Counter-Gradient Term Applied to the Turbulence Parameterization in the BRAMS

2017 ◽  
pp. 299-309
Author(s):  
M. E. S. Welter ◽  
H. F. de Campos Velho ◽  
S. R. Freitas ◽  
R. S. R. Ruiz
Keyword(s):  
Gradient Term ◽  
Turbulence Parameterization

Boundary behaviour for solutions of elliptic singular equations with a gradient term

2008 ◽  
Vol 69 (12) ◽  
pp. 4550-4566 ◽  
Author(s):  
F. Cuccu ◽  
E. Giarrusso ◽  
G. Porru
Keyword(s):  
Gradient Term ◽  
Boundary Behaviour ◽  
Singular Equations

One-dimensionalφ4theory with a long-range gradient term: A1Nexpansion

1981 ◽  
Vol 24 (7) ◽  
pp. 4083-4086
Author(s):  
Sudip Chakravarty ◽  
Douglas B. Stein
Keyword(s):  
Long Range ◽  
Gradient Term

scholarly journals Reexamining the Gradient and Countergradient Representation of the Local and Nonlocal Heat Fluxes in the Convective Boundary Layer

2018 ◽  
Vol 75 (7) ◽  
pp. 2317-2336 ◽  
Author(s):  
Bowen Zhou ◽  
Shiwei Sun ◽  
Kai Yao ◽  
Kefeng Zhu
Keyword(s):  
Boundary Layer ◽  
Temperature Gradient ◽  
Mixed Layer ◽  
Convective Boundary Layer ◽  
Correction Term ◽  
Potential Temperature ◽  
Heat Fluxes ◽  
Gradient Term ◽  
Convective Boundary ◽  
Upper Mixed Layer

Abstract Turbulent mixing in the daytime convective boundary layer (CBL) is carried out by organized nonlocal updrafts and smaller local eddies. In the upper mixed layer of the CBL, heat fluxes associated with nonlocal updrafts are directed up the local potential temperature gradient. To reproduce such countergradient behavior in parameterizations, a class of planetary boundary layer schemes adopts a countergradient correction term in addition to the classic downgradient eddy-diffusion term. Such schemes are popular because of their simple formulation and effective performance. This study reexamines those schemes to investigate the physical representations of the gradient and countergradient (GCG) terms, and to rebut the often-implied association of the GCG terms with heat fluxes due to local and nonlocal (LNL) eddies. To do so, large-eddy simulations (LESs) of six idealized CBL cases are performed. The GCG fluxes are computed a priori with horizontally averaged LES data, while the LNL fluxes are diagnosed through conditional sampling and Fourier decomposition of the LES flow field. It is found that in the upper mixed layer, the gradient term predicts downward fluxes in the presence of positive mean potential temperature gradient but is compensated by the upward countergradient correction flux, which is larger than the total heat flux. However, neither downward local fluxes nor larger-than-total nonlocal fluxes are diagnosed from LES. The difference reflects reduced turbulence efficiency for GCG fluxes and, in terms of physics, conceptual deficiencies in the GCG representation of CBL heat fluxes.

scholarly journals Synoptic fluctuation of the Taiwan Warm Current in winter on the East China Sea shelf

2016 ◽  
Author(s):  
Jiliang Xuan ◽  
Daji Huang ◽  
Thomas Pohlmann ◽  
Jian Su ◽  
Bernhard Mayer ◽  
...  
Keyword(s):  
Ocean Model ◽  
Coastal Current ◽  
Gradient Term ◽  
Taiwan Warm Current ◽  
Offshore Area ◽  
Warm Current ◽  
Geostrophic Balance ◽  
The North ◽  
The Cross ◽  
The Taiwan Strait

Abstract. The seasonal mean and synoptic fluctuation of the wintertime Taiwan Warm Current (TWC) were investigated using a well validated finite volume community ocean model. The spatial distribution and dynamics of the synoptic fluctuation were highlighted. The seasonal mean of the wintertime TWC has two branches: an inshore branch between the 30 and 100 m isobaths and an offshore branch between the 100 and 200 m isobaths. The Coriolis term is much larger than the inertia term and is almost balanced by the pressure gradient term in both branches, indicating the geostrophic balance of the mean current. Two areas with significant fluctuations of the TWC were identified during wintertime. One of the areas is located to the north of Taiwan with velocities varying in the cross-shore direction. These significant cross-shore fluctuations are driven by barotropic pressure gradients associated with the intrusion of the Taiwan Strait Current (TSC). When a larger TSC intrudes north of Taiwan, the isobaric slope tilts downward from south to north, leading to a cross-shore current from the coastal area to the offshore area. When the TSC intrusion is weak, the cross-shore current to the north of Taiwan is directed from offshore to inshore. The other area of significant fluctuation is located in the inshore area, extending in the region between the 30 and 100 m isobaths. The fluctuations are generally strong in the alongshore direction, in particular at the latitudes 26.5° N and 28° N where they are important for the local cross-shore transports. Wind affects the synoptic fluctuation through episodic events. When the northeasterly monsoon prevails, the southward Zhe-Min Coastal Current dominates the inshore area associated with a deepening of the mixed layer. When the winter monsoon is weakened or the southerly wind prevails, the northward TWC dominates in the inshore area.

scholarly journals A semilinear problem with a gradient term in the nonlinearity

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Ignacio Guerra
Keyword(s):  
Unit Ball ◽  
Radial Solution ◽  
The Other ◽  
Smooth Domain ◽  
Gradient Term ◽  
Radial Solutions ◽  
Bounded Smooth Domain ◽  
Other Hand ◽  
Bounded Smooth ◽  
Semilinear Problem

<p style='text-indent:20px;'>We consider the following semilinear problem with a gradient term in the nonlinearity</p><p style='text-indent:20px;'><disp-formula> <label/> <tex-math id="FE1"> \begin{document}$ \begin{align*} -\Delta u = \lambda \frac{(1+|\nabla u|^q)}{(1-u)^p}\quad\text{in}\quad\Omega,\quad u&gt;0\quad \text{in}\quad \Omega, \quad u = 0\quad\text{on}\quad \partial \Omega. \end{align*} $\end{document} </tex-math></disp-formula></p><p style='text-indent:20px;'>where <inline-formula><tex-math id="M1">\begin{document}$ \lambda,p,q&gt;0 $\end{document}</tex-math></inline-formula> and <inline-formula><tex-math id="M2">\begin{document}$ \Omega $\end{document}</tex-math></inline-formula> be a bounded, smooth domain in <inline-formula><tex-math id="M3">\begin{document}$ {\mathbb R}^N $\end{document}</tex-math></inline-formula>. We prove that when <inline-formula><tex-math id="M4">\begin{document}$ \Omega $\end{document}</tex-math></inline-formula> is a unit ball and <inline-formula><tex-math id="M5">\begin{document}$ p = 1 $\end{document}</tex-math></inline-formula> for <inline-formula><tex-math id="M6">\begin{document}$ q\in (0,q^*(N)) $\end{document}</tex-math></inline-formula> with <inline-formula><tex-math id="M7">\begin{document}$ q^*(N)\in (1,2) $\end{document}</tex-math></inline-formula>, we have infinitely many radial solutions for <inline-formula><tex-math id="M8">\begin{document}$ 2\leq N&lt;2\frac{6-q+2\sqrt{8-2q}}{(2-q)^2}+1 $\end{document}</tex-math></inline-formula> and <inline-formula><tex-math id="M9">\begin{document}$ \lambda = \tilde \lambda $\end{document}</tex-math></inline-formula>. On the other hand, for <inline-formula><tex-math id="M10">\begin{document}$ N&gt;2\frac{6-q+2\sqrt{8-2q}}{(2-q)^2}+1 $\end{document}</tex-math></inline-formula> there exists a unique radial solution for <inline-formula><tex-math id="M11">\begin{document}$ 0&lt;\lambda&lt;\tilde \lambda $\end{document}</tex-math></inline-formula>.</p>

Sign in / Sign up

Export Citation Format

Share Document