A Numerical Study of the Effects of Ambient Flow and Shear On Density Currents

Changhai Liu National Center for Atmospheric Research, Boulder, Colorado

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Mitchell W. Moncrieff National Center for Atmospheric Research, Boulder, Colorado

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Abstract

A numerical model investigation is conducted of the effects of ambient flow and shear upon the propagation and morphology of density currents. The model is initialized with a horizontally homogeneous wind profile superimposed on a cold-air source that initiates and maintains the density currents. The base state is neutrally stratified and free-slip lower and upper boundary conditions are used.

A headwind (i.e., relative flow in the direction opposing the system movement) raises the density current head compared to calm surroundings, while a tailwind has the opposite effect. A weak or moderate shear elevates the head for the downshear-traveling system and a shallow multihead structure appears in strong shear. In contrast, the upshear-moving system is largely insensitive to the shear. In uniform flow, the propagation speed is linearly proportional to the ambient wind speed, reduced or enhanced by about three-quarters depending on the airflow direction. In uniform shear, a linear relationship approximates the relationship between the advance rate of density current and the value of the shear, particularly for the upshear-moving system.

An idealized dynamical model is developed for the moderate shear case in terms of a Froude number ℱ. The model has three branches, namely, a borelike region, an overturning updraft, and a stagnant region that moves bodily with the system. The Froude number calculated from the numerical model data is ℱ ≈ 0.7, which lies within die range of analytic solutions obtained.

With regard to the initiation of convection over an island or peninsula in an unsheared or weakly sheared ambient flow, a sea-breeze circulation will preferentially cause convection on the leeward side and a land breeze on the windward side. The opposite occurs when the ambient flow has moderate to strong low-level shear—that is, the sea breeze will cause convection on the windward side and a land breeze on the leeward side. The mean-flow momentum and mean-flow shear thus affect convection initiation in opposing ways. There is a dearth of observational data on density currents in shear flow with which to evaluate our dynamical model—in particular, the role of the overturning updraft, which is a new concept as regards density current dynamics.

Abstract

A numerical model investigation is conducted of the effects of ambient flow and shear upon the propagation and morphology of density currents. The model is initialized with a horizontally homogeneous wind profile superimposed on a cold-air source that initiates and maintains the density currents. The base state is neutrally stratified and free-slip lower and upper boundary conditions are used.

A headwind (i.e., relative flow in the direction opposing the system movement) raises the density current head compared to calm surroundings, while a tailwind has the opposite effect. A weak or moderate shear elevates the head for the downshear-traveling system and a shallow multihead structure appears in strong shear. In contrast, the upshear-moving system is largely insensitive to the shear. In uniform flow, the propagation speed is linearly proportional to the ambient wind speed, reduced or enhanced by about three-quarters depending on the airflow direction. In uniform shear, a linear relationship approximates the relationship between the advance rate of density current and the value of the shear, particularly for the upshear-moving system.

An idealized dynamical model is developed for the moderate shear case in terms of a Froude number ℱ. The model has three branches, namely, a borelike region, an overturning updraft, and a stagnant region that moves bodily with the system. The Froude number calculated from the numerical model data is ℱ ≈ 0.7, which lies within die range of analytic solutions obtained.

With regard to the initiation of convection over an island or peninsula in an unsheared or weakly sheared ambient flow, a sea-breeze circulation will preferentially cause convection on the leeward side and a land breeze on the windward side. The opposite occurs when the ambient flow has moderate to strong low-level shear—that is, the sea breeze will cause convection on the windward side and a land breeze on the leeward side. The mean-flow momentum and mean-flow shear thus affect convection initiation in opposing ways. There is a dearth of observational data on density currents in shear flow with which to evaluate our dynamical model—in particular, the role of the overturning updraft, which is a new concept as regards density current dynamics.

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