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Numerical Study of Terrain-Induced Mesoscale Motions and Hydrostatic Form Drag in a Heated, Growing Mixed Layer

J. W. DeardorffDepartment of Atmospheric Sciences, Oregon State University, Corvallis, OR 97331

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K. UeyoshiDepartment of Atmospheric Sciences, Oregon State University, Corvallis, OR 97331

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Y-J. HanDepartment of Atmospheric Sciences, Oregon State University, Corvallis, OR 97331

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Abstract

A four-layer three-dimensional model whose lowest layer is a time and space-dependent, well-mixed boundary layer is employed over artificial, irregular terrain on the mesoscale during a daytime heating cycle. Only if the surface heating and mixed-layer entrainment am suppressed does the Row field become steady as found previously using a shallow-water model. Unsteadiness is due both to diurnal effects, especially the relaxation of the frictional force as the mixed layer deepens irregularly, and to the presence of horizontal vacations in potential temperature. The latter can develop with time due to the negative feedback between mixed-layer depth and warming rate; after the early morning hours, however, this feedback causes a damping of the temperature anomalies to much smaller values by late afternoon.

Cool-air anomalies in the mixed layer are found to develop lesser mixed-layer depths than warm anomalies, yet to be accompanied by greater “reduced” surface pressures. As a result, a thermal-anomaly form drag occurs of very significant amplitude, since the cool air pools spend most of the day moving upslope, on the average, and the warm air pockets downslope. The thermal-anomaly form-drag coefficients are typically of greater magnitude than the shallow-water form-drag coefficients associated with a mixed layer of uniform potential temperature capped by a temperature jump. However, the former can on occasion become negative. Parameterizations for both types of form drag are offered as a function of terrain heights and slopes, mixed-layer wind speed and inversion strength, and horizontal temperature variability.

Abstract

A four-layer three-dimensional model whose lowest layer is a time and space-dependent, well-mixed boundary layer is employed over artificial, irregular terrain on the mesoscale during a daytime heating cycle. Only if the surface heating and mixed-layer entrainment am suppressed does the Row field become steady as found previously using a shallow-water model. Unsteadiness is due both to diurnal effects, especially the relaxation of the frictional force as the mixed layer deepens irregularly, and to the presence of horizontal vacations in potential temperature. The latter can develop with time due to the negative feedback between mixed-layer depth and warming rate; after the early morning hours, however, this feedback causes a damping of the temperature anomalies to much smaller values by late afternoon.

Cool-air anomalies in the mixed layer are found to develop lesser mixed-layer depths than warm anomalies, yet to be accompanied by greater “reduced” surface pressures. As a result, a thermal-anomaly form drag occurs of very significant amplitude, since the cool air pools spend most of the day moving upslope, on the average, and the warm air pockets downslope. The thermal-anomaly form-drag coefficients are typically of greater magnitude than the shallow-water form-drag coefficients associated with a mixed layer of uniform potential temperature capped by a temperature jump. However, the former can on occasion become negative. Parameterizations for both types of form drag are offered as a function of terrain heights and slopes, mixed-layer wind speed and inversion strength, and horizontal temperature variability.

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