대기 중력파(Atmospheric Gravity Wave) 테일러-골드스타인 안정성 & 1,000Hz 0-Alloc C# 켈빈-헬름홀츠 난류 분쇄 엔진

using System;
using System.Runtime.CompilerServices;

namespace ZeliDesk.Stem.Meteorology.AtmosphericDynamics
{
    /// 

    /// 대기 중력파 테일러-골드스타인 안정도 및 청천난류(CAT) 예측 엔진 (0-Alloc C#)
    /// 
    public ref struct AtmosphericGravityWaveEngine
    {
        private const double GravityG = 9.80665; // m/s^2
        private const double CriticalRichardson = 0.25;

        private readonly double _scaleHeightM;     // 대기 척도고 (~7500 m)
        private double _bruntVaisalaN2;             // N^2 부력 주파수 제곱
        private double _localRichardsonRi;          // 리차드슨 수
        private double _turbulenceDissipationEps;   // 난류 소산율 (m^2/s^3)
        private bool _isCatAlertTriggered;

        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        public AtmosphericGravityWaveEngine(double scaleHeightM = 7500.0)
        {
            _scaleHeightM = scaleHeightM;
            _bruntVaisalaN2 = 0.0004; // 통상 성층권 N ~ 0.02 rad/s -> N^2 ~ 4e-4
            _localRichardsonRi = 1.0;
            _turbulenceDissipationEps = 0.0;
            _isCatAlertTriggered = false;
        }

        /// 

        /// 고도 z에서의 온위 구배(dTheta/dz) 및 풍속 전단(dU/dz)으로부터 리차드슨 수와 난류도를 계산 (1,000Hz)
        /// 
        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        public void EvaluateStabilityStep(
            double potentialTempThetaK,
            double dThetaDz,
            double windShearDuDz,
            out double richardsonNumber,
            out double edrIndex,
            out bool isTurbulent)
        {
            // 브룬트-바이살라 주파수: N^2 = (g / theta) * (dTheta/dz)
            _bruntVaisalaN2 = (GravityG / Math.Max(potentialTempThetaK, 150.0)) * dThetaDz;
            if (_bruntVaisalaN2 < 1e-6) _bruntVaisalaN2 = 1e-6; // 대류 불안정 완화

            // 리차드슨 수: Ri = N^2 / (dU/dz)^2
            double shearSquared = (windShearDuDz * windShearDuDz);
            _localRichardsonRi = _bruntVaisalaN2 / Math.Max(shearSquared, 1e-6);

            // KHI 임계치 0.25 붕괴 점검
            _isCatAlertTriggered = _localRichardsonRi < CriticalRichardson;

            // 난류 소산율(EDR, Eddy Dissipation Rate) 지수 추정: eps^(1/3)
            if (_isCatAlertTriggered)
            {
                double excessShear = (windShearDuDz * windShearDuDz) - (4.0 * _bruntVaisalaN2);
                _turbulenceDissipationEps = 0.05 * Math.Max(0.0, excessShear);
                edrIndex = Math.Cbrt(_turbulenceDissipationEps);
            }
            else
            {
                _turbulenceDissipationEps = 0.0;
                edrIndex = 0.02; // 평온 기류
            }

            richardsonNumber = _localRichardsonRi;
            isTurbulent = _isCatAlertTriggered;
        }

        public double LocalRichardsonRi => _localRichardsonRi;
        public double BruntVaisalaN2 => _bruntVaisalaN2;
    }
}