. Milinazzo ◽  
Marvin Shinbrot ◽  
N. W. Evans
Keyword(s):  
Aspect Ratio ◽  
Good Description ◽  
Ice Sheet ◽  
Phase Speed ◽  
Surface Displacement ◽  
Fourier Integral ◽  
Uniform Motion ◽  
Far Field ◽  
Line Load ◽  
Aspect Ratios

In this article, we considered the steady response of an infinite unbroken floating ice sheet to the uniform motion of a rectangular load. It is assumed that the ice sheet is supported below by water of finite uniform depth. The ice displacement is expressed as a Fourier integral and the method of residues is combined with a numerical quadrature scheme to calculate the displacement of the surface. In addition, asymptotic estimates of the displacement are given for the far field and for the case where the aspect ratio of the load is large. The far-field approximation provides a good description of the surface displacement at distances greater than about one or two wavelengths away from the load. The behaviour of the steady solution at the two critical speeds Um, where the phase speed takes on its minimum, and Ug, the speed of gravity waves on shallow water, observed in Schulkes & Sneyd (1988) for an impulsively started line load is examined to see if these speeds are critical for two-dimensional loads. Unlike the steady part of the solution in Schulkes & Sneyd (1988), the solution is everywhere finite at the critical speed Ug. However, at the load speed Um, the solution is unbounded. At all load speeds the change in surface displacement is greatest near the load. A comparison with the experimental observations of Takizawa (1985) is made. Our calculations show a significant dependence of the amplitude of the ice displacement on the aspect ratio of the load. For wide loads the surface deflection has much more structure than does the surface displacement corresponding to loads of smaller aspect ratios.

scholarly journals Steady-State Approach to Low-Aspect-Ratio Reversed-Field Pinch Nuclear Fusion Reactor

2005 ◽  
Vol 81 (11) ◽  
pp. 932-943 ◽  
Author(s):  
Shoichi SHIINA ◽  
Yasuyuki YAGI ◽  
Hisaya SUGIMOTO ◽  
Hisao ASHIDA ◽  
Yoichi HIRANO ◽  
...  
Keyword(s):  
Steady State ◽  
Aspect Ratio ◽  
Fusion Reactor ◽  
Nuclear Fusion ◽  
Reversed Field Pinch ◽  
Nuclear Fusion Reactor ◽  
Low Aspect Ratio ◽  
Reversed Field

scholarly journals Gravity Wave Propagation from the Stratosphere into the Mesosphere Studied with Lidar, Meteor Radar, and TIMED/SABER

Atmosphere ◽  
2019 ◽  
Vol 10 (2) ◽  
pp. 81 ◽  
Author(s):  
Shaohua Gong ◽  
Guotao Yang ◽  
Jiyao Xu ◽  
Xiao Liu ◽  
Qinzeng Li
Keyword(s):  
Wave Propagation ◽  
Gravity Wave ◽  
Low Frequency ◽  
Phase Speed ◽  
Static Stability ◽  
Temperature Structure ◽  
Meteor Radar ◽  
Atmospheric Gravity Wave ◽  
Vertical Wavelength ◽  
Hodograph Method

A low-frequency inertial atmospheric gravity wave (AGW) event was studied with lidar (40.5° N, 116° E), meteor radar (40.3° N, 116.2° E), and TIMED/SABER at Beijing on 30 May 2012. Lidar measurements showed that the atmospheric temperature structure was persistently perturbed by AGWs propagating upward from the stratosphere into the mesosphere (35–86 km). The dominant contribution was from the waves with vertical wavelengths λ z = 8 − 10   km and wave periods T ob = 6.6 ± 0.7   h . Simultaneous observations from a meteor radar illustrated that MLT horizontal winds were perturbed by waves propagating upward with an azimuth angle of θ = 247 ° , and the vertical wavelength ( λ z = 10   km ) and intrinsic period ( T in = 7.4   h ) of the dominant waves were inferred with the hodograph method. TIMED/SABER measurements illustrated that the vertical temperature profiles were also perturbed by waves with dominant vertical wavelength λ z = 6 − 9   km . Observations from three different instruments were compared, and it was found that signatures in the temperature perturbations and horizontal winds were induced by identical AGWs. According to these coordinated observation results, the horizontal wavelength and intrinsic phase speed were inferred to be ~560 km and ~21 m/s, respectively. Analyses of the Brunt-Väisälä frequency and potential energy illustrated that this persistent wave propagation had good static stability.

The Influence of Aspect Ratio on Incompressible, Turbulent Flows From Rectangular Slots

1980 ◽  
Vol 31 (4) ◽  
pp. 285-305 ◽  
Author(s):  
G.F. Marsters ◽  
J. Fotheringham
Keyword(s):  
Aspect Ratio ◽  
Turbulent Flows ◽  
Turbulence Intensity ◽  
Three Dimensional ◽  
Thin Plates ◽  
Shear Stresses ◽  
Mean Velocity ◽  
Contour Maps ◽  
Velocity Decay ◽  
Spreading Rates

SummaryJets issuing from rectangular slots cut in thin plates exhibit some unusual features, including unequal spreading rates in the spanwise and transverse directions, the appearance of velocity peaks near the “ends” of the jet and changing rates of centreline velocity decay in the downstream direction. This study examines the effects of aspect ratio on such flows. The flow field has been investigated using both total head tubes and hot wire anemometry. The results are presented in the form of three-dimensional plots of total pressure and contour maps of constant velocity, streamwise turbulence intensity and the Reynolds shear stresses. The decay of mean velocity and stream-wise turbulence intensity along the centreline are presented. The rates of spanwise spreading and the location of the velocity peaks at various downstream stations are discussed. If the aspect ratio is small enough, spanwise peaks in the mean velocity distribution are suppressed.

Stationary waves on an inclined sheet of viscous fluid at high Reynolds and moderate Weber numbers

1996 ◽  
Vol 307 ◽  
pp. 191-229 ◽  
Author(s):  
Jeng-Jong Lee ◽  
Chiang C. Mei
Keyword(s):  
Dynamical System ◽  
Phase Speed ◽  
Propagation Speed ◽  
Reynolds Numbers ◽  
Homoclinic Orbits ◽  
Finite Amplitude ◽  
Stationary Waves ◽  
Asymptotic Equations ◽  
Wave Propagation Speed ◽  
High Reynolds

A theory is described for the nonlinear waves on the surface of a thin film flowing down an inclined plane. Attention is focused on stationary waves of finite amplitude and long wavelength at high Reynolds numbers and moderate Weber numbers. Based on asymptotic equations accurate to the second order in the depth-to-wavelength ratio, a third-order dynamical system is obtained after changing to the frame of reference moving at the wave propagation speed. By examining the fixed-point stability of the dynamical system, parametric regimes of heteroclinc orbits and Hopf bifurcations are delineated. Extensive numerical experiments guided by the linear analyses reveal a variety of bifurcation scenarios as the phase speed deviates from the Hopf-bifurcation thresholds. These include homoclinic bifurcations which lead to homoclinic orbits corresponding to well separated solitary waves with one or several humps, some of which occur after passing through chaotic zones generated by period-doublings. There are also cases where chaos is the ultimate state following cascades of period-doublings, as well as cases where only limit cycles prevail. The dependence of bifurcation scenarios on the inclination angle, and Weber and Reynolds numbers is summarized.

Analysis of EHL Circular Contact Shut Down

2002 ◽  
Vol 125 (1) ◽  
pp. 76-90 ◽  
Author(s):  
Jiaxin Zhao ◽  
Farshid Sadeghi
Keyword(s):  
Steady State ◽  
Film Thickness ◽  
Contact Area ◽  
Elastohydrodynamic Lubrication ◽  
Hertzian Contact ◽  
Analytical Prediction ◽  
Transient Pressure ◽  
Mean Velocity ◽  
Thickness Change ◽  
Contact Width

In this paper, an isothermal study of the shut down process of elastohydrodynamic lubrication under a constant load is performed. The surface mean velocity is decreased linearly from the initial steady state value to zero. The details of the pressure and film thickness distributions in the contact area are discussed for the two stages of shut down process, namely the deceleration stage and the subsequent pure squeeze motion stage with zero entraining velocity. The nature of the balance between the pressure, the wedge and the squeeze terms in Reynolds equation enables an analytical prediction of the film thickness change on the symmetry line of the contact in the deceleration period, provided that the steady state central film thickness relationship with velocity is known. The results indicate that for a fixed deceleration rate, if the initial steady state surface mean velocity is large enough, the transient pressure and film thickness distributions in the deceleration period solely depend on the transient velocity. The pressure and film thickness at the end of the deceleration period are then the same and do not depend on the initial steady state velocity. From the same initial steady state velocity, larger deceleration rates provide higher central pressure increase, but also preserve a higher film thickness in the contact area at the end of the deceleration period. Later in the second stage when the axisymmetric pressure and film thickness patterns typical of pure squeeze motion form, the pressure distribution in the contact area resembles a Hertzian contact pressure profile with a higher maximum Hertzian pressure and a smaller Hertzian half contact width. As a result, the film thickness is close to a parabolic distribution in the contact area. The volume of the lubricant trapped in the contact area is then estimated using this parabolic film thickness profile.

A resonance mechanism in plane Couette flow

1980 ◽  
Vol 98 (1) ◽  
pp. 149-159 ◽  
Author(s):  
L. HÅKan Gustavsson ◽  
Lennart S. Hultgren
Keyword(s):  
Reynolds Number ◽  
Couette Flow ◽  
Velocity Component ◽  
Three Dimensional ◽  
Phase Speed ◽  
Maximum Amplitude ◽  
Streamwise Velocity ◽  
Plane Couette Flow ◽  
Mean Velocity ◽  
Streamwise Velocity Component

The temporal evolution of small three-dimensional disturbances on viscous flows between parallel walls is studied. The initial-value problem is formally solved by using Fourier–Laplace transform techniques. The streamwise velocity component is obtained as the solution of a forced problem. As a consequence of the three-dimensionality, a resonant response is possible, leading to algebraic growth for small times. It occurs when the eigenvalues of the Orr–Sommerfeld equation coincide with the eigenvalues of the homogeneous operator for the streamwise velocity component. The resonance has been investigated numerically for plane Couette flow. The phase speed of the resonant waves equals the average mean velocity. The wavenumber combination that leads to the largest amplitude corresponds to structures highly elongated in the streamwise direction. The maximum amplitude, and the time to reach this maximum, scale with the Reynolds number. The aspect ratio of the most rapidly growing wave increases with the Reynolds number, with its spanwise wavelength approaching a constant value of about 3 channel heights.

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