Tropical cyclone boundary layer shocks

Abstract

This paper presents numerical solutions and idealized analytical solutions of axisymmetric, f -plane models of the tropical cyclone boundary layer. In the numerical model, the boundary layer radial and tangential flow is forced by a specified pressure field, which can also be interpreted as a specified gradient balanced tangential wind field vgr(r) or vorticity field ζgr(r). When the specified ζgr(r) field is changed from one that is radially concentrated in the inner core to one that is radially spread, the quasi-steady-state boundary layer flow transitions from a single eyewall shock-like structure to a double eyewall shock-like structure. To better understand these structures, analytical solutions are presented for two simplified versions of the model. In the simplified analytical models, which do not include horizontal diffusion, the u(∂u/∂r) term in the radial equation of motion and the u[f + (∂v/∂r) + (v/r)] term in the tangential equation of motion produce discontinuities in the radial and tangential wind, with associated singularities in the boundary layer pumping and the boundary layer vorticity. In the numerical model, which does include horizontal diffusion, the radial and tangential wind structures are not true discontinuities, but are shock-like, with wind changes of 20 or 30 m s −1 over a radial distance of a few kilometers. When double shocks form, the outer shock can control the strength of the inner shock, an effect that likely plays an important role in concentric eyewall cycles.

Bernhard Haurwitz Memorial Lecture (2017): Potential Vorticity Aspects of Tropical Dynamics

“…In the absence of the horizontal diffusion terms, the slab boundary layer equations constitute a hyperbolic system that can be written in characteristic form (Slocum et al 2014). A knowledge of the characteristic form is useful in understanding the formation of shocks.…”

Barotropic Instability during Eyewall Replacement

“…As observational evidence has accumulated, numerical modeling efforts have proceeded at an increasing pace, using a hierarchy of models of different complexity [5,[15][16][17][18][19][20][21][22][23][24][25][26][27][28][29][30][31][32][33][34]. This body of work has garnered important physical information from careful analysis of the relevant boundary layer dynamics [35][36][37][38][39][40][41][42][43]. This recent research on concentric eyewalls has also led to improvements in our ability to operationally forecast secondary eyewall formation and associated intensity variations [44][45][46][47].…”

Basic Concepts Involved in Tropical Cyclone Boundary Layer Shocks

“…can also be interpreted as a specified gradient wind, since the gradient wind v gr is defined in terms of the boundary layer density and pressure by (f +v gr /r)v gr = (1/ρ)(∂p/∂r). Slocum et al (2014) presented three numerical experiments with a slightly generalized version of the slab boundary layer equations (1). Their generalized version includes vertical advection terms and an empirical relation for c D as a function of U .…”

“…In the following sections the radial inflow for case C3 will be interpreted as a triangular wave while the radial inflows for cases C1 and C2 will be interpreted as N-waves. From Slocum et al (2014).…”