scholarly journals Instabilities within Rotating mode-2 Internal Waves

2017 ◽  
Author(s):  
David Deepwell ◽  
Marek Stastna ◽  
Aaron Coutino
Keyword(s):  
Three Dimensional ◽  
Side Wall ◽  
Kelvin Waves ◽  
Kelvin Wave ◽  
Rotation Rates ◽  
Mode 2 ◽  
Schmidt Numbers ◽  
Poincare Waves ◽  
The Right ◽  
Three Dimensional Simulations

Abstract. We present high resolution, three dimensional simulations of rotation modified mode-2 internal solitary waves at various rotation rates and Schmidt numbers. Rotation is seen to change the internal solitary-like waves observed in the absence of rotation into a leading Kelvin wave followed by Poincaré waves. Mass and energy is found to be advected towards the right-most side wall (for Northern hemisphere rotation) which led to Kelvin-Helmholtz instabilities within the leading Kelvin wave that form above and below the pycnocline. These instabilities are localized within a region near the side wall and intensify in vigour with increasing rotation rate. Secondary Kelvin waves form further behind the wave from either resonance with radiating Poincaré waves or the remnants of the K-H instability. The first of these mechanisms is in accord with published work on mode-1 Kelvin waves. Both types of secondary Kelvin waves form on the same side of the channel as the leading Kelvin wave. Comparisons of equivalent cases with different Schmidt numbers indicate that while low Schmidt number results in the correct general characteristics of the modified ISWs, it does not correctly predict the trailing Poincaré wave field or the intensity and duration of the K-H instabilities.

scholarly journals Multi-scale phenomena of rotation-modified mode-2 internal waves

2018 ◽  
Vol 25 (1) ◽  
pp. 217-231 ◽  
Author(s):  
David Deepwell ◽  
Marek Stastna ◽  
Aaron Coutino
Keyword(s):  
Three Dimensional ◽  
Side Wall ◽  
Kelvin Waves ◽  
Kelvin Wave ◽  
Rotation Rates ◽  
Multi Scale ◽  
Mode 2 ◽  
Schmidt Numbers ◽  
Poincare Waves ◽  
The Right

Abstract. We present high-resolution, three-dimensional simulations of rotation-modified mode-2 internal solitary waves at various rotation rates and Schmidt numbers. Rotation is seen to change the internal solitary-like waves observed in the absence of rotation into a leading Kelvin wave followed by Poincaré waves. Mass and energy is found to be advected towards the right-most side wall (for a Northern Hemisphere rotation), leading to increased amplitude of the leading Kelvin wave and the formation of Kelvin–Helmholtz (K–H) instabilities on the upper and lower edges of the deformed pycnocline. These fundamentally three-dimensional instabilities are localized within a region near the side wall and intensify in vigour with increasing rotation rate. Secondary Kelvin waves form further behind the wave from either resonance with radiating Poincaré waves or the remnants of the K–H instability. The first of these mechanisms is in accord with published work on mode-1 Kelvin waves; the second is, to the best of our knowledge, novel to the present study. Both types of secondary Kelvin waves form on the same side of the channel as the leading Kelvin wave. Comparisons of equivalent cases with different Schmidt numbers indicate that while adopting a numerically advantageous low Schmidt number results in the correct general characteristics of the Kelvin waves, excessive diffusion of the pycnocline and various density features precludes accurate representation of both the trailing Poincaré wave field and the intensity and duration of the Kelvin–Helmholtz instabilities.

scholarly journals Magnetar formation through a convective dynamo in protoneutron stars

2020 ◽  
Vol 6 (11) ◽  
pp. eaay2732 ◽  
Author(s):  
Raphaël Raynaud ◽  
Jérôme Guilet ◽  
Hans-Thomas Janka ◽  
Thomas Gastine
Keyword(s):  
Gamma Ray ◽  
Magnetic Energy ◽  
Three Dimensional ◽  
Observational Constraints ◽  
Rotation Rates ◽  
Theoretical Support ◽  
Firm Basis ◽  
Protoneutron Stars ◽  
Protoneutron Star ◽  
Three Dimensional Simulations

The release of spin-down energy by a magnetar is a promising scenario to power several classes of extreme explosive transients. However, it lacks a firm basis because magnetar formation still represents a theoretical challenge. Using the first three-dimensional simulations of a convective dynamo based on a protoneutron star interior model, we demonstrate that the required dipolar magnetic field can be consistently generated for sufficiently fast rotation rates. The dynamo instability saturates in the magnetostrophic regime with the magnetic energy exceeding the kinetic energy by a factor of up to 10. Our results are compatible with the observational constraints on galactic magnetar field strength and provide strong theoretical support for millisecond protomagnetar models of gamma-ray burst and superluminous supernova central engines.

scholarly journals An Analysis of Convectively Coupled Kelvin Waves in 20 WCRP CMIP3 Global Coupled Climate Models

2010 ◽  
Vol 23 (11) ◽  
pp. 3031-3056 ◽  
Author(s):  
Katherine H. Straub ◽  
Patrick T. Haertel ◽  
George N. Kiladis
Keyword(s):  
Climate Models ◽  
Global Climate ◽  
Three Dimensional ◽  
Kelvin Waves ◽  
Global Climate Models ◽  
Specific Humidity ◽  
Tropospheric Temperature ◽  
Wave Band ◽  
Kelvin Wave ◽  
Shallow Convection

Abstract Output from 20 coupled global climate models is analyzed to determine whether convectively coupled Kelvin waves exist in the models, and, if so, how their horizontal and vertical structures compare to observations. Model data are obtained from the World Climate Research Program’s (WCRP’s) Coupled Model Intercomparison Project phase 3 (CMIP3) multimodel dataset. Ten of the 20 models contain spectral peaks in precipitation in the Kelvin wave band, and, of these 10, only 5 contain wave activity distributions and three-dimensional wave structures that resemble the observations. Thus, the majority (75%) of the global climate models surveyed do not accurately represent convectively coupled Kelvin waves, one of the primary sources of submonthly zonally propagating variability in the tropics. The primary feature common to the five successful models is the convective parameterization. Three of the five models use the Tiedtke–Nordeng convective scheme, while the other two utilize the Pan and Randall scheme. The 15 models with less success at generating Kelvin waves predominantly contain convective schemes that are based on the concept of convective adjustment, although it appears that those schemes can be improved by the addition of convective “trigger” functions. Three-dimensional Kelvin wave structures in the five successful models resemble observations to a large degree, with vertically tilted temperature, specific humidity, and zonal wind anomalies. However, no model completely captures the observed signal, with most of the models being deficient in lower-tropospheric temperature and humidity signals near the location of maximum precipitation. These results suggest the need for improvements in the representations of shallow convection and convective downdrafts in global models.

The experimental generation of double Kelvin waves

1971 ◽  
Vol 326 (1564) ◽  
pp. 39-52 ◽  
Keyword(s):  
Boundary Layer ◽  
Kelvin Waves ◽  
Bottom Boundary Layer ◽  
Maximum Frequency ◽  
Kelvin Wave ◽  
Bottom Slope ◽  
Shallow Water Theory ◽  
Constant Depth ◽  
Bottom Boundary ◽  
The Right

Experiments carried out with a rotating model basin confirm the existence of a type of slow oscillation (double Kelvin wave) predicted by linearized shallow-water theory. Such oscillations may occur in the neighbourhood of any zone where a bottom slope separates two regions of uniform depth. The energy is propagated along the contours of constant depth, with the shallower water always to the right of the direction of propagation (in the northern hemisphere). The theoretical dispersion relation is well verified, including the existence of a maximum frequency, and consequently a vanishing group-velocity, at a certain wavenumber. When the wavemaker is operated at a frequency greater than this maximum, steady currents are sometimes generated. The effects of curvature of the bottom contours are discussed, as well as the loss of energy by viscous dissipation in the bottom boundary-layer.

scholarly journals Dynamics and Energetics of Trapped Diurnal Internal Kelvin Waves around a Midlatitude Island

2017 ◽  
Vol 47 (10) ◽  
pp. 2479-2498 ◽  
Author(s):  
Eiji Masunaga ◽  
Oliver B. Fringer ◽  
Yujiro Kitade ◽  
Hidekatsu Yamazaki ◽  
Scott M. Gallager
Keyword(s):  
Three Dimensional ◽  
Internal Tide ◽  
Kelvin Waves ◽  
Internal Tides ◽  
Navier Stokes ◽  
Kelvin Wave ◽  
Sagami Bay ◽  
Study Region ◽  
Topographic Slope ◽  
Terrain Following

AbstractThe generation of trapped and radiating internal tides around Izu‐Oshima Island located off Sagami Bay, Japan, is investigated using the three-dimensional Stanford Unstructured Nonhydrostatic Terrain-following Adaptive Navier–Stokes Simulator (SUNTANS) that is validated with observations of isotherm displacements in shallow water. The model is forced by barotropic tides, which generate strong baroclinic internal tides in the study region. Model results showed that when diurnal K1 barotropic tides dominate, resonance of a trapped internal Kelvin wave leads to large-amplitude internal tides in shallow waters on the coast. This resonance produces diurnal motions that are much stronger than the semidiurnal motions. The weaker, freely propagating, semidiurnal internal tides are generated on the western side of the island, where the M2 internal tide beam angle matches the topographic slope. The internal wave energy flux due to the diurnal internal tides is much higher than that of the semidiurnal tides in the study region. Although the diurnal internal tide energy is trapped, this study shows that steepening of the Kelvin waves produces high-frequency internal tides that radiate from the island, thus acting as a mechanism to extract energy from the diurnal motions.

The wake behind a cylinder rolling on a wall at varying rotation rates

2010 ◽  
Vol 648 ◽  
pp. 225-256 ◽  
Author(s):  
B. E. STEWART ◽  
M. C. THOMPSON ◽  
T. LEWEKE ◽  
K. HOURIGAN
Keyword(s):  
Reynolds Number ◽  
Three Dimensional ◽  
Reynolds Numbers ◽  
Wake Flow ◽  
Recirculation Region ◽  
Two Dimensional ◽  
Number Range ◽  
Rotation Rates ◽  
Transition Mechanism ◽  
Three Dimensional Simulations

A study investigating the flow around a cylinder rolling or sliding on a wall has been undertaken in two and three dimensions. The cylinder motion is specified from a set of five discrete rotation rates, ranging from prograde through to retrograde rolling. A Reynolds number range of 20–500 is considered. The effects of the nearby wall and the imposed body motion on the wake structure and dominant wake transitions have been determined. Prograde rolling is shown to destabilize the wake flow, while retrograde rotation delays the onset of unsteady flow to Reynolds numbers well above those observed for a cylinder in an unbounded flow.Two-dimensional simulations show the presence of two recirculation zones in the steady wake, the lengths of which increase approximately linearly with the Reynolds number. Values of the lift and drag coefficient are also reported for the steady flow regime. Results from a linear stability analysis show that the wake initially undergoes a regular bifurcation from a steady two-dimensional flow to a steady three-dimensional wake for all rotation rates. The critical Reynolds number Rec of transition and the spanwise wavelength of the dominant mode are shown to be highly dependent on, but smoothly varying with, the rotation rate of the cylinder. Varying the rotation from prograde to retrograde rolling acts to increase the value of Rec and decrease the preferred wavelength. The structure of the fully evolved wake mode is then established through three-dimensional simulations. In fact it is found that at Reynolds numbers only marginally (~5%) above critical, the three-dimensional simulations indicate that the saturated state becomes time dependent, although at least initially, this does not result in a significant change to the mode structure. It is only at higher Reynolds numbers that the wake undergoes a transition to vortex shedding.An analysis of the three-dimensional transition indicates that it is unlikely to be due to a centrifugal instability despite the superficial similarity to the flow over a backward-facing step, for which the transition mechanism has been speculated to be centrifugal. However, the attached elongated recirculation region and distribution of the spanwise perturbation vorticity field, and the similarity of these features with those of the flow through a partially blocked channel, suggest the possibility that the mechanism is elliptic in nature. Some analysis which supports this conjecture is undertaken.

Wake Flow of Single and Multiple Yawed Cylinders

2004 ◽  
Vol 126 (5) ◽  
pp. 861-870 ◽  
Author(s):  
A. Thakur ◽  
X. Liu ◽  
J. S. Marshall
Keyword(s):  
Computational Study ◽  
Three Dimensional ◽  
Side Wall ◽  
Wake Flow ◽  
Upstream Region ◽  
Two Dimensional ◽  
Cylinder Wake ◽  
Dimensional Approximation ◽  
The Face ◽  
Drag And Lift

An experimental and computational study is performed of the wake flow behind a single yawed cylinder and a pair of parallel yawed cylinders placed in tandem. The experiments are performed for a yawed cylinder and a pair of yawed cylinders towed in a tank. Laser-induced fluorescence is used for flow visualization and particle-image velocimetry is used for quantitative velocity and vorticity measurement. Computations are performed using a second-order accurate block-structured finite-volume method with periodic boundary conditions along the cylinder axis. Results are applied to assess the applicability of a quasi-two-dimensional approximation, which assumes that the flow field is the same for any slice of the flow over the cylinder cross section. For a single cylinder, it is found that the cylinder wake vortices approach a quasi-two-dimensional state away from the cylinder upstream end for all cases examined (in which the cylinder yaw angle covers the range 0⩽ϕ⩽60°). Within the upstream region, the vortex orientation is found to be influenced by the tank side-wall boundary condition relative to the cylinder. For the case of two parallel yawed cylinders, vortices shed from the upstream cylinder are found to remain nearly quasi-two-dimensional as they are advected back and reach within about a cylinder diameter from the face of the downstream cylinder. As the vortices advect closer to the cylinder, the vortex cores become highly deformed and wrap around the downstream cylinder face. Three-dimensional perturbations of the upstream vortices are amplified as the vortices impact upon the downstream cylinder, such that during the final stages of vortex impact the quasi-two-dimensional nature of the flow breaks down and the vorticity field for the impacting vortices acquire significant three-dimensional perturbations. Quasi-two-dimensional and fully three-dimensional computational results are compared to assess the accuracy of the quasi-two-dimensional approximation in prediction of drag and lift coefficients of the cylinders.

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