scholarly journals A Formulation of a Three-Dimensional Spectral Model for the Primitive Equations

2022 ◽  
Author(s):  
Keiichi ISHIOKA ◽  
Naoto YAMAMOTO ◽  
Masato FUJITA
Keyword(s):  
Three Dimensional ◽  
Spectral Model ◽  
Primitive Equations

ON THE REGULARITY OF THREE-DIMENSIONAL ROTATING EULER–BOUSSINESQ EQUATIONS

1999 ◽  
Vol 09 (07) ◽  
pp. 1089-1121 ◽  
Author(s):  
A. BABIN ◽  
A. MAHALOV ◽  
B. NICOLAENKO
Keyword(s):  
Initial Data ◽  
Three Dimensional ◽  
Fluid Flows ◽  
Boussinesq Equations ◽  
Stable Stratification ◽  
Primitive Equations ◽  
Time Interval ◽  
Regular Solutions ◽  
Time Intervals ◽  
Long Time

The 3-D rotating Boussinesq equations (the "primitive" equations of geophysical fluid flows) are analyzed in the asymptotic limit of strong stable stratification. The resolution of resonances and a nonstandard small divisor problem are the basis for error estimates for such fast singular oscillating limits. Existence on infinite time intervals of regular solutions to the viscous 3-D "primitive" equations is proven for initial data in Hα, α≥ 3/4. Existence on a long-time interval T*of regular solutions to the 3-D inviscid equations is proven for initial data in Hα, α > 5/2 (T*→∞ as the frequency of gravity waves →∞).

scholarly journals A three-dimensional numerical model of the response of the Australian North West Shelf to tropical cyclones

1994 ◽  
Vol 36 (1) ◽  
pp. 64-100 ◽  
Author(s):  
Songping Zhu ◽  
Jörg Imberger
Keyword(s):  
Tropical Cyclones ◽  
Three Dimensional ◽  
Primitive Equations ◽  
Induced Response ◽  
Temperature Changes ◽  
North West ◽  
The North ◽  
Baroclinic Model ◽  
Induced Currents ◽  
Explicit Finite Difference

AbstractA three-dimensional barotropic and baroclinic model is developed to simulate currents and temperature changes induced by tropical cyclones traversing the continental shelf and slope region of the Australian North West Shelf. The model is based on a layered, explicit, finite difference formulation using the nonlinear primitive equations with an embedded entrainment scheme; a mixed-surface-layer interface is defined, which is allowed to shift from one interface to another, depending on the strength of a storm. The model has been tested by simulating the currents and temperature changes induced by tropical cyclones Orson and Ian. The modelled currents and temperatures agreed well with the available measured records except near the seabed. It has been found that the pre-storm currents have very little influence on the peak of the storm-induced currents and the currents in the wake of a tropical cyclone. The model contained no coefficients which must be calibrated for a particular application and clearly illustrated the importance of the baroclinic effects on the storm-induced response over the North West Shelf of Australia.

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