CN107273334A - Mobile PBL of typhoon three-component wind speed analytic method - Google Patents

Mobile PBL of typhoon three-component wind speed analytic method Download PDF

Info

Publication number
CN107273334A
CN107273334A CN201710434263.7A CN201710434263A CN107273334A CN 107273334 A CN107273334 A CN 107273334A CN 201710434263 A CN201710434263 A CN 201710434263A CN 107273334 A CN107273334 A CN 107273334A
Authority
CN
China
Prior art keywords
mrow
msub
mfrac
msup
prime
Prior art date
Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
Granted
Application number
CN201710434263.7A
Other languages
Chinese (zh)
Other versions
CN107273334B (en
Inventor
段忠东
周华
Current Assignee (The listed assignees may be inaccurate. Google has not performed a legal analysis and makes no representation or warranty as to the accuracy of the list.)
Shenzhen Graduate School Harbin Institute of Technology
Original Assignee
Shenzhen Graduate School Harbin Institute of Technology
Priority date (The priority date is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the date listed.)
Filing date
Publication date
Application filed by Shenzhen Graduate School Harbin Institute of Technology filed Critical Shenzhen Graduate School Harbin Institute of Technology
Priority to CN201710434263.7A priority Critical patent/CN107273334B/en
Publication of CN107273334A publication Critical patent/CN107273334A/en
Application granted granted Critical
Publication of CN107273334B publication Critical patent/CN107273334B/en
Active legal-status Critical Current
Anticipated expiration legal-status Critical

Links

Classifications

    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F17/00—Digital computing or data processing equipment or methods, specially adapted for specific functions
    • G06F17/10—Complex mathematical operations
    • G06F17/11—Complex mathematical operations for solving equations, e.g. nonlinear equations, general mathematical optimization problems
    • G06F17/13—Differential equations
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01P—MEASURING LINEAR OR ANGULAR SPEED, ACCELERATION, DECELERATION, OR SHOCK; INDICATING PRESENCE, ABSENCE, OR DIRECTION, OF MOVEMENT
    • G01P5/00—Measuring speed of fluids, e.g. of air stream; Measuring speed of bodies relative to fluids, e.g. of ship, of aircraft
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02A—TECHNOLOGIES FOR ADAPTATION TO CLIMATE CHANGE
    • Y02A90/00—Technologies having an indirect contribution to adaptation to climate change
    • Y02A90/10—Information and communication technologies [ICT] supporting adaptation to climate change, e.g. for weather forecasting or climate simulation

Landscapes

  • Engineering & Computer Science (AREA)
  • Physics & Mathematics (AREA)
  • General Physics & Mathematics (AREA)
  • Mathematical Physics (AREA)
  • Computational Mathematics (AREA)
  • Mathematical Analysis (AREA)
  • Mathematical Optimization (AREA)
  • Pure & Applied Mathematics (AREA)
  • Data Mining & Analysis (AREA)
  • Theoretical Computer Science (AREA)
  • Operations Research (AREA)
  • Databases & Information Systems (AREA)
  • Software Systems (AREA)
  • General Engineering & Computer Science (AREA)
  • Algebra (AREA)
  • Aviation & Aerospace Engineering (AREA)
  • Management, Administration, Business Operations System, And Electronic Commerce (AREA)
  • Aerodynamic Tests, Hydrodynamic Tests, Wind Tunnels, And Water Tanks (AREA)
  • Other Investigation Or Analysis Of Materials By Electrical Means (AREA)

Abstract

The invention provides a kind of mobile PBL of typhoon three-component wind speed analytic method, first, vertical wind speed equation is added in the initial differential equation of Yan Meng models, abbreviation is carried out by the processing method of Smith typhoon models, then the method from iteration is modified to above-mentioned result of calculation.The beneficial effects of the invention are as follows：By introducing vertical wind speed in existing wind-field model, by the PBL of typhoon model extension of two variables to ternary, driving wind field is provided to heavy showers simulation caused by Research on typhoon.

Description

Mobile PBL of typhoon three-component wind speed analytic method
Technical field
The present invention relates to wind speed analytic method, more particularly to a kind of mobile PBL of typhoon three-component wind speed analytic method.
Background technology
Boundary layer typhoon model is to carry out hurricane simulation, weather forecast and the necessary instrument of Hazard Risk Analysis, its essence For the solution of Navier-Stokes typhoons equation (N-S equations).Physicist, meteorologist have developed a series of description typhoons The model of wind field, these models include Shapiro typhoons model (1983), Yan Meng typhoons models (1996), Kepert platforms Wind model (2001) and Smith typhoons model (2003) etc..Other models in addition to Yan Meng models describe ground The flowing of ball surface free atmosphere layer of air, obtains influenceing the atmospheric boundary layer (surface layer) of mankind's activity by boundary layer model Typhoon Wind Field.Yan Meng models are then a kind of models of direct description PBL of typhoon wind field.
Prior art problem and defect are：
(1) existing boundary layer typhoon model is essentially two component typhoon models, i.e. variable in equation for border at present The horizontal radial wind speed of typhoon wind speed and horizontal tangential wind speed in layer.These models lack vertical wind speed component, thus can not be complete Site preparation describes wind field.
(2) wind speed vertical component is an important parameter to the vertical transport of description earth's surface heat and steam, is simulation table The key factor of wind boundary layer heavy showers.Current typhoon wind-field model cannot be used for strong drop due to lacking vertical wind speed component Rain is simulated.
(3) although Smith typhoons model is a three-component typhoon model, but it describes static typhoon, it is impossible to Portray real Typhoon Tracks wind field；And the model needs to carry out the solution of partial differential equation, it is impossible to obtain analytic solutions.
The content of the invention
In order to solve the problems of the prior art, parsed the invention provides a kind of mobile PBL of typhoon three-component wind speed Method,
First, vertical wind speed equation is added in the initial differential equation of Yan Meng models, it is as follows,
In above formula, v represents vector of the broad sense level to wind speed, i.e. v=vr+vθ, represent vertical wind speed size, vrRepresent Broad sense horizontal radial wind speed, is the size v of horizontal radial wind speed in Yan Meng model boundaries layerrs, vθRepresent horizontal cutting aweather Speed, is horizontal tangential wind speed size v in Yan Meng model boundaries layerθs, its implication is identical with the implication in Yan Meng models；
For formula (2), abbreviation is carried out by the processing method of Smith typhoon models, for static typhoon, i.e., mobile speed C=0 is spent, level is to wind speed (vθ,vr) without azimuthal change, therefore, formula (2) can be reduced to
To formula (3), from z=0 to z=, δ is to be integrated at the top of boundary layer, and hypothetical boundary thickness degree δ is fixed value, can
To above formula integrate, both sides with divided by boundary layer thickness δ, obtain
Further deformation is obtained
Above formula vrbThe horizontal radial wind speed size at boundary layer thickness δ is represented, i.e., in Yan Meng modelsIt is big It is small, wδThe vertical wind speed size at boundary layer thickness δ is represented, and for the size of the vertical wind speed w at arbitrary height, to formula (3) from z=0 to z=Z from integrate, arrange
For c ≠ 0, that is, consider the big I for moving integrally the vertical wind speed w at speed, arbitrary height of typhoon to formula (2) from z=0 to z=Z from integration obtain
Wind speed (v can tentatively be tried to achieve by the deformation of formula (1) and above-mentioned formula (2)r,vθ, w), then from the method pair of iteration Above-mentioned result of calculation is modified；
Vertical wind speed w is introduced in Yan Meng typhoons models are on differential equation in boundary layer, can be obtained
IntroduceWithAbove formula (9), (10) become For：
Above formula vθ"=vθ', vr"=- vr′/ξ.Then being multiplied by i merging (12) simultaneously to formula (11) both sides can obtain
V "=v in above formulaθ″+ivr″.The solution for meeting boundary layer condition is：
Further abbreviation is
Wherein
And D=D1+iD2, it is the multiple constant of boundary layer earth's surface, can finally obtain wind speed component in boundary layer is
In above formula
V is solved by iterating to calculateθsAnd vrs, and then solve vertical wind speed w.
The beneficial effects of the invention are as follows：(1) by introducing vertical wind speed in existing wind-field model, by the typhoon of two variables Boundary layer model extends to ternary, and driving wind field is provided to heavy showers simulation caused by Research on typhoon；
(2) to the improvement of wind-field model so that the simulation of horizontal radial wind speed is more accurate, so that the mould of typhoon wind speed Intend forecast more reliable.
Brief description of the drawings
Fig. 1 is vertical for the horizontal tangential wind speed of MYS models, YS models and the quasi stationary axial symmetry typhoon of MM5 pattern dies AverageRadial cutaway view.
Fig. 2 is vertical for the horizontal radial wind speed of MYS models, YS models and the quasi stationary axial symmetry typhoon of MM5 pattern dies AverageRadial cutaway view.
Fig. 3 is the footpath of vertical velocity w at the 1km of MYS models, YS models and the quasi stationary axial symmetry typhoon of MM5 pattern dies To profile.
Embodiment
The invention will be further described for explanation and embodiment below in conjunction with the accompanying drawings.
A kind of mobile PBL of typhoon three-component wind speed analytic method, first, Yan is added to by vertical wind speed equation Meng models[1]It is as follows in the initial differential equation.
In above formula, v represents vector of the broad sense level to wind speed, i.e. v=vr+vθ, represent vertical wind speed size.vrRepresent Broad sense horizontal radial wind speed, it is to be understood that being the size v of horizontal radial wind speed in Yan Meng model boundaries layerrs, vθTable Show horizontal tangential wind speed, be horizontal tangential wind speed size v in Yan Meng model boundaries layerθs, its implication and Yan Meng models In implication it is identical.
For formula (2), the processing method that Smith typhoon models are used for reference herein carries out abbreviation.For static typhoon (movement Speed c=0), level is to wind speed (vθ,vr) without azimuthal change.Therefore, formula (2) can be reduced to
To formula (3), from z=0 to z=, δ is to be integrated at the top of boundary layer, and hypothetical boundary thickness degree δ is fixed value, can
To above formula integrate, both sides with divided by boundary layer thickness δ, obtain
Further deformation is obtained
Above formula vrbThe horizontal radial wind speed size at boundary layer thickness δ is represented, i.e., in Yan Meng modelsIt is big It is small, wδRepresent the vertical wind speed size at boundary layer thickness δ.And for the size of the vertical wind speed w at arbitrary height, to formula (3) from z=0 to z=Z from integrate, arrange
For c ≠ 0, that is, consider the big I for moving integrally the vertical wind speed w at speed, arbitrary height of typhoon to formula (2) from z=0 to z=Z from integration obtain
Wind speed (v can tentatively be tried to achieve by the deformation of formula (1) and above-mentioned formula (2)r,vθ, w), then from the method pair of iteration Above-mentioned result of calculation is modified.
Vertical wind speed w is introduced in Yan Meng typhoons models are on differential equation in boundary layer, can be obtained
IntroduceWithAbove formula (9), (10) become For：
Above formula vθ"=vθ', vr"=- vr′/ξ.Then being multiplied by i merging (12) simultaneously to formula (11) both sides can obtain
V "=v in above formulaθ″+ivr″.The solution for meeting boundary layer condition is：
Further abbreviation is
Wherein
And D=D1+iD2, it is the multiple constant of boundary layer earth's surface.Wind speed component in boundary layer, which can finally be obtained, is
In above formula
V is solved by iterating to calculateθsAnd vrs, and then solve vertical wind speed w.From formula (1) and the solution (v of (2)r′,vθ′, W) it is iterated calculating as initial value.
Improved method above, might as well be called improved Yan Meng, referred to as Smith models, MYS (Modified Yan Meng, Smith) model.
Fig. 1 is the radial cutaway view of the horizontal tangential wind speed of MYS models, YS models and MM5 modeling axial symmetry typhoons, Each parameter value of typhoon is identical, and vertical height 1km takes wind speed to be averaged.
Wherein kinematic viscosity k is selected in simulated experimentm=50m2/ s, Karman constant k=0.4, maximum wind speed radius rmax= 40km, B=1.6, pressure differential Δ p=50hpa, resistance coefficient z0=0.05, maximum wind velocity vmax=50m/s.
MYS models and MS models are for horizontal tangential wind speed v as shown in Figure 1θBasically identical, the radial section that predicts the outcome Figure is essentially coincided, and compared with the predicting the outcome of MM5 models, error is smaller in the range of away from center of typhoon 100km, its maximum Relative error is limited within 8%.
Fig. 2,3 for MYS models, YS models and MM5 modeling axial symmetry typhoons horizontal radial wind speed vertical averageWith the radial cutaway view of w at vertical velocity 1km.Each parameter value of typhoon is identical with Fig. 1, and vertical height 1km takes wind speed to put down .
For radial direction wind speed v it can be seen from upper figurerWith vertical wind speed w, compared to YS models, the prediction knot of MYS models Fruit, which has, to be more markedly improved.Compared with the predicting the outcome of MM5 models, radial direction wind speed vrThe relative error of maximum is limited 17% Within, and the relative error of vertical wind speed w maximums is limited within 5%.And the two is obtained at maximum, away from center of typhoon Distance is more slightly smaller than the result that MM5 is simulated.
To sum up, this method has to horizontal radial wind speed is more markedly improved effect, and can obtain the big of vertical wind speed w It is small.
A kind of mobile PBL of typhoon three-component wind speed analytic method that the present invention is provided has advantages below：
(1) the inventive method in existing wind-field model by introducing vertical wind speed, by the PBL of typhoon mould of two variables Type extends to ternary, and driving wind field is provided to heavy showers simulation caused by Research on typhoon.
(2) improvement of this method to wind-field model so that the simulation of horizontal radial wind speed is more accurate, so that typhoon wind The Simulation prediction of speed is more reliable.
A kind of mobile PBL of typhoon three-component wind speed analytic method that the present invention is provided, applied to typhoon and rainfall simulation And Hazard Risk Analysis, insure in catastrophe insurance and again, have wide practical use in terms of the design of catastrophe security and exploitation；Should With with determining that engineering is set up defences typhoon and rainfall grade, there is application prospect to the disaster prevention of design and the operation of important engineering； Taken precautions against natural calamities and emergency preplan planning applied to city wind resistance, disaster management and emergency response decision-making to government administration section have should Use prospect.
Above content is to combine specific preferred embodiment further description made for the present invention, it is impossible to assert The specific implementation of the present invention is confined to these explanations.For general technical staff of the technical field of the invention, On the premise of not departing from present inventive concept, some simple deduction or replace can also be made, should all be considered as belonging to the present invention's Protection domain.

Claims (2)

1. a kind of mobile PBL of typhoon three-component wind speed analytic method, it is characterised in that：
First, vertical wind speed equation is added in the initial differential equation of Yan Meng models, it is as follows,
<mrow> <mfrac> <mrow> <mo>&amp;part;</mo> <mi>v</mi> </mrow> <mrow> <mo>&amp;part;</mo> <mi>t</mi> </mrow> </mfrac> <mo>+</mo> <mi>v</mi> <mo>&amp;CenterDot;</mo> <mo>&amp;dtri;</mo> <mi>v</mi> <mo>=</mo> <mo>-</mo> <mfrac> <mn>1</mn> <mi>&amp;rho;</mi> </mfrac> <mo>&amp;dtri;</mo> <mi>p</mi> <mo>-</mo> <mi>f</mi> <mi>k</mi> <mo>&amp;times;</mo> <mi>v</mi> <mo>+</mo> <mi>F</mi> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>1</mn> <mo>)</mo> </mrow> </mrow>
<mrow> <mfrac> <mo>&amp;part;</mo> <mrow> <mo>&amp;part;</mo> <mi>r</mi> </mrow> </mfrac> <mrow> <mo>(</mo> <msub> <mi>rv</mi> <mi>r</mi> </msub> <mo>)</mo> </mrow> <mo>+</mo> <mfrac> <mo>&amp;part;</mo> <mrow> <mo>&amp;part;</mo> <mi>&amp;theta;</mi> </mrow> </mfrac> <mrow> <mo>(</mo> <msub> <mi>v</mi> <mi>&amp;theta;</mi> </msub> <mo>)</mo> </mrow> <mo>+</mo> <mfrac> <mo>&amp;part;</mo> <mrow> <mo>&amp;part;</mo> <mi>z</mi> </mrow> </mfrac> <mrow> <mo>(</mo> <mi>r</mi> <mi>w</mi> <mo>)</mo> </mrow> <mo>=</mo> <mn>0</mn> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>2</mn> <mo>)</mo> </mrow> </mrow>
In above formula, v represents vector of the broad sense level to wind speed, i.e. v=vr+vθ, represent vertical wind speed size, vrRepresent broad sense Horizontal radial wind speed, is the size v of horizontal radial wind speed in Yan Meng model boundaries layerrs, vθHorizontal tangential wind speed is represented, is Horizontal tangential wind speed size v in Yan Meng model boundaries layerθs, its implication is identical with the implication in Yan Meng models；
For formula (2), abbreviation is carried out by the processing method of Smith typhoon models, for static typhoon, i.e. translational speed c =0, level is to wind speed (vθ,vr) without azimuthal change, therefore, formula (2) can be reduced to
<mrow> <mfrac> <mo>&amp;part;</mo> <mrow> <mo>&amp;part;</mo> <mi>r</mi> </mrow> </mfrac> <mrow> <mo>(</mo> <msub> <mi>rv</mi> <mi>r</mi> </msub> <mo>)</mo> </mrow> <mo>+</mo> <mfrac> <mo>&amp;part;</mo> <mrow> <mo>&amp;part;</mo> <mi>z</mi> </mrow> </mfrac> <mrow> <mo>(</mo> <mi>r</mi> <mi>w</mi> <mo>)</mo> </mrow> <mo>=</mo> <mn>0</mn> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>3</mn> <mo>)</mo> </mrow> </mrow>
To formula (3), from z=0 to z=, δ is to be integrated at the top of boundary layer, and hypothetical boundary thickness degree δ is fixed value, can be obtained
<mrow> <mfrac> <mi>d</mi> <mrow> <mi>d</mi> <mi>r</mi> </mrow> </mfrac> <msubsup> <mo>&amp;Integral;</mo> <mn>0</mn> <mi>&amp;delta;</mi> </msubsup> <msub> <mi>rv</mi> <mi>r</mi> </msub> <mi>d</mi> <mi>z</mi> <mo>+</mo> <mo>&amp;lsqb;</mo> <mi>r</mi> <mi>w</mi> <mo>&amp;rsqb;</mo> <msub> <mo>|</mo> <mrow> <mi>z</mi> <mo>=</mo> <mi>&amp;delta;</mi> </mrow> </msub> <mo>=</mo> <mn>0</mn> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>4</mn> <mo>)</mo> </mrow> </mrow>
To above formula integrate, both sides with divided by boundary layer thickness δ, obtain
<mrow> <mfrac> <mi>d</mi> <mrow> <mi>d</mi> <mi>r</mi> </mrow> </mfrac> <mrow> <mo>(</mo> <msub> <mi>rv</mi> <mrow> <mi>r</mi> <mi>b</mi> </mrow> </msub> <mo>)</mo> </mrow> <mo>=</mo> <mo>-</mo> <mi>r</mi> <mfrac> <msub> <mi>w</mi> <mi>&amp;delta;</mi> </msub> <mi>&amp;delta;</mi> </mfrac> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>5</mn> <mo>)</mo> </mrow> </mrow>
Further deformation is obtained
<mrow> <msub> <mi>w</mi> <mi>&amp;delta;</mi> </msub> <mo>=</mo> <mo>-</mo> <mi>&amp;delta;</mi> <mrow> <mo>(</mo> <mfrac> <msub> <mi>v</mi> <mrow> <mi>r</mi> <mi>b</mi> </mrow> </msub> <mi>r</mi> </mfrac> <mo>+</mo> <mfrac> <mrow> <msub> <mi>dv</mi> <mrow> <mi>r</mi> <mi>b</mi> </mrow> </msub> </mrow> <mrow> <mi>d</mi> <mi>r</mi> </mrow> </mfrac> <mo>)</mo> </mrow> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>6</mn> <mo>)</mo> </mrow> </mrow>
Above formula vrbRepresent the horizontal radial wind speed size at boundary layer thickness δ, i.e. v in Yan Meng modelsθs|Z=δSize, wδ The vertical wind speed size at boundary layer thickness δ is represented, and for the size of the vertical wind speed w at arbitrary height, to formula (3) from z Integrate, arrange at=0 to z=Z
<mrow> <mi>w</mi> <mo>=</mo> <mo>-</mo> <mfrac> <mn>1</mn> <mi>r</mi> </mfrac> <mo>&amp;lsqb;</mo> <msubsup> <mo>&amp;Integral;</mo> <mn>0</mn> <mi>Z</mi> </msubsup> <mfrac> <mrow> <mo>&amp;part;</mo> <mrow> <mo>(</mo> <msub> <mi>rv</mi> <mi>r</mi> </msub> <mo>)</mo> </mrow> </mrow> <mrow> <mo>&amp;part;</mo> <mi>r</mi> </mrow> </mfrac> <mi>d</mi> <mi>z</mi> <mo>&amp;rsqb;</mo> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>7</mn> <mo>)</mo> </mrow> </mrow>
For c ≠ 0, that is, consider the big I for moving integrally the vertical wind speed w at speed, arbitrary height of typhoon to formula (2) from z Integration is obtained at=0 to z=Z
<mrow> <mi>w</mi> <mo>=</mo> <mo>-</mo> <mfrac> <mn>1</mn> <mi>r</mi> </mfrac> <mo>&amp;lsqb;</mo> <munderover> <mo>&amp;Integral;</mo> <mn>0</mn> <mi>Z</mi> </munderover> <mfrac> <mrow> <mo>&amp;part;</mo> <mrow> <mo>(</mo> <msub> <mi>rv</mi> <mi>r</mi> </msub> <mo>)</mo> </mrow> </mrow> <mrow> <mo>&amp;part;</mo> <mi>r</mi> </mrow> </mfrac> <mi>d</mi> <mi>z</mi> <mo>+</mo> <munderover> <mo>&amp;Integral;</mo> <mn>0</mn> <mi>Z</mi> </munderover> <mfrac> <mrow> <mo>&amp;part;</mo> <msub> <mi>v</mi> <mi>&amp;theta;</mi> </msub> </mrow> <mrow> <mo>&amp;part;</mo> <mi>&amp;theta;</mi> </mrow> </mfrac> <mi>d</mi> <mi>z</mi> <mo>&amp;rsqb;</mo> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>8</mn> <mo>)</mo> </mrow> </mrow>
Wind speed (v can tentatively be tried to achieve by the deformation of formula (1) and above-mentioned formula (2)r,vθ, w), then from iteration method to above-mentioned Result of calculation is modified；
Vertical wind speed w is introduced in Yan Meng typhoons models are on differential equation in boundary layer, can be obtained
<mrow> <mo>-</mo> <mrow> <mo>(</mo> <mn>2</mn> <mfrac> <msub> <mi>v</mi> <mrow> <mi>&amp;theta;</mi> <mi>g</mi> </mrow> </msub> <mi>r</mi> </mfrac> <mo>+</mo> <mi>f</mi> <mo>)</mo> </mrow> <msup> <msub> <mi>v</mi> <mi>&amp;theta;</mi> </msub> <mo>&amp;prime;</mo> </msup> <mo>+</mo> <mi>w</mi> <mfrac> <mrow> <mo>&amp;part;</mo> <msup> <msub> <mi>v</mi> <mi>r</mi> </msub> <mo>&amp;prime;</mo> </msup> </mrow> <mrow> <mo>&amp;part;</mo> <mi>z</mi> </mrow> </mfrac> <mo>=</mo> <msub> <mi>k</mi> <mi>m</mi> </msub> <mfrac> <mrow> <msup> <mo>&amp;part;</mo> <mn>2</mn> </msup> <msup> <msub> <mi>v</mi> <mi>r</mi> </msub> <mo>&amp;prime;</mo> </msup> </mrow> <mrow> <mo>&amp;part;</mo> <msup> <mi>z</mi> <mn>2</mn> </msup> </mrow> </mfrac> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>9</mn> <mo>)</mo> </mrow> </mrow>
<mrow> <mo>(</mo> <mfrac> <mrow> <mo>&amp;part;</mo> <msub> <mi>v</mi> <mrow> <mi>&amp;theta;</mi> <mi>g</mi> </mrow> </msub> </mrow> <mrow> <mo>&amp;part;</mo> <mi>r</mi> </mrow> </mfrac> <mo>+</mo> <mfrac> <msub> <mi>v</mi> <mrow> <mi>&amp;theta;</mi> <mi>g</mi> </mrow> </msub> <mi>r</mi> </mfrac> <mo>+</mo> <mi>f</mi> <mo>)</mo> <msup> <msub> <mi>v</mi> <mi>r</mi> </msub> <mo>&amp;prime;</mo> </msup> <mo>+</mo> <mi>w</mi> <mfrac> <mrow> <mo>&amp;part;</mo> <msup> <msub> <mi>v</mi> <mi>&amp;theta;</mi> </msub> <mo>&amp;prime;</mo> </msup> </mrow> <mrow> <mo>&amp;part;</mo> <mi>z</mi> </mrow> </mfrac> <mo>=</mo> <msub> <mi>k</mi> <mi>m</mi> </msub> <mfrac> <mrow> <msup> <mo>&amp;part;</mo> <mn>2</mn> </msup> <msup> <msub> <mi>v</mi> <mi>&amp;theta;</mi> </msub> <mo>&amp;prime;</mo> </msup> </mrow> <mrow> <mo>&amp;part;</mo> <msup> <mi>z</mi> <mn>2</mn> </msup> </mrow> </mfrac> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>10</mn> <mo>)</mo> </mrow> </mrow> 1
IntroduceWithAbove formula (9), (10) are changed into：
<mrow> <mn>2</mn> <msup> <mi>&amp;lambda;</mi> <mn>2</mn> </msup> <msup> <msub> <mi>v</mi> <mi>&amp;theta;</mi> </msub> <mrow> <mo>&amp;prime;</mo> <mo>&amp;prime;</mo> </mrow> </msup> <mo>+</mo> <mfrac> <mi>w</mi> <msub> <mi>k</mi> <mi>m</mi> </msub> </mfrac> <mfrac> <mrow> <mo>&amp;part;</mo> <msup> <msub> <mi>v</mi> <mi>r</mi> </msub> <mo>&amp;prime;</mo> </msup> </mrow> <mrow> <mo>&amp;part;</mo> <mi>z</mi> </mrow> </mfrac> <mo>=</mo> <mfrac> <mrow> <mo>&amp;part;</mo> <msup> <msub> <mi>v</mi> <mi>r</mi> </msub> <mrow> <mo>&amp;prime;</mo> <mo>&amp;prime;</mo> </mrow> </msup> </mrow> <mrow> <mo>&amp;part;</mo> <msup> <mi>z</mi> <mn>2</mn> </msup> </mrow> </mfrac> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>11</mn> <mo>)</mo> </mrow> </mrow>
<mrow> <mo>-</mo> <mn>2</mn> <msup> <mi>&amp;lambda;</mi> <mn>2</mn> </msup> <msup> <msub> <mi>v</mi> <mi>r</mi> </msub> <mrow> <mo>&amp;prime;</mo> <mo>&amp;prime;</mo> </mrow> </msup> <mo>+</mo> <mfrac> <mi>w</mi> <msub> <mi>k</mi> <mi>m</mi> </msub> </mfrac> <mfrac> <mrow> <mo>&amp;part;</mo> <msup> <msub> <mi>v</mi> <mi>&amp;theta;</mi> </msub> <mo>&amp;prime;</mo> </msup> </mrow> <mrow> <mo>&amp;part;</mo> <mi>z</mi> </mrow> </mfrac> <mo>=</mo> <mfrac> <mrow> <mo>&amp;part;</mo> <msup> <msub> <mi>v</mi> <mi>&amp;theta;</mi> </msub> <mrow> <mo>&amp;prime;</mo> <mo>&amp;prime;</mo> </mrow> </msup> </mrow> <mrow> <mo>&amp;part;</mo> <msup> <mi>z</mi> <mn>2</mn> </msup> </mrow> </mfrac> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>12</mn> <mo>)</mo> </mrow> </mrow>
Above formula v "θ=v 'θ, v "r=-v 'r/ξ.Then being multiplied by i merging (12) simultaneously to formula (11) both sides can obtain
<mrow> <mfrac> <mrow> <msup> <mo>&amp;part;</mo> <mn>2</mn> </msup> <msup> <mi>v</mi> <mrow> <mo>&amp;prime;</mo> <mo>&amp;prime;</mo> </mrow> </msup> </mrow> <mrow> <mo>&amp;part;</mo> <msup> <mi>z</mi> <mn>2</mn> </msup> </mrow> </mfrac> <mo>-</mo> <mfrac> <mi>w</mi> <msub> <mi>k</mi> <mi>m</mi> </msub> </mfrac> <mfrac> <mrow> <mo>&amp;part;</mo> <msup> <mi>v</mi> <mo>&amp;prime;</mo> </msup> </mrow> <mrow> <mo>&amp;part;</mo> <mi>z</mi> </mrow> </mfrac> <mo>-</mo> <mn>2</mn> <msup> <mi>i&amp;lambda;</mi> <mn>2</mn> </msup> <msup> <mi>v</mi> <mrow> <mo>&amp;prime;</mo> <mo>&amp;prime;</mo> </mrow> </msup> <mo>=</mo> <mn>0</mn> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>13</mn> <mo>)</mo> </mrow> </mrow>
V "=v " in above formulaθ+iv″r.The solution for meeting boundary layer condition is：
<mrow> <msup> <mi>v</mi> <mrow> <mo>&amp;prime;</mo> <mo>&amp;prime;</mo> </mrow> </msup> <mo>=</mo> <msup> <mi>De</mi> <mrow> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> <mrow> <mo>(</mo> <mfrac> <mi>w</mi> <msub> <mi>k</mi> <mi>m</mi> </msub> </mfrac> <mo>-</mo> <msqrt> <mrow> <msup> <mrow> <mo>(</mo> <mfrac> <mi>w</mi> <msub> <mi>k</mi> <mi>m</mi> </msub> </mfrac> <mo>)</mo> </mrow> <mn>2</mn> </msup> <mo>+</mo> <mn>8</mn> <msup> <mi>i&amp;lambda;</mi> <mn>2</mn> </msup> </mrow> </msqrt> <mo>)</mo> </mrow> <msup> <mi>z</mi> <mo>&amp;prime;</mo> </msup> </mrow> </msup> </mrow>
Further abbreviation is
<mrow> <msup> <mi>v</mi> <mrow> <mo>&amp;prime;</mo> <mo>&amp;prime;</mo> </mrow> </msup> <mo>=</mo> <msup> <mi>De</mi> <mrow> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> <mo>&amp;lsqb;</mo> <mrow> <mo>(</mo> <mfrac> <mi>w</mi> <msub> <mi>k</mi> <mi>m</mi> </msub> </mfrac> <mo>-</mo> <mi>c</mi> <mn>1</mn> <mo>)</mo> </mrow> <mo>-</mo> <mi>c</mi> <mn>2</mn> <mi>i</mi> <mo>&amp;rsqb;</mo> <msup> <mi>z</mi> <mo>&amp;prime;</mo> </msup> </mrow> </msup> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>14</mn> <mo>)</mo> </mrow> </mrow>
Wherein
And D=D1+iD2, it is the multiple constant of boundary layer earth's surface, can finally obtain wind speed component in boundary layer is
<mrow> <msup> <msub> <mi>v</mi> <mi>&amp;theta;</mi> </msub> <mo>&amp;prime;</mo> </msup> <mo>=</mo> <mi>exp</mi> <mrow> <mo>(</mo> <mo>-</mo> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> <mo>(</mo> <mrow> <mfrac> <mi>w</mi> <msub> <mi>k</mi> <mi>m</mi> </msub> </mfrac> <mo>-</mo> <msub> <mi>c</mi> <mn>1</mn> </msub> </mrow> <mo>)</mo> <msup> <mi>z</mi> <mo>&amp;prime;</mo> </msup> <mo>)</mo> </mrow> <mo>&amp;lsqb;</mo> <msub> <mi>D</mi> <mn>1</mn> </msub> <mi>c</mi> <mi>o</mi> <mi>s</mi> <mrow> <mo>(</mo> <mfrac> <mrow> <msub> <mi>c</mi> <mn>2</mn> </msub> <mo>&amp;CenterDot;</mo> <msup> <mi>z</mi> <mo>&amp;prime;</mo> </msup> </mrow> <mn>2</mn> </mfrac> <mo>)</mo> </mrow> <mo>+</mo> <msub> <mi>D</mi> <mn>2</mn> </msub> <mi>s</mi> <mi>i</mi> <mi>n</mi> <mrow> <mo>(</mo> <mfrac> <mrow> <msub> <mi>c</mi> <mn>1</mn> </msub> <mo>&amp;CenterDot;</mo> <msup> <mi>z</mi> <mo>&amp;prime;</mo> </msup> </mrow> <mn>2</mn> </mfrac> <mo>)</mo> </mrow> <mo>&amp;rsqb;</mo> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>15</mn> <mo>)</mo> </mrow> </mrow>
<mrow> <msup> <msub> <mi>v</mi> <mi>r</mi> </msub> <mo>&amp;prime;</mo> </msup> <mo>=</mo> <mo>-</mo> <mi>&amp;xi;</mi> <mi>exp</mi> <mrow> <mo>(</mo> <mo>-</mo> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> <mo>(</mo> <mrow> <mfrac> <mi>w</mi> <msub> <mi>k</mi> <mi>m</mi> </msub> </mfrac> <mo>-</mo> <mi>c</mi> <mn>1</mn> </mrow> <mo>)</mo> <msup> <mi>z</mi> <mo>&amp;prime;</mo> </msup> <mo>)</mo> </mrow> <mo>&amp;lsqb;</mo> <msub> <mi>D</mi> <mn>2</mn> </msub> <mi>c</mi> <mi>o</mi> <mi>s</mi> <mrow> <mo>(</mo> <mfrac> <mrow> <msub> <mi>c</mi> <mn>2</mn> </msub> <mo>&amp;CenterDot;</mo> <msup> <mi>z</mi> <mo>&amp;prime;</mo> </msup> </mrow> <mn>2</mn> </mfrac> <mo>)</mo> </mrow> <mo>-</mo> <msub> <mi>D</mi> <mn>1</mn> </msub> <mi>s</mi> <mi>i</mi> <mi>n</mi> <mrow> <mo>(</mo> <mfrac> <mrow> <msub> <mi>c</mi> <mn>2</mn> </msub> <mo>&amp;CenterDot;</mo> <msup> <mi>z</mi> <mo>&amp;prime;</mo> </msup> </mrow> <mn>2</mn> </mfrac> <mo>)</mo> </mrow> <mo>&amp;rsqb;</mo> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>16</mn> <mo>)</mo> </mrow> </mrow>
In above formula
<mrow> <msub> <mi>D</mi> <mn>1</mn> </msub> <mo>=</mo> <mo>-</mo> <mfrac> <mrow> <mi>&amp;chi;</mi> <mo>&amp;lsqb;</mo> <mi>&amp;chi;</mi> <mo>+</mo> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> <mrow> <mo>(</mo> <mfrac> <mi>w</mi> <msub> <mi>k</mi> <mi>m</mi> </msub> </mfrac> <mo>-</mo> <msub> <mi>c</mi> <mn>1</mn> </msub> <mo>)</mo> </mrow> <mo>&amp;rsqb;</mo> <msub> <mi>v</mi> <mrow> <mi>&amp;theta;</mi> <mi>g</mi> </mrow> </msub> <mo>-</mo> <msub> <mi>&amp;chi;c</mi> <mn>2</mn> </msub> <msub> <mi>v</mi> <mrow> <mi>r</mi> <mi>g</mi> </mrow> </msub> <mo>/</mo> <mrow> <mo>(</mo> <mn>2</mn> <mi>&amp;xi;</mi> <mo>)</mo> </mrow> </mrow> <mrow> <mfrac> <mrow> <msup> <msub> <mi>c</mi> <mn>2</mn> </msub> <mn>2</mn> </msup> </mrow> <mn>4</mn> </mfrac> <mo>+</mo> <msup> <mrow> <mo>&amp;lsqb;</mo> <mi>&amp;chi;</mi> <mo>+</mo> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> <mrow> <mo>(</mo> <mfrac> <mi>w</mi> <msub> <mi>k</mi> <mi>m</mi> </msub> </mfrac> <mo>-</mo> <msub> <mi>c</mi> <mn>1</mn> </msub> <mo>)</mo> </mrow> <mo>&amp;rsqb;</mo> </mrow> <mn>2</mn> </msup> </mrow> </mfrac> </mrow>
<mrow> <msub> <mi>D</mi> <mn>2</mn> </msub> <mo>=</mo> <mfrac> <mrow> <msub> <mi>&amp;chi;c</mi> <mn>2</mn> </msub> <msub> <mi>v</mi> <mrow> <mi>&amp;theta;</mi> <mi>g</mi> </mrow> </msub> <mo>/</mo> <mn>2</mn> <mo>+</mo> <mi>&amp;chi;</mi> <mo>&amp;lsqb;</mo> <mi>&amp;chi;</mi> <mo>+</mo> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> <mrow> <mo>(</mo> <mfrac> <mi>w</mi> <msub> <mi>k</mi> <mi>m</mi> </msub> </mfrac> <mo>-</mo> <msub> <mi>c</mi> <mn>1</mn> </msub> <mo>)</mo> </mrow> <mo>&amp;rsqb;</mo> <msub> <mi>v</mi> <mrow> <mi>r</mi> <mi>g</mi> </mrow> </msub> <mo>/</mo> <mi>&amp;xi;</mi> </mrow> <mrow> <mfrac> <mrow> <msup> <msub> <mi>c</mi> <mn>2</mn> </msub> <mn>2</mn> </msup> </mrow> <mn>4</mn> </mfrac> <mo>+</mo> <msup> <mrow> <mo>&amp;lsqb;</mo> <mi>&amp;chi;</mi> <mo>+</mo> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> <mrow> <mo>(</mo> <mfrac> <mi>w</mi> <msub> <mi>k</mi> <mi>m</mi> </msub> </mfrac> <mo>-</mo> <msub> <mi>c</mi> <mn>1</mn> </msub> <mo>)</mo> </mrow> <mo>&amp;rsqb;</mo> </mrow> <mn>2</mn> </msup> </mrow> </mfrac> </mrow>
<mrow> <mi>&amp;chi;</mi> <mo>=</mo> <mfrac> <msub> <mi>C</mi> <mi>d</mi> </msub> <msub> <mi>k</mi> <mi>m</mi> </msub> </mfrac> <mrow> <mo>|</mo> <msub> <mi>v</mi> <mi>s</mi> </msub> <mo>|</mo> </mrow> <mo>=</mo> <mfrac> <msub> <mi>C</mi> <mi>d</mi> </msub> <msub> <mi>k</mi> <mi>m</mi> </msub> </mfrac> <msqrt> <mrow> <msup> <msub> <mi>v</mi> <mrow> <mi>&amp;theta;</mi> <mi>s</mi> </mrow> </msub> <mn>2</mn> </msup> <mo>+</mo> <msup> <msub> <mi>v</mi> <mrow> <mi>r</mi> <mi>s</mi> </mrow> </msub> <mn>2</mn> </msup> </mrow> </msqrt> </mrow>
V is solved by iterating to calculateθsAnd vrs, and then solve vertical wind speed w.
2. mobile PBL of typhoon three-component wind speed analytic method according to claim 1, it is characterised in that：From formula (1) with the solution (v ' of (2)r,v′θ, w) it is iterated calculating as initial value.
CN201710434263.7A 2017-06-09 2017-06-09 Method for analyzing three-component wind speed of boundary layer of mobile typhoon Active CN107273334B (en)

Priority Applications (1)

Application Number Priority Date Filing Date Title
CN201710434263.7A CN107273334B (en) 2017-06-09 2017-06-09 Method for analyzing three-component wind speed of boundary layer of mobile typhoon

Applications Claiming Priority (1)

Application Number Priority Date Filing Date Title
CN201710434263.7A CN107273334B (en) 2017-06-09 2017-06-09 Method for analyzing three-component wind speed of boundary layer of mobile typhoon

Publications (2)

Publication Number Publication Date
CN107273334A true CN107273334A (en) 2017-10-20
CN107273334B CN107273334B (en) 2020-07-10

Family

ID=60067490

Family Applications (1)

Application Number Title Priority Date Filing Date
CN201710434263.7A Active CN107273334B (en) 2017-06-09 2017-06-09 Method for analyzing three-component wind speed of boundary layer of mobile typhoon

Country Status (1)

Country Link
CN (1) CN107273334B (en)

Cited By (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN111967203A (en) * 2020-08-10 2020-11-20 哈尔滨工业大学（深圳） Semi-analytic half-numerical atmospheric boundary layer three-dimensional typhoon wind field modeling method

Citations (4)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US20070168155A1 (en) * 2006-01-13 2007-07-19 Sai Ravela Statistical-deterministic approach to natural disaster prediction
US20120046917A1 (en) * 2010-08-23 2012-02-23 Hsin-Fa Fang Wind energy forecasting method with extreme wind speed prediction function
CN102938075A (en) * 2012-11-29 2013-02-20 浙江师范大学 RVM (relevant vector machine) method for maximum wind radius and typhoon eye dimension modeling
CN103679734A (en) * 2013-12-25 2014-03-26 浙江师范大学 Method for eyed typhoon two-dimensional surface wind field inversion on basis of SVM and PDE

Patent Citations (4)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US20070168155A1 (en) * 2006-01-13 2007-07-19 Sai Ravela Statistical-deterministic approach to natural disaster prediction
US20120046917A1 (en) * 2010-08-23 2012-02-23 Hsin-Fa Fang Wind energy forecasting method with extreme wind speed prediction function
CN102938075A (en) * 2012-11-29 2013-02-20 浙江师范大学 RVM (relevant vector machine) method for maximum wind radius and typhoon eye dimension modeling
CN103679734A (en) * 2013-12-25 2014-03-26 浙江师范大学 Method for eyed typhoon two-dimensional surface wind field inversion on basis of SVM and PDE

Non-Patent Citations (3)

* Cited by examiner, † Cited by third party
Title
SHAN-HWEI OU等: "An Analytical Model for Simulation of the Wind Field in a Typhoon Boundary Layer", 《JOURNAL OF WIND ENGINEERING AND INDUSTRIAL AERODYNAMICS》 *
杨剑: "WRF与CFD嵌套的局地台风风场数值模拟研究", 《中国优秀硕士学位论文全文数据库 工程科技Ⅱ辑》 *
谢汝强: "基于CE风场和Yan Meng风场的台风数值模拟与危险性分析", 《中国优秀硕士学位论文全文数据库 基础科学辑》 *

Cited By (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN111967203A (en) * 2020-08-10 2020-11-20 哈尔滨工业大学（深圳） Semi-analytic half-numerical atmospheric boundary layer three-dimensional typhoon wind field modeling method

Also Published As

Publication number Publication date
CN107273334B (en) 2020-07-10

Similar Documents

Publication Publication Date Title
CN104898183B (en) Heavy rain urban waterlogging modelling evaluation method
CN113723024B (en) &#34;stream&#34; - &#34;river course&#34; - &#34;river mouth&#34; distributed flood process simulation method suitable for coastal region
Dimri et al. Western disturbances-an Indian meteorological perspective
Heydari et al. Flood Zoning Simulation byHEC-RAS Model (Case Study: Johor River-Kota Tinggi Region)
CN105741037A (en) Typhoon disaster assessment system
Wang et al. A numerical study of back-building process in a quasistationary rainband with extreme rainfall over northern Taiwan during 11–12 June 2012
CN106844856A (en) Consider Field Flow Numerical Simulation method near the urban viaduct of Dynamic Traffic Flow influence
Lee et al. Enhancement of orographic precipitation in Jeju Island during the passage of Typhoon Khanun (2012)
Janssen et al. Use of CFD simulations to improve the pedestrian wind comfort around a high-rise building in a complex urban area
Medhi et al. On identifying relationships between the flood scaling exponent and basin attributes
Adhikari et al. Achieving residential coastal communities resilient to tropical cyclones and climate change
Williams et al. Development and testing of meteorology and air dispersion models for Mexico City
CN107273334A (en) Mobile PBL of typhoon three-component wind speed analytic method
Ying et al. An intelligent planning method to optimize high-density residential layouts considering the influence of wind environments
He et al. Evaluation of planetary boundary layer schemes in WRF model for simulating sea-land breeze in Shanghai, China
Derickson et al. Development of a powerful hybrid tool for evaluating wind power in complex terrain: atmospheric numerical models and wind tunnels
CN107657331A (en) TYPHOON PRECIPITATION analytic method based on boundary layer model
KR102537488B1 (en) Wind speed analyzing system in urban area based on inflow wind speed and morphological parameters, and wind speed analyzing method using the same
Ackerman et al. Hydrologic and hydraulic models for performing dam break studies
Santiago-Hernandez et al. Predicting topographic effect multipliers in complex terrain with shallow neural networks
Park et al. Influence analysis of land use by population growth on urban flood risk using system dynamics
Fang et al. Numerical investigation of the wind environment around tall buildings in a central business district
Moosakhaani et al. Developing Flood Economic Loss Evaluation Model in Residential and Commercial Sectors Case Study: Darband and Golab Darreh Rivers
Jadhav et al. Large Scale Modelling of Wind Comfort and Safety Using ‘Pedestrian Comfort Analysis’-A Cloud-based App Crafted for Architects
Li et al. An initialization scheme for weak tropical cyclones in the South China Sea

Legal Events

Date Code Title Description
PB01 Publication
PB01 Publication
SE01 Entry into force of request for substantive examination
SE01 Entry into force of request for substantive examination
GR01 Patent grant
GR01 Patent grant