16C.2 CRITICAL ALIGNMEHT NUMBER AND MAXIMUM POTENTIAL INTENSITY OF TROPICAL HURRICANE Irakli G. Shekriladze 1 Georgian Technical University, Tbilisi, Georgia 1. INTRODUCTION Characteristic scales of a tropical cyclone linking TC development to conformity of vary from the sizes of sprayed by wind water dynamical and thermal fields of the system COA droplets to the sizes of lengthy spiral rainbands. at integral scales. Description of such a complex and multi-scale According to the MET a TC always is phenomenon requires accounting of great variety influenced by certain internal thermal driving of interrelated irreversible thermo-hydrodynamic mechanism caused by thermal asymmetry at its processes. That is why numerical methods of outer boundary. As a result it tends to certain modeling in combination with wide field equilibrium between translation speed and measurements become main instrument of intensity of heat removal from ocean upper layer. research of TC phenomenon. By now this "great At the same time such an equilibrium translation numerical attack” is in progress with certain is impossible without favoring by large-scale achievements, for instance, in TC track environmental wind that, as a rule, holds forecasting (Webber 2005a, Chan and Li 2005, prevailing driving influence. Pasad 2006, DeMaria 2007). If internal tendency of a TC is found to be in At the same time forecasting of TC intensity tune with large-scale environmental wind, this still remains as a challenging problem huge natural heat engine gains "freedom to (Krishnamurti et al. 2005, Webber 2005b, Balling operate" and becomes mostly efficient in terms and Cerveny 2006, DeMaria et al. 2007, Zhou of conversion of oceanic heat into cyclonic and Wang 2008). Despite permanent motion of atmospheric air. As a result, the TC improvement of resolution of numerical models, freely develops in self-organized manner and even in 2008-2009, regular predictions have intensifies rapidly (alignment effect). overlooked or significantly underestimated According to the MET, non-dimensional practically all cases of rapid intensification alignment number, incorporating integral thermal (UNISYS Weather 2003-2009). and dynamical parameters of the system COA, is Of special interest is the problem of potential the main characteristic of TC development. influence of global climate change (Trenberth In general case of a TC of non-circular 2005, Kerr 2005, Emanuel 2005, Shepherd and geometry alignment number can be determined Knutson 2007) that also may be linked to TC in the following manner (Shekriladze 2006a; intensification phenomenon. In addition, it is left 2006b; 2008): aside consideration potential of analysis at integral scales of the system COA. Most likely all these challenges reflect rather UbbQ typical contemporary problem with proper N = , (1) qR combination of numerical methods with adequate ef physical models. A model of equilibrium translation (MET) (Shekriladze 2004; 2006a, 2008) bridges this gap where Ubb is translation speed of the center of TC back boundary; Q is average initial hurricane heat potential (HHP) (according Leipper and 1 Corresponding author address: Irakli G. Shekriladze, Volgenau (1972)) fixed before entering of a TC in Georgian Technical Univ., 77 Kostava Street, Tbilisi, 0175, the given area; q is average integral heat flux Georgia; e-mail: [email protected] (sensitive and latent) from sea surface to a TC; Ref is effective radius of a TC (Ref is equal to TC In this connection slowing of translation, radius in the case of circular TC). leading to prolonging of TC passage through the given area, steps up cooling of an ocean, and Another important problem, naturally linked to vice versa, gathering of translation reduces alignment effect, is assessment of maximum cooling, all other things being the same. potential intensity (MPI) of a TC. The inverse dependence introduces rather Alongside with theoretical studies (Emanuel strong feedback into thermal driving mechanism. 1986, 1988, 1991, 1995, 1999, Holland 1997, As a result a TC not only prefers to shift toward Persing and Montgomery 2003) semi-empirical SST elevation, but it also tends to establish and purely empirical approaches also have been certain equilibrium between translation speed developed (DeMaria and Kaplan 1994, Whitney and integral heat flux. According to the central and Hobgood 1997). Besides, quite robust theory assumption of the MET corresponding so-called (Emanuel 1996) is brought up to real time equilibrium translation roughly is linked to hurricane MPI maps. The theory establishes constancy of heat involvement factor that is relationship between MPI and sea thermal equal to the share of initial HHP removed by a parameters under acting TC. TC through full passage of given area (the Empirical approaches mainly assumed assumption previously was confirmed by field governing role of sea surface temperature (SST) data on TC Opal (1995) (Shekriladze 2006a)). although this concept has become the subject of Development of a TC of non-circular rather wide discussion (Sun et al. 2006, Wada geometry was considered in (Shekriladze 2006a) and Usui 2007, Shepherd and Knutson 2007). in the framework of the MET using HHP maps At the same time, it is different matter (Hurricane heat potential maps 2003-2009) and assessment of MPI during forecasting procedures parameters specified in regular forecast that cannot be made based on sea parameters advisories (UNISYS Weather 2003-2009). Full under acting TC. Such an assessment can be set of equations and description of calculation performed only through using sea parameters procedures are presented in (Shekriladze fixed prior to entering of a TC in given area. 2006a). The key relationships are reproduced Discovery of alignment effect reveals some below. new dimensions of the problem of potential Taking in account minimum value of tangent influence of global climate change on TC activity. wind indicated in regular advisories, outer It also gains certain significance possible boundary of a TC is accepted at tangent wind interpretation of alignment effect as an emergent speed 34 knots (17.5 m s-1). property of the system COA occurring at integral Integral heat flux (sensitive and latent) scales. removed by a TC from left behind sea strip, with Abovementioned aspects of the problem are regard to insignificance of sea drift, can be discussed below. written in the following form: 2. STARTING ASSUMPTIONS AND RELATIONSHIPS A q = C QW U , (2) 34 i 34 bb According to the MET realization of internal tendency of a TC at intensification is linked to two external factors: heat inflow from an ocean and where A34 is an area inside tangent wind 34 dynamical influence of surrounding atmosphere. knots; Ci is heat involvement factor; W34 is Besides, oceanic heat inflow is assumed as the transverse size of A34; Production W34Ubb, to a single energy source for TC development. certain approximation, represents increment of In general case internal driving mechanism of cooled sea surface. a TC is linked to longitudinal SST gradient induced by TC itself through considerable A condition of establishment of equilibrium lowering of SST on its rear. translation mode was determined by critical Intensity of heat and mass transfer from sea alignment number (Shekriladze 2006a; 2008): surface to a TC is little affected by translation speed. Here main role is played by much higher air tangent speeds (for instance, beginning from U Q πW U Q N = bb = 34 bb ≈ 30, (3) outer boundary at tangent wind speed 17.5 ms-1). cr qRef 2A34q where Ref is equal: 3. MAXIMUM POTENTIAL INTENSITY The work performed by a TC during ideal R = 2A /πW (4) thermodynamic cycle depends on heat removed ef 34 34 from an ocean and efficiency of heat conversion. The latter, for its part, depends on SST field under acting TC and temperature of air outflow. In addition, equations (2-4) were In real cycle the efficiency additionally depends supplemented by empirical equation for average on other parameters of the system SOA. heat flux from sea surface to a TC specifically Besides, in the context of the MET, alignment fitted to equilibrium translation. The equation is number evidently claims to serve as generalized based at three-zone model of heat transfer characteristic of such an additional influence. (Shekriladze 2006a, 2006b, 2008). As maximum intensity of a TC takes place at In connection with inverse negative the same (critical) alignment number at any relationship between translation speed and initial conditions, this number can be excluded from the HHP (other things being the same) equilibrium number of influencing MPI variables. In addition, translation is comparatively slow at high HHP and the same conclusion can be extended to the comparatively fast at low HHP. In this connection temperature of air outflow assuming rough the area with high initial HHP undergoes more uniformity of this parameter during life cycle of intensive cooling than the area with low initial different TCs. HHP. In such a framework, finally, SST and HHP Reasoning from this circumstance it was fields under acting TC become the main variable assumed that, during equilibrium translation SST parameters of upper oceanic layer that field under TH is roughly the same irrespective of influences MPI. initial value of HHP. Average integral heat flux At the same time, forecasting of SST field was considered as single-valued function of under acting TC based on SST field existed tangent wind distribution and following empirical before entering of a TC in given sea area equation was offered (Shekriladze 2006a, 2006b, presents rather complicated problem. 2008): The matter is that dynamical impact of acting TC leads to intensive vertical mixing of seawater with drastic transformation of initial SST field 2 2 2 2 q = [375(R1 − R2 )+ 600(R2 − R3 )+ (Shay et al. 2000). It is easy to verify that in such a situation 2 2 2 +1600()U max /155 R3 ]/ R1 W/m , (5) resultant SST field mainly is dependent on initial HHP field (Shekriladze 2006a).