Riemann problems and delta-shock solutions for a Keyfitz-Kranzer system with a forcing term

2021 ◽  
Vol 502 (2) ◽  
pp. 125267
Author(s):  
Eduardo Abreu ◽  
Richard De la cruz ◽  
Wanderson Lambert
2018 ◽  
Vol 2018 ◽  
pp. 1-11
Author(s):  
Xinli Han ◽  
Lijun Pan

In this paper, we study the perturbed Riemann problem with delta shock for a hyperbolic system. The problem is different from the previous perturbed Riemann problems which have no delta shock. The solutions to the problem are obtained constructively. From the solutions, we see that a delta shock in the corresponding Riemann solution may turn into a shock and a contact discontinuity under a perturbation of the Riemann initial data. This shows the instability and the internal mechanism of a delta shock. Furthermore, we find that the Riemann solution of the hyperbolic system is instable under this perturbation, which is also quite different from the previous perturbed Riemann problems.


2017 ◽  
Vol 47 (4) ◽  
pp. 755-774 ◽  
Author(s):  
Lingling Xie ◽  
Enric Pallàs-Sanz ◽  
Quanan Zheng ◽  
Shuwen Zhang ◽  
Xiaolong Zong ◽  
...  

AbstractUsing the generalized omega equation and cruise observations in July 2012, this study analyzes the 3D vertical circulation in the upwelling region and frontal zone east of Hainan Island, China. The results show that there is a strong frontal zone in subsurface layer along the 100-m isobath, which is characterized by density gradient of O(10−4) kg m−4 and vertical eddy diffusivity of O(10−5–10−4) m2 s−1. The kinematic deformation term SDEF, ageostrophic advection term SADV, and vertical mixing forcing term SMIX are calculated from the observations. Their distribution patterns are featured by banded structure, that is, alternating positive–negative alongshore bands distributed in the cross-shelf direction. Correspondingly, alternating upwelling and downwelling bands appear from the coast to the deep waters. The maximum downward velocity reaches −5 × 10−5 m s−1 within the frontal zone, accompanied by the maximum upward velocity of 7 × 10−5 m s−1 on two sides. The dynamic diagnosis indicates that SADV contributes most to the coastal upwelling, while term SDEF, which is dominated by the ageostrophic component SDEFa, plays a dominant role in the frontal zone. The vertical mixing forcing term SMIX, which includes the momentum and buoyancy flux terms SMOM and SBUO, is comparable to SDEF and SADV in the upper ocean, but negligible below the thermocline. The effect of the vertical mixing on the vertical velocity is mainly concentrated at depths with relatively large eddy diffusivity and eddy diffusivity gradient in the frontal zone.


2011 ◽  
Vol 380 (2) ◽  
pp. 475-485 ◽  
Author(s):  
Hongjun Cheng ◽  
Hanchun Yang

Author(s):  
E. E. Burniston ◽  
C. E. Siewert

AbstractA method of finding explicit expressions for the roots of a certain class of transcendental equations is discussed. In particular it is shown by determining a canonical solution of an associated Riemann boundary-value problem that expressions for the roots may be derived in closed form. The explicit solutions to two transcendental equations, tan β = ωβ and β tan β = ω, are discussed in detail, and additional specific results are given.


Sign in / Sign up

Export Citation Format

Share Document