Search Results

You are looking at 1 - 10 of 62 items for

  • Author or Editor: George Bryan x
  • All content x
Clear All Modify Search
George H. Bryan

Abstract

Using numerical simulations, this study examines the sensitivity of hurricane intensity and structure to changes in the surface exchange coefficients and to changes in the length scales of a turbulence parameterization. Compared to other recent articles on the topic, this study uses higher vertical resolution, more values for the turbulence length scales, a different initial environment (including higher sea surface temperature), a broader specification of surface exchange coefficients, a more realistic microphysics scheme, and a set of three-dimensional simulations. The primary conclusions from a recent study by Bryan and Rotunno are all upheld: maximum intensity is strongly affected by the horizontal turbulence length scale lh but not by the vertical turbulence length scale lυ, and the ratio of surface exchange coefficients for enthalpy and momentum, Ck/Cd, has less effect on maximum wind speed than suggested by an often-cited theoretical model. The model output is further evaluated against various metrics of hurricane intensity and structure from recent observational studies, including maximum wind speed, minimum pressure, surface wind–pressure relationships, height of maximum wind, and surface inflow angle. The model settings lh ≈ 1000 m, lυ ≈ 50 m, and Ck/Cd ≈ 0.5 produce the most reasonable match to the observational studies. This article also reconciles a recent controversy about the likely value of Ck/Cd in high wind speeds by noting that simulations in a study by Emanuel used relatively large horizontal diffusion and low sea surface temperature. The model in this study can produce category 5 hurricanes with Ck/Cd as low as 0.25.

Full access
George H. Bryan

Abstract

A set of approximate equations for pseudoadiabatic thermodynamics is developed. The equations are derived by neglecting the entropy of water vapor and then compensating for this error by using a constant (but relatively large) value for the latent heat of vaporization. The subsequent formulations for entropy and equivalent potential temperature have errors that are comparable to those of previous formulations, but their simple form makes them attractive for use in theoretical studies. It is also shown that, if the latent heat of vaporization is replaced with a constant value, an optimal value should be chosen to minimize error; a value of 2.555 × 106 J kg−1 is found in tests herein.

Full access
George H. Bryan

Abstract

A spurious updraft pattern has been documented in some numerical simulations of squall lines. The pattern is notable because of a regular, repeating pattern of updrafts and downdrafts that are three–six grid lengths wide. This study examines the environmental and numerical conditions that lead to this problem. The spurious pattern is found only in simulations of upshear-tilted convective systems. Furthermore, the pattern coincides with deep (2–3 km) and wide (5–20 km) moist absolutely unstable layers (MAULs)—saturated layers of air that are statically unstable. In this physical environment, small-scale perturbations grow rapidly. The necessarily imperfect numerical schemes of the model introduce spurious small-scale perturbations into the MAULs, and these perturbations amplify owing to the unstable stratification. Some techniques are investigated that diffuse the perturbations or minimize their introduction in the statically unstable flow.

Full access
George H. Bryan and Richard Rotunno

Abstract

This study examines properties of gravity currents in confined channels with sheared environmental flow. Under the assumptions of steady and inviscid flow, two-dimensional analytic solutions are obtained for a wide range of shear values. The slope of a gravity current interface just above the surface increases as environmental shear α increases, which is consistent with previous studies, although here it is shown that the interface slope can exceed 80° for nondimensional shear α > 2. Then the inviscid-flow analytic solutions are compared with two- and three-dimensional numerical model simulations, which are turbulent and thus have dissipation. The simulated current depths are systematically lower, compared to a previous study, apparently because of different numerical techniques in this study that allow for a faster transition to turbulence along the gravity current interface. Furthermore, simulated gravity current depths are 10%–40% lower than the inviscid analytic values. To explain the model-produced current depths, a steady analytic theory with energy dissipation is revisited. It is shown that the numerical model current depths are close to values associated with the maximum possible dissipation rate in the simplest form of the analytic model for all values of α examined in this study. A primary conclusion is that dissipation plays an important and nonnegligible role in gravity currents within confined channels, with or without environmental shear.

Full access
Richard Rotunno and George H. Bryan

Abstract

In this study the authors analyze and interpret the effects of parameterized diffusion on the nearly steady axisymmetric numerical simulations of hurricanes presented in a recent study. In that study it was concluded that horizontal diffusion was the most important control factor for the maximum simulated hurricane intensity. Through budget analysis it is shown here that horizontal diffusion is a major contributor to the angular momentum budget in the boundary layer of the numerically simulated storms. Moreover, a new scale analysis recognizing the anisotropic nature of the parameterized model diffusion shows why the horizontal diffusion plays such a dominant role. A simple analytical model is developed that captures the essence of the effect. The role of vertical diffusion in the boundary layer in the aforementioned numerical simulations is more closely examined here. It is shown that the boundary layer in these simulations is consistent with known analytical solutions in that boundary layer depth increases and the amount of “overshoot” (maximum wind in excess of the gradient wind) decreases with increasing vertical diffusion. However, the maximum wind itself depends mainly on horizontal diffusion and is relatively insensitive to vertical diffusion; the overshoot variation with vertical viscosity mainly comes from changes in the gradient wind with vertical viscosity. The present considerations of parameterized diffusion allow a new contribution to the dialog in the literature on the meaning and interpretation of the Emanuel potential intensity theory.

Full access
George H. Bryan and Richard Rotunno

Abstract

Using a time-dependent axisymmetric numerical model, the authors evaluate whether high-entropy air near the surface in hurricane eyes can substantially increase hurricanes’ maximum intensity. This local high-entropy anomaly is ultimately created by surface entropy fluxes in the eye. Therefore, simulations are conducted in which these surface fluxes are set to zero; results show that the high-entropy anomaly is eliminated, yet the axisymmetric tangential wind speed is only slightly weakened (by ∼4%, on average). These results contradict the hypothesis that transport of high-entropy air from the eye into the eyewall can significantly increase the maximum axisymmetric intensity of hurricanes. In fact, all simulations (with or without high-entropy anomalies) have an intensity that is 25–30 m s−1 higher than Emanuel’s theoretical maximum intensity. Further analysis demonstrates that less then 3% of the total surface-entropy input to the hurricane comes from the eye, and therefore the total magnitude of entropy transport between the eye and eyewall is a negligible component of the entropy budget of the simulated hurricanes. This latter finding is consistent with a cursory comparison with observations.

Full access
George H. Bryan and Richard Rotunno

Abstract

Several studies have shown that the intensity of numerically simulated tropical cyclones can exceed (by 50%) a theoretical upper limit. To investigate the cause, this study evaluates the underlying components of Emanuel’s commonly cited analytic theory for potential intensity (herein referred to as E-PI). A review of the derivation of E-PI highlights three primary components: a dynamical component (gradient-wind and hydrostatic balance); a thermodynamical component (reversible or pseudoadiabatic thermodynamics, although the pseudoadiabatic assumption yields greater intensity); and a planetary boundary layer (PBL) closure (which relates the horizontal gradients of entropy and angular momentum at the top of the PBL to fluxes and stresses at the ocean surface). These three components are evaluated using output from an axisymmetric numerical model. The present analysis finds the thermodynamical component and the PBL closure to be sufficiently accurate for several different simulations. In contrast, the dynamical component is clearly violated. Although the balanced portion of the flow (υg, to which E-PI applies) appears to also exceed E-PI, it is shown that this difference is attributable to the method used to calculate υg from the model output. Evidence is shown that υg for a truly balanced cyclone does not exceed E-PI. To clearly quantify the impact of unbalanced flow, a more complete analytic model is presented. The model is not expressed in terms of external conditions and thus cannot be used to predict maximum intensity for a given environment; however, it does allow for evaluation of the relative contributions to maximum intensity from balanced and unbalanced (i.e., inertial) terms in the governing equations. Using numerical model output, this more complete model is shown to accurately model maximum intensity. Analysis against observations further confirms that the effects of unbalanced flow on maximum intensity are not always negligible. The contribution to intensity from unbalanced flow can become negligible in axisymmetric models as radial turbulence (i.e., viscosity) increases, and this explains why some previous studies concluded that E-PI was an accurate upper bound for their simulations. Conclusions of this study are also compared and contrasted to those from previous studies.

Full access
Richard Rotunno and George H. Bryan

Abstract

Laboratory observations of the leeside hydraulic jump indicate it consists of a statistically stationary turbulent motion in an overturning wave. From the point of view of the shallow-water equations (SWE), the hydraulic jump is a discontinuity in fluid-layer depth and velocity at which kinetic energy is dissipated. To provide a deeper understanding of the leeside hydraulic jump, three-dimensional numerical solutions of the Navier–Stokes equations (NSE) are carried out alongside SWE solutions for nearly identical physical initial-value problems. Starting from a constant-height layer flowing over a two-dimensional obstacle at constant speed, it is demonstrated that the SWE solutions form a leeside discontinuity owing to the collision of upstream-moving characteristic curves launched from the obstacle. Consistent with the SWE solution, the NSE solution indicates the leeside hydraulic jump begins as a steepening of the initially horizontal density interface. Subsequently, the NSE solution indicates overturning of the density interface and a transition to turbulence. Analysis of the initial-value problem in these solutions shows that the tendency to form either the leeside height–velocity discontinuity in the SWE or the overturning density interface in the exact NSE is a feature of the inviscid, nonturbulent fluid dynamics. Dissipative turbulent processes associated with the leeside hydraulic jump are a consequence of the inviscid fluid dynamics that initiate and maintain the locally unstable conditions.

Full access
George H. Bryan and Richard Rotunno

Abstract

This study examines the lifting of sheared environmental air by gravity currents, focusing primarily on the theoretical “optimal state” in which near-surface flow is turned into a vertically oriented jet. Theoretical models are presented from multiple perspectives, including the vorticity perspective that was first presented by Rotunno, Klemp, and Weisman and a flow-force balance perspective based on conservation of mass and momentum. The latter approach reveals a constraint on the depth of the environmental shear layer relative to the depth of the cold pool. Based on these control-volume constraints, a numerical solution for steady, inviscid, isentropic flow is obtained that shows how the cold-pool interface has a slightly concave shape and is nearly (although not strictly) vertical. Then, by initializing a time-dependent numerical model with a stagnant cold pool in an environment with low-level shear, it is shown that a statistically steady flow can be maintained with all the important elements of the analytic solution. Most notably, the front-relative flow is negligible behind the surface gust front at all levels, the interface of the cold pool maintains a predominantly vertical structure, and the net generation of vorticity by buoyancy within a control volume closely matches the horizontal flux of environmental vorticity on the side of the control volume. Sensitivity simulations confirm that the constraints identified by the analytic study must be met for the optimal state to be realized and that lifting of near-surface environmental air is optimized when a vertically oriented jet is created and maintained.

Full access
George H. Bryan and Richard Rotunno

Abstract

An axisymmetric numerical model is used to evaluate the maximum possible intensity of tropical cyclones. As compared with traditionally formulated nonhydrostatic models, this new model has improved mass and energy conservation in saturated conditions. In comparison with the axisymmetric model developed by Rotunno and Emanuel, the new model produces weaker cyclones (by ∼10%, in terms of maximum azimuthal velocity); the difference is attributable to several approximations in the Rotunno–Emanuel model. Then, using a single specification for initial conditions (with a sea surface temperature of 26°C), the authors conduct model sensitivity tests to determine the sensitivity of maximum azimuthal velocity (υ max) to uncertain aspects of the modeling system. For fixed mixing lengths in the turbulence parameterization, a converged value of υ max is achieved for radial grid spacing of order 1 km and vertical grid spacing of order 250 m. The fall velocity of condensate (Vt) changes υ max by up to 60%, and the largest υ max occurs for pseudoadiabatic thermodynamics (i.e., for Vt > 10 m s−1). The sensitivity of υ max to the ratio of surface exchange coefficients for entropy and momentum (CE/CD) matches the theoretical result, υ max ∼ (CE/CD)1/2, for nearly inviscid flow, but simulations with increasing turbulence intensity show less dependence on CE/CD; this result suggests that the effect of CE/CD is less important than has been argued previously. The authors find that υ max is most sensitive to the intensity of turbulence in the radial direction. However, some settings, such as inviscid flow, yield clearly unnatural structures; for example, υ max exceeds 110 m s−1, despite a maximum observed intensity of ∼70 m s−1 for this environment. The authors show that turbulence in the radial direction limits maximum axisymmetric intensity by weakening the radial gradients of angular momentum (which prevents environmental air from being drawn to small radius) and of entropy (which is consistent with weaker intensity by consideration of thermal wind balance). It is also argued that future studies should consider parameterized turbulence as an important factor in simulated tropical cyclone intensity.

Full access