![]() ![]() ![]() If shear-production and viscous dissipation of turbulent kinetic energy (TKE) are in approximate balance, then mean shear ( ∂ U ¯ / ∂ z ) and viscous dissipation ε are characterized by the same velocity and length scales ( u and ℓ, respectively). MOST is applicable to statistically steady, horizontally homogeneous, fully developed, shear-dominated turbulent flows above a rigid, flat, rough surface. These characteristic scales are essential ingredients of empirical flux–profile relationships like the Monin–Obukhov similarity theory. According to Richardson’s concept of energy cascade, the lifetime of a turbulent eddy is of the order of the so-called turnover time computed as the ratio between characteristic length and velocity scales ( ℓ and u, respectively see Davidson 2015, p. However, turbulence is always generated and dissipated at finite rates, corresponding to a nonzero lifetime. Thus, (1) is an eddy-viscosity model that assumes an instant equilibrium between unresolved stress and resolved strain rate, implying that unresolved turbulent motions are generated at a rate much faster than the rate of change of resolved motions (assumptions and potential issues associated with eddy-viscosity models are discussed in detail by Davidson 2015, 169–171). Equation (2) suggests that the relationship between the unresolved stress ( τ w) and resolved strain rate ( U ¯ 1 / z 1 ) is characterized by a scalar, − ( u * / U ¯ 1 ) ( u * z 1 ), which has the same dimensions as kinematic viscosity. Τ w = − u * U ¯ 1 u * z 1 U ¯ 1 z 1, (2)where z 1 is the first-grid-level height. The configuration and results of the aforementioned numerical simulations of tornadoes are presented in sections 3 and 4, respectively. The approach that is used to account for the memory of turbulence is presented in section 2. ![]() These two possibilities will be explored via idealized numerical simulations of tornadoes. On the other hand, if the magnitude of the friction force is enhanced, vortex weakening is a possibility. On one hand, the inward-directed friction force potentially could enhance the convergence of angular momentum toward the axis of rotation, leading to stronger vortices and/or more rapid vortex formation. In this article it will be shown that an inward-directed friction force acts on air parcels in a vortex (either cyclonic or anticyclonic) when the memory of turbulence is accounted for. In the opening paragraph, the inward acceleration of air parcels is brought about not by an inward-directed friction force, but because of the effect of friction in weakening the outward-directed centrifugal force. In this article we will demonstrate a simple way of accounting for the memory of turbulence in strongly curved flow. Because of the memory of turbulence, a more realistic treatment of the effects of turbulent mixing and friction should not constrain the friction to be opposite the velocity vector, particularly in the strongly curved flows of a vortex. Turbulent motions are generated and dissipated at finite rates-in effect, turbulence (and friction) has a memory through its lifetime. However, this assumption ignores the fact that friction really is manifest through the actions of turbulent eddies. It is traditionally assumed that the surface friction is directed opposite the near-surface velocity, with its magnitude being proportional to the product of the wind speed squared and a drag coefficient. However, tornadoes in a transient state may be especially sensitive to turbulence memory. The influence of turbulence memory on the intensity of quasi-steady-state tornadoes remains negligible as long as assumptions employed by the modified lower boundary condition hold over a relatively large fraction of the flow region of interest. In the accompanying large-eddy simulation (LES) of idealized tornadoes, the normal surface-shear-stress component is a source of additional dynamic instability, which provides an extra pathway for the development of turbulent motions. ![]() Specifically, when an air parcel moves along a curved trajectory, a normal surface-shear-stress component arises owing to turbulence memory. In this work, a modified lower boundary condition is proposed to account for the effect of turbulence memory. This assumption ignores the physics that turbulent motions are generated and dissipated at finite rates-in effect, turbulence has a memory through its lifetime. The traditional lower boundary condition in atmospheric models typically assumes an instant equilibrium between the unresolved stress and the resolved shear. Surface friction contributes to tornado formation and maintenance by enhancing the convergence of angular momentum. ![]()
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