Large-amplitude motion of a compressible fluid in the atmosphere

Claus, A. J.

doi:10.1017/s0022112064000714

Cited by 12 publications

(1 citation statement)

References 10 publications

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“…In the case of large-amplitude motion the initial nonlinear equation of the task can be reduced to the linear one and solved by the well-developed techniques only for a limited class of flows which are of practical interest for the atmospheric tasks (Claus, 1963;Kozhevnikov and Moiseenko, 2004). The most investigated are still the case when upstream wind velocity and static stability do not depend on height (Long's model for compressible fluid) (Long, 1955;Gutman, 1969).…”

Section: Introductionmentioning

confidence: 99%

On the role of the stratosphere in the process of overflow of mesoscale mountains

Moiseenko

2005

Ann. Geophys.

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Abstract.A 2-D, two-and three-layer stratified airflow over a mountain of arbitrary shape is considered on the assumptions that upstream wind velocity and static stability within each layer are constant (Long's model). The stratosphere is simulated by an infinitely deep upper layer with enhanced static stability.The analytical solution for the stream function, as well as first (linear) and second order approximations to the wave drag, are obtained in hydrostatic limit N 1 L/U 0 →∞, where N 1 is the Brunt-Väsälä frequency in the troposphere, L is a characteristic length of the obstacle, and U 0 is upstream velocity. The results of numerical computations show the principal role of long waves in the process of interaction between the model layers for a typical mesoscale mountains for which the hydrostatic approximation proves valid in a wide range of flow parameters, in accordance with the earlier conclusions of Klemp and Lilly (1975). Partial reflection of wave energy from the tropopause produces strong influence on the value of wave drag for typical middle and upper tropospheric lapse rates, leading to a quasi-periodic dependance of wave drag on a reduced frequency k=N 1H /πU 0 (H is tropopause height) in the troposphere. The flow seems to be statically unstable for k≥2 for sufficiently large obstacles (whose height exceeds 1 km). In this case, vast regions of rotor motions and strong turbulence are predicted from model calculations in the middle troposphere and the lower stratosphere. The model calculations also point to a testify for possible important role of nonlinear effects associated with finite height of the mountain on the conditions of wave drag amplification in the process of overflow of real mountains.

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Section: Introductionmentioning

confidence: 99%

On the role of the stratosphere in the process of overflow of mesoscale mountains

Moiseenko

2005

Ann. Geophys.

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Inviscid flows of stably stratified fluids over barriers

Pao

1969

Quart J Royal Meteoro Soc

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Steady, inviscid, incompressible, two-dimensional flows of stably stratified fluids over a barrier or barriers are examined theoretically. The density gradient and up4 are assumed to be constant upstream, where p is the density and u is the horizontal velocity. Exact solutions of large amplitude waves valid for arbitrary Richardson numbers are obtained for barriers of finite height in a semi-infinite domain or in a confined channel. These barriers are constructed from vortex pairs and doublets.

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An operational linear lee wave model for arbitrary basic flow and two‐dimensional topography

Vergeiner

1971

Quart J Royal Meteoro Soc

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A partial survey of recent theoretical work on the flow over obstacles is presented. A model for linear, stationary mountain waves with arbitrary basic flow and two-dimensional topography is described in detail. It contains the option of a nonlinear lower boundary condition. The wave drag is computed by three methods and the complete flow field is obtained. The sensitivity of the solutions to small changes of the upstream flow is demonstrated as a critical factor limiting the applicability of the model. The strong downslope wind storms of the Boulder area are briefly discussed in the general context of foehn phenomena. Computations indicate that resonance lee waves do not seem to be part of the mechanism of these winds. NOTATIONCartesian co-ordinates, x pointing along basic wind ii and z pointing upward ( 3 / 3 x , 3/22) 3 2 / w + 32/322 $ / a t + u a/>% + a/ay + w A /~Z

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Large-amplitude motion of a compressible fluid in the atmosphere

Cited by 12 publications

References 10 publications

On the role of the stratosphere in the process of overflow of mesoscale mountains

On the role of the stratosphere in the process of overflow of mesoscale mountains

Inviscid flows of stably stratified fluids over barriers

An operational linear lee wave model for arbitrary basic flow and two‐dimensional topography

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