Effects of the Pressure Perturbation Field in Numerical Models of Unidirectionally Sheared Thunderstorm Convection: Two versus Three Dimensions

Abstract

Two- and three-dimensional anelastic numerical modeling experiments with common environmental profiles are used to study two aspects of the pressure perturbation field in strongly sheared convective storms: 1) the physical roles of the so-called ?buoyant? and ?dynamic? pressure components, and 2) the distinction between the buoyant and hydrostatic pressure perturbations. The two- and three-dimensional models are analogous except that the two-dimensional grid domain is about 50% longer in order to accommodate a broadening of the two-dimensional storm circulation with time. The pressure analysis helps to clarify certain marked differences between the two-dimensional and three-dimensional storms, most notably a much weaker main updraft in two dimensions pronounced downshear tilt of the two-dimensional storm core versus an erect three-dimensional storm core, and a dry secondary updraft downshear of the main cloudy updraft in two dimensions with no analog in three dimensions: In the main updraft, strong midlevel thermal buoyancy is partly opposed by a downward-perturbed vertical pressure gradient force, but to a much greater extent in two dimensions than in three dimensions contributing to smaller net upward accelerations. This difference resides fully in the buoyant pressure component. In three dimensions the dominant mesolow is a few kilometers aloft within the active cloudy updraft, whereas in two dimensions it is at the surface, far downshear of the active updraft, and roughly three times stronger. Parcels feeding the main updraft therefore accelerate downshear earlier and more strongly in two dimensions than in three dimensions. The intense mesolow in two dimensions contributes strongly to a density deficit beneath the anvil, i.e., induces an upward ?pressure buoyancy force? that helps drive the dry secondary updraft. The contrasting mesolow strengths in two dimensions and three dimensions reflect largely the buoyant component, which in two dimensions attains large negative values at low levels due to excessive overlying warming from previous strong environmental subsidence exaggerated by the two-dimensional slab geometry. The dynamic pressure minimum lies well above and downshear of the buoyant pressure minimum in three dimensions, but is colocated with it in two dimensions, further contributing to the very deep two-dimensional mesolow. Formally, in both two dimensions and three dimensions, the buoyant and hydrostatic pressure perturbations satisfy elliptic diagnostic equations which are similar except that a horizontal Laplacian in the linear operator for the buoyant field is absent for the hydrostatic field. Thus, while both fields are intimately related to the distribution of total buoyancy (thermal buoyancy plus liquid water drag), the buoyant pressure perturbation is smoother and of lower amplitude than its hydrostatic counterpart. For the model experiments reported here, this distinction is far greater in three dimensions than in two dimensions, in association with the smaller horizontal scale of the active convection in three dimensions. Beneath the main updraft core, the maximum hydrostatic deficit is some 250% greater than the maximum buoyant deficit in three dimensions, but only about 50% greater in two dimensions.