Asymmetry of Jet Streams Formed under Nonlinear Geostrophic Adjustment in Shallow Water

Oceanology ◽  
2019 ◽  
Vol 59 (2) ◽  
pp. 191-198
Author(s):  
M. V. Kalashnik
Keyword(s):  
Shallow Water ◽  
Geostrophic Adjustment ◽  
Jet Streams

Asymmetry of jet streams formed under nonlinear geostrophic adjustment in shallow water

2019 ◽  
Vol 59 (2) ◽  
pp. 208-215
Author(s):  
M. V. Kalashnik
Keyword(s):  
Velocity Profile ◽  
Shallow Water ◽  
Negative Sign ◽  
Initial Disturbance ◽  
Positive Sign ◽  
Adjustment Process ◽  
Jet Stream ◽  
Geostrophic Adjustment ◽  
Jet Streams ◽  
Initial Distributions

The process of geostrophic adjustment in a rotating layer of shallow water is considered. For initial distributions of the fluid depth in the form of a step and a localized rectangle, this process results in the formation of an isolated jet stream and a system of two counter jet streams, respectively. In this paper, the features of these flows structure, related to the nonlinearity of the adjustment process, are studied. The main feature for an isolated jet stream is the horizontal asymmetry of its velocity profile. For a system of two opposing flows, a mirror asymmetry is characteristic, which is caused by the dependence on the sign of the amplitude of the initial disturbance of depth. The velocity of flows with a negative sign (depression) always exceeds the velocity with a positive sign (elevation).

scholarly journals A Finite-Volume Grid Using Multimoments for Geostrophic Adjustment

2006 ◽  
Vol 134 (9) ◽  
pp. 2515-2526 ◽  
Author(s):  
F. Xiao ◽  
X. D. Peng ◽  
X. S. Shen
Keyword(s):  
Shallow Water ◽  
Finite Volume Method ◽  
Finite Volume ◽  
Shallow Water Equations ◽  
Control Volume ◽  
Numerical Dispersion ◽  
Geostrophic Adjustment ◽  
Simple Formulation ◽  
Volume Method

Abstract This paper presents a novel finite-volume grid that uses not only the volume-integrated average (VIA) like the traditional finite-volume method, but also the surface-integrated average (SIA) as the model variables. The VIA and SIA are generically called “moments” in the context used here and are carried forward in time separately as the prognostic quantities. With the VIA defined in the control volume while the SIA is on the surface of the control volume, the discretization based on VIA and SIA leads to some new features in the numerical dispersions. A simple formulation using both VIA and SIA for shallow-water equations is presented. The numerical dispersion of the resulting grid, which is denoted as the “M grid,” is discussed with comparisons to the existing ones.

Nonlinear theory of geostrophic adjustment. Part 1. Rotating shallow-water model

2001 ◽  
Vol 445 ◽  
pp. 93-120 ◽  
Author(s):  
G. M. REZNIK ◽  
V. ZEITLIN ◽  
M. BEN JELLOUL
Keyword(s):  
Shallow Water ◽  
Slow Component ◽  
Fast Component ◽  
Water Dynamics ◽  
Water Model ◽  
Rossby Number ◽  
Geostrophic Adjustment ◽  
Perturbation Expansions ◽  
Modulation Equation ◽  
Rotating Shallow Water

We develop a theory of nonlinear geostrophic adjustment of arbitrary localized (i.e. finite-energy) disturbances in the framework of the non-dissipative rotating shallow-water dynamics. The only assumptions made are the well-defined scale of disturbance and the smallness of the Rossby number Ro. By systematically using the multi-time-scale perturbation expansions in Rossby number it is shown that the resulting field is split in a unique way into slow and fast components evolving with characteristic time scales f−10 and (f0Ro)−1 respectively, where f0 is the Coriolis parameter. The slow component is not influenced by the fast one and remains close to the geostrophic balance. The algorithm of its initialization readily follows by construction.The scenario of adjustment depends on the characteristic scale and/or initial relative elevation of the free surface ΔH/H0, where ΔH and H0 are typical values of the initial elevation and the mean depth, respectively. For small relative elevations (ΔH/H0 = O(Ro)) the evolution of the slow motion is governed by the well-known quasi-geostrophic potential vorticity equation for times t [les ] (f0Ro)−1. We find modifications to this equation for longer times t [les ] (f0Ro2)−1. The fast component consists mainly of linear inertia–gravity waves rapidly propagating outward from the initial disturbance.For large relative elevations (ΔH/H0 [Gt ] Ro) the slow field is governed by the frontal geostrophic dynamics equation. The fast component in this case is a spatially localized packet of inertial oscillations coupled to the slow component of the flow. Its envelope experiences slow modulation and obeys a Schrödinger-type modulation equation describing advection and dispersion of the packet. A case of intermediate elevation is also considered.

scholarly journals Geostrophic Adjustment for Reversibly Staggered Grids

2005 ◽  
Vol 133 (5) ◽  
pp. 1119-1128 ◽  
Author(s):  
John L. McGregor
Keyword(s):  
Shallow Water ◽  
Gravity Wave ◽  
Shallow Water Equations ◽  
Geostrophic Adjustment ◽  
Staggered Grids ◽  
Dispersion Properties ◽  
Dispersion Behavior ◽  
Interpolation Procedure ◽  
Meteorological Modeling

Abstract A technique is presented for meteorological modeling in which all variables are held on an unstaggered grid, but the winds are transformed to a staggered C grid for the gravity wave calculations. An important feature is the use of a new reversible interpolation procedure for the staggering–unstaggering of the winds. This reversible procedure has excellent dispersion properties for geostrophic adjustment of the linearized shallow-water equations, being generally superior to those of the A, B, and C grids. Its dispersion behavior is generally similar to that of the unstaggered Z grid of Randall, which carries divergence and vorticity as primary variables. The scheme has fewer computational overheads than the Z grid.

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