Computation of clear-air radar backscatter from numerical simulations of turbulence: 3. Off-zenith measurements and biases throughout the lifecycle of a Kelvin-Helmholtz instability

2012 ◽  
Vol 117 (D17) ◽  
pp. n/a-n/a ◽  
Author(s):  
David C. Fritts ◽  
Kam Wan ◽  
Patricia M. Franke ◽  
Tom Lund
Keyword(s):  
Numerical Simulations ◽  
Helmholtz Instability ◽  
Radar Backscatter

scholarly journals Evaluation of Sub-Kilometric Numerical Simulations of C-Band Radar Backscatter over the French Alps against Sentinel-1 Observations

2018 ◽  
Vol 11 (1) ◽  
pp. 8 ◽  
Author(s):  
Gaëlle Veyssière ◽  
Fatima Karbou ◽  
Samuel Morin ◽  
Matthieu Lafaysse ◽  
Vincent Vionnet
Keyword(s):  
Numerical Simulations ◽  
Radar Data ◽  
Microwave Emission ◽  
Radiative Transfer Model ◽  
Transfer Model ◽  
Emission Model ◽  
Radar Backscatter ◽  
French Alps ◽  
Snow Conditions ◽  
The Impact

This study compares numerical simulations and observations of C-band radar backscatter in a wide region (2300 km 2 ) in the Northern French Alps. Numerical simulations were performed using a model chain composed of the SAFRAN meteorological reanalysis, the Crocus snowpack model and the radiative transfer model Microwave Emission Model for Layered Snowpacks (MEMLS3&a), operating at a spatial resolution of 250-m. The simulations, without any bias correction, were evaluated against 141 Sentinel-1 synthetic aperture radar observation scenes with a resolution of 20 m over three snow seasons from October 2014 to June 2017. Results show that there is good agreement between observations and simulations under snow-free or dry snow conditions, consistent with the fact that dry snow is almost transparent at C-band. Under wet snow conditions, although the changes in time and space are well correlated, there is a significant deviation, up to 5 dB, between observations and simulations. The reasons for these discrepancies were explored, including a sensitivity analysis on the impact of the liquid water percolation scheme in Crocus. This study demonstrates the feasibility of performing end-to-end simulations of radar backscatter over extended geographical region. This makes it possible to envision data assimilation of radar data into snowpack models in the future, pending that deviations are mitigated, either through bias corrections or improved physical modeling of both snow properties and corresponding radar backscatter.

scholarly journals Numerical simulations of magnetic Kelvin–Helmholtz instability at a twisted solar flux tube

2016 ◽  
Vol 459 (3) ◽  
pp. 2566-2572 ◽  
Author(s):  
K. Murawski ◽  
P. Chmielewski ◽  
T.V. Zaqarashvili ◽  
E. Khomenko
Keyword(s):  
Numerical Simulations ◽  
Flux Tube ◽  
Solar Flux ◽  
Helmholtz Instability

Two-dimensional secondary instabilities in a strongly stratified shear layer

1995 ◽  
Vol 296 ◽  
pp. 73-126 ◽  
Author(s):  
Chantal Staquet
Keyword(s):  
Reynolds Number ◽  
Equilibrium State ◽  
Numerical Simulations ◽  
Shear Layer ◽  
Stagnation Point ◽  
Numerical Study ◽  
Secondary Instability ◽  
Two Dimensional ◽  
Helmholtz Instability ◽  
The Stability

In a stably stratified shear layer, thin vorticity layers (‘baroclinic layers’) are produced by buoyancy effects and strain in between the Kelvin–Helmholtz vortices. A two-dimensional numerical study is conducted, in order to investigate the stability of these layers. Besides the secondary Kelvin–Helmholtz instability, expected but never observed previously in two-dimensional numerical simulations, a new instability is also found.The influence of the Reynolds number (Re) upon the dynamics of the baroclinic layers is first studied. The layers reach an equilibrium state, whose features have been described theoretically by Corcos & Sherman (1976). An excellent agreement between those predictions and the results of the numerical simulations is obtained. The baroclinic layers are found to remain stable almost up to the time the equilibrium state is reached, though the local Richardson number can reach values as low as 0.05 at the stagnation point. On the basis of the work of Dritschel et al. (1991), we show that the stability of the layer at this location is controlled by the outer strain field induced by the large-scale Kelvin–Helmholtz vortices. Numerical values of the strain rate as small as 3% of the maximum vorticity of the layer are shown to stabilize the stagnation point region.When non-pairing flows are considered, we find that only for Re ≤ 2000 does a secondary instability eventually amplify in the layer. (Re is based upon half the initial vorticity thickness and half the velocity difference at the horizontally oriented boundaries.) This secondary instability is not of the Kelvin–Helmholtz type. It develops in the neighbourhood of convectively unstable regions of the primary Kelvin–Helmholtz vortex, apparently once a strong jet has formed there, and moves along the baroclinic layer while amplifying. It next perturbs the layer around the stagnation point and a secondary instability, now of the Kelvin–Helmholtz type, is found to develop there.We next examine the influence of a pairing upon the flow behaviour. We show that this event promotes the occurrence of a secondary Kelvin–Helmholtz instability, which occurs for Re ≥ 400. Moreover, at high Reynolds number (≥ 2000), secondary Kelvin–Helmholtz instabilities develop successively in the baroclinic layer, at smaller and smaller scales, thereby transferring energy towards dissipative scales through a mechanism eventually leading to turbulence. Because the vorticity of such a two-dimensional stratified flow is no longer conserved following a fluid particle, an analogy with three-dimensional turbulence can be drawn.

Saturation mechanism and generated viscosity in gravito-turbulent accretion disks

2020 ◽  
Vol 640 ◽  
pp. A53
Author(s):  
L. Löhnert ◽  
S. Krätschmer ◽  
A. G. Peeters
Keyword(s):  
Growth Rate ◽  
Numerical Simulations ◽  
Accretion Disks ◽  
Gravitational Instability ◽  
Turbulent Viscosity ◽  
Radial Distance ◽  
Maximum Growth ◽  
Wave Number ◽  
Radiative Cooling ◽  
Mixing Length

Here, we address the turbulent dynamics of the gravitational instability in accretion disks, retaining both radiative cooling and irradiation. Due to radiative cooling, the disk is unstable for all values of the Toomre parameter, and an accurate estimate of the maximum growth rate is derived analytically. A detailed study of the turbulent spectra shows a rapid decay with an azimuthal wave number stronger than ky−3, whereas the spectrum is more broad in the radial direction and shows a scaling in the range kx−3 to kx−2. The radial component of the radial velocity profile consists of a superposition of shocks of different heights, and is similar to that found in Burgers’ turbulence. Assuming saturation occurs through nonlinear wave steepening leading to shock formation, we developed a mixing-length model in which the typical length scale is related to the average radial distance between shocks. Furthermore, since the numerical simulations show that linear drive is necessary in order to sustain turbulence, we used the growth rate of the most unstable mode to estimate the typical timescale. The mixing-length model that was obtained agrees well with numerical simulations. The model gives an analytic expression for the turbulent viscosity as a function of the Toomre parameter and cooling time. It predicts that relevant values of α = 10−3 can be obtained in disks that have a Toomre parameter as high as Q ≈ 10.

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